ABSTRACT
The Asian hornet (Vespa velutina) is a major invasive predator of honeybees.
Theoretical ecology techniques were used to give managers insight into a potential
invasion, and to allow managers to formulate counter-strategies. An invasion of North
America (Canada and the United States) was simulated using the standard, four-stage
model of invasion: transportation phase; establishment phase; growth and spread phase;
and impact phase. The transportation phase was modeled with pathway analysis. Pathway
analysis showed 5.461% of US imports by value, and 9.345% of Canadian imports by
value, are potential vectors for invasion. The establishment phase was modeled using
niche analysis. Niche analysis showed the western coast and eastern coast of North
America, and the southern United States east of the Mississippi River, are highly suitable
to V. velutina invasion, while the middle of the continent is inhospitable. All ports (n=24)
studied in the United States and Canada were suitable for invasion except Anchorage,
AK. Growth and Spread was simulated using a continuous Fisher-Skellam ReactionDiffusion model, and a discrete Markov model. The continuous model projects a mean
nest population of 222.745 nests after ten years, while the discrete model projects a mean
nest population of 289.823 nests after ten years. The impact phase was modeled using
estimates of losses to agricultural output. The United States agricultural industry could
face a loss of $565,181,398.135 USD, and Canada could face a loss of at least
$6,475,218.878 CAD.
Monitoring invasion vectors, and prioritizing certain ports above others, were
deemed impractical for managers. The distribution of suitable habitat suggests North

i

American managers have the option, unavailable to managers in Europe and Asia, of
containing an invasion to a single coast.

ii

MODELING AN ASIAN HORNET (Vespa velutina) INVASION IN
NORTH AMERICA
A
THESIS
SUBMITTED TO THE SCHOOL OF GRADUATE STUDIES
of
BLOOMSBURG UNIVERSITY OF PENNSYLVANIA
IN PARTIAL FULFILLMENT FOR THE REQUIREMENTS FOR
THE DEGREE OF MASTER OF SCIENCE
PROGRAM IN BIOLOGY
DEPARTMENT OF BIOLOGY

BY
THOMAS A. O’ROURKE
BLOOMSBURG PENNSYLVANIA
2020

iii

ACKNOWLEDGEMENTS
I would like to thank my Advisor Dr. John M. Hranitz, my committee members Dr. Abby
Hare-Harris and Dr. Clay Corbin, and Graduate Chair Dr. Thomas Klinger, for all of their
hard work. I would like to thank Bloomsburg University’s Dr. Nonlhe Mziniso for her
advice on constructing the statistical models. I would like to thank Dr. Allen Smith-Pardo
at USDA-APHIS, Carrie Lima-Brown at Cornell University’s New York Invasive
Species Institute, and Belle Bergner at the North American Invasive Species Management
Association for putting me in contact with people who can use this information.

v

Table of Contents

Abstract……………………………………………………………………..……………..i
Title Page…………………………………………………………………………...……iii
Approval Form………………………………………………………………………,,,..iv
Acknowledgements……………………………………………………………………....v
Table of Contents……………………………………………………………….……….vi
List of Tables………………………………………………………………………….....ix
List of Figures…………………………………………………………………..………..x
List of Appendices……………………………………………………………………..xii
Main Work
1-Introduction…….…………………………………………………………………..…1
1.1-Life History of Vespa velutina…………………………………..………….2
1.2-Invasion Biology of the Asian Hornet………………………………………4
1.3-Ecology and Natural History of the Asian Hornet………………….…....10
1.4-Invasion as Habitat Distribution: Niche Modeling ………………………15
1.5-Invasion as Population Dynamics: Growth and Spread………………....16
1.5.1-Continuous Growth and Spread……………………………………...…17
1.5.2- Stochastic Growth and Spread………………………………………....20
1.5.3-Discrete Growth…………………………………………………………..22
1.5.4-Discrete Spread…………………………………………………………...24
2-Aims…………………………………………………………………………………..26
3-Materials and Methods……………………………………………………………...27

vi

3.1-Transportation Phase……………………………………………………...28
3.2-Establishment Phase……………………………………………………….,29
3.3-Growth and Spread Phase………………………………………………..31
3.3.1-Refining Model…………………………………………………………..32
3.3.2-Minor Variables………………………………………………………….34
3.3.3-Input Dating and Processing……………………………………………35
3.3.4-Trial Ports………………………………………………………………..37
3.3.5-Methods of Calculating r(x,y)…………………………………………...38
3.3.6-Measurements ……………………..…………………………………….39
3.3.7-Experimental Control and Statistical Tests …………..……………….40
3.4-Impact Phase………………………...…………………………………….43
3.5-Model Validation……………….…………………………………………44
4-Results………………………………………………………………………………..43
4.1-Transportation Phase…………………………………………………..…46
4.2-Establishment Phase…………………………………………………….…47
4.3-Growth and Spread Phase……………………………………………..…47
4.3.1-Continuous Growth and Spread……………………………………….49
4.3.2 – Discrete Growth and Spread………………………………………….53
4.3.3-Both Discrete and Continuous Results………………………………….56
4.4-Impact Phase………………………………………………………………57
4.5-Model Validation…………………………………………………………..59
5-Discussion………………………………………………………………….………...59
LITERATURE CITED ………………………………………………………………65

vii

TABLES…………………………………….…………………………………………71
FIGURES……………………………………………………………………………...98
APPENDICES
APPENDIX A: PYTHON SOURCE CODE………………………………………120
APPENDIX II: STATISTIAL ANALYSIS………………………………………..176
APPENDIX III: RAW OUTPUT…………………………………………………..213

viii

LIST OF TABLES
1. Hulme’s Transportation Criteria with Respect to V. velutina Biology
2. Table of Equations Used in this Study.
3. Summary of Constants Used for the Growth and Spread Simulation.
4. Ports in the Test Group with GPS Coordinates and Matrix Indices.
5. Locations in the Positive and Negative Control Groups with GPS
Coordinates and Matrix Indices.
6. Model Statements and Calculations.
7. Honey Impact by State
8. Summary of Transportation Calculations for the United States.
9. Summary of Transportation Calculations for Canada.
10. Summary Statistics for N10 Projections for the Test Group.
11. Summary Statistics for N10 Projections for the Positive Control Group.
12. Summary Statistics for N10 Projections for the Negative Control Group.
13. Summary Statistics for Mean Nest Density for the Test Group.
14. Summary Statistics for Mean Nest Density for the Positive Control Group.
15. Summary Statistics for Mean Nest Density for the NegativeControl Group
16. ANOVA Results for Sites, Model Statements, and Trial Groups.
17. Summary of Economic Impact Calculations for the United States.
18. Summary of Economic Impact Calculations for Canada.

ix

LIST OF FIGURES
1. Life Cycle of V. velutina.
2. Flow Chart of Study Aims.
3. V. velutina Occurrence in Europe.
4. V. velutina Occurrence in Asia.
5. World V. velutina Occurrence Probability Raster.
6. Program Architecture of Niche Analysis Model.
7. Program Architecture of Growth and Spread Simulations.
8. Human Population Density of North America.
9. Major River Presence in North America.
10. Elevation (m) in North America.
11. V. velutina Occurrence Probability by State.
12. Example of Negative Nest Density-St. Paul, MN.
13. Trial Means with Standard Error.
14. Boxplots of Trials for the Test Group, Positive Control Group, and Negative
Control Group.
15. Distribution of N10 Projections by Site.
16. Comparison of Discrete and Continuous Geometry – New Orleans, LA.
17. Boxplot of Continuous and Discrete Trial Means.
18. Boxplot of Continuous and Discrete N10 Population Projections Based on
Occurrence.
19. Boxplot of N10 Population Projections for the Test Group, Negative Control
Group, and Positive Control Group.

x

20. Principal Components Analysis.
21. Correlation between Human Population Density and Land Area
22. M. apicalis Occurrence Probability

xi

LIST OF APPENDICES
A. Python Source Code
A.1 Script 1-Niche Analysis Modeling
A.2 Script 2-Continuous Growth and Spread Model
A.3 Script 3- Discrete Growth and Spread Model
A.4 Script 4-Statistical and Arithmetic Function Module “funx”
A.5 Script 5-Matrix Manipulation Function Module “mfunx”
A.6 Script 6- String Functions from Useful Functions Module “ufunx
B. Statistical Analysis and Scripts
B.1 R Script for Statistical Analysis
B.2 Python Script for Statistical Analysis
C. Raw Data
C.1 N10 Projections for Test Groups.
C.2 N10 Projections for Positive Control Groups.
C.3 N10 Projections for Negative Control Groups.
C.4 Mean Nest Density for Trial Groups.
C.5 Mean Nest Density for Positive Control Groups.
C.6 Mean Nest Density for Negative Control Groups.
C.7 Z-Score for the Test Group
C.8 Z-Scores for the Positive Control Group
C.9 Z-Scores for the Negative Control Group.

xii

1-INTRODUCTION

Vespa velutina, commonly known as the Asian hornet, or the yellow-legged Asian
hornet, is one of the greatest threats faced by pollinators in the world today. Native to
southern Asia, V. velutina has been pushing north into Korea and Japan as climate change
expands this hornet’s range. On the Korean Peninsula, V. velutina’s range has been
pushing north at a rate of 12 km per year, on average. In Busan, South Korea, V. velutina
is now the dominant hornet species after ten years of invasion, accounting for 37% of
observed hornet nests. V. velutina accounted for 47% of emergency calls for nest
removal, and in one Busan apiary 50 of 300 beehives were destroyed by V. velutina
(Choi et al. 2012). V. velutina was first observed on Tsushima Island, Nagasaki
Prefecture, Japan, near Tsushima City, in 2012. Impacts of V. velutina in Japan have not
been observed at this time (Ueno 2014).
In approximately 2004, likely due to the increase of international
trade, V. velutina became invasive in France (Arca et al. 2015). The impacts of the Asian
hornet in France, where these wasps have no natural predators, no known pathogens, and
prey with no natural defenses, have been even more devastating than those in Korea, as
Asian honeybees (Apis cerana) have evolved defensive strategies against Asian hornets
(Choi et al. 2012). V. velutina has experienced explosive growth in France, with the front
of the invasion wave sweeping northward at an average rate of 60 km per year
(Monceau et al. 2014), much faster than the 12 km rate of spread observed in South

1

Korea (Choi et al. 2012), though the reason for this faster spread is not understood at this
time (Monceau et al. 2012; Robinet et al. 2017).
In recent years, the French V. velutia population has begun to spread into the
Iberian and Italian Peninsulas (Bertolini et al. 2016). In 2016, V. velutina was observed in
Gloucestershire, UK: Keeling et al. (2017) speculate V. velutina crossed the English
Channel by flight from France.
The international trade that probably brought V. velutina to France will likely
bring V. velutina to North America (Canada and the United States) and, if it is just a
matter of time until V. velutina becomes in North America, then it behooves American
and Canadian authorities to investigate the possibilities, and formulate counterstrategies.
This study is intended to be an important first step in that process.

1.1-The Life History of Vespa velutina

V. velutina’s life cycle begins when a fertilized gyne emerges from winter
hibernation and builds a primary nest. The new queen then lays its first round of eggs in
the primary nest. Once these first-generation workers have reached maturity, the colony
then builds a much larger secondary nest. In the secondary nests, more workers and males
come to maturity, and the queen begins laying gynes, potential future queens. Adults
consume carbohydrates, chiefly nectar, but the adults feed the larvae with proteins,
chiefly proteins from insects. One third to two thirds of this protein come from
honeybees. As autumn comes to an end, the gynes migrate out of the nest, mate, and find

2

a place to hibernate for the winter as the parent colony dies, and the cycle begins again
(Monceau et al. 2014). This life cycle is summarized in Figure 1.
V. velutina does best in urban and suburban environments where human structures
likely provide safe microhabitat for overwintering, and primary nest construction
(Monceau et al. 2014). In Busan, South Korea, V. velutina nests were observed under the
eaves of buildings, possibly due to the lack of tall trees near the center of the city (Choi et
al. 2012). In France, they have been observed in the rafters of sheds (Monceau et al.
2014). V. velutina’s secondary nests are often found in proximity to rivers, through the
reason for this preference is unknown at this time (Bessa et al. 2015). Data from
the French population (Franklin et al. 2016) suggests that V. velutina does quite well
where there is an active fishing industry, as V. velutina seems to have an affinity for
seafood protein. The native range of V. velutina is quite warm, but the population data
from Korea suggests that V. velutina can do well in more temperate climatic zones (Choi
et al. 2017). This ability to adapt to cooler temperatures may be due a preference for
highland areas in the tropical native range (Bessa et al. 2015). In the Iberian peninsula,
Bessa et al. (2015) observe V. velutina occurring at a temperature range of 15.2℃ - 30.2
℃. The one environmental condition seemingly repulsive to V. velutina is aridity: V.
velutina was not observed in the arid regions of southern Spain, and were only observed
to occur in regions with annual rainfall ranging from 410 mm – 1572 mm (Bessa et al.
2015). Thus, the ideal location for a V. velutina population might be a warm, humid port
city located at a river mouth with a bustling seafood trade and expansive suburban and
agricultural development outside the city.

3

1.2-Invasion Biology and the Asian Hornet

Invasion is a biological and ecological process. It is therefore necessary to discuss
invasion biology theory generally, and apply that theory to the context of V. velutina.
Firstly, an invasive species is a non-native species that has substantial potential to grow,
spread and outcompete endemic species in the introduced habitat: while all invasive
species are non-native species, most non-native species are not invasive species (Sakai et
al. 2001). Sakai, et al. (2001) identify four major stages of biological invasion:
Transportation, Establishment, Growth and Spread, and Impact.
The transportation phase is defined as the period during which the non-native
species is transferred from its previous habitat (to which the species may have been
native, though the species could have been non-native or invasive there as well) to the
new (“introduced”) habitat (Sakai et al. 2001). When this new habitat is far from the
species’ native range, transportation usually happens because of human economic
activity, either intentionally (e.g. an exotic plant brought for cultivation for sale
as ornamentation (Sakai et al. 2001)) or unintentionally, as V. velutina was likely
transported to France in a shipping container (Arca et al. 2015). As trade frequency and
efficiency have increased, biological invasions have increased through these economic
pathways (Hulme 2009).
Hulme (2009) identifies ten important factors associated with working out the
pathways of invasion: a) the strength of the association between the species and the
vector (commodity, mode of transport, etc.) at the point of export; b) volume of vector
imports at the point of interest; c) frequency of importation; d) survivorship and growth

4

during transport; e) suitability of the importing point to species
establishment; f) appropriateness of the time of year for the establishment of the
species; g) the ease of containing the species within the vector; h) effectiveness of
management measures; i) distribution of the vector post importation;
and j) the likelihood of post-importation transport to suitable habitat.
Unfortunately, there is no literature on what commodities may be favored by
V. velutina, and while the vector of invasion in the French case has been speculated to be
shipping containers (Arca et al. 2015), this is not certain. There is also no literature on the
validity of control measures while a V. velutina gyne is in transit. While it is not possible
to ascertain the rate of survivorship in transit, it can be inferred from the life history of
V. velutina that growth in transit is not very likely: Growth in colonies occurs only once a
year, and supporting a nest without a reliable source of protein will not be possible. It can
be likewise inferred from life history that the most dangerous time for transit would be in
late winter or early spring: From late spring through early summer, the gyne is building
her primary nest; from the middle of summer through early fall, the queen is growing her
secondary nest; and in late fall, the colony is in the process of die-back, and the
offspring gynes are in the process of mating and preparing for hibernation. If
transportation takes place too early in the winter, e.g November or December,
the gyne may not survive exposure to the winter in the introduced habitat. If some
material containing a hibernating gyne is transported in late winter or early spring,
the gyne could take full advantage of settling the introduced habitat at the right time in its
life cycle. The biology of V. velutina in relation to Hulme’s criteria is summarized in
Table 1.

5

In the establishment phase, after the non-native species has disembarked its vector
and settled in the introduced habitat, the non-native species produces its first generation.
If the introduced habitat is not suitable, the invader will not be able to effectively
establish itself and go to extinction. It is common for an invasive population to remain in
the area of establishment for several generations before spreading to new areas-known in
the literature as lag time - due to adaptation, inbreeding depression, and the need to
reach some critical population density (Sakai et al. 2001). The critical population density
of V. velutina is currently unknown, but this population-density dependent growth and
spread is known as the Alee effect, the decrease in per capita growth due to lower
population density. The Alee effect has numerous potential causes: inbreeding depression
(lower fecundity due to high levels of inbreeding); lack of available mates; and a lack of
sufficient competition to incentivize emigration from the establishment habitat, inter alia
(Monceau et al. 2014).
In V. velutina, inbreeding depression has been observed in the invasive population
in the form of diploid males, though there is no evidence that this effect negatively
impacted their rate of spread in France. Hymenopteran males are usually haploid, as
hymenopterans exhibit haplodiploid sex determination (Daurrouzet et al. 2015).
What habitats are suitable for establishment of V. velutina? Given that cities are
ideal environments for V. velutina (Choi et al. 2012; Franklin et al. 2016), and most
ports are located in large cities, it is reasonable to conclude that any port which is
sufficiently warm and wet (Bessa et al. 2015) would suit an invasive V. velutina
population.

6

In the growth and spread phase of the invasion, the population moves out of
its newly established range and expands to a new range. This can happen because of the
organism’s innate ability to spread in the new environment or by human-mediated
transport (Sakai et al. 2001). V. velutina gynes are capable of flying up to 200 km to
establish new nest locations, and human-mediated dispersal has been discussed as
a possibility for rapid and incongruous jumps in range in the context of the French
population (Robinet et al. 2017).
Spread and growth of the population is not merely a function of whether a habitat
is suitable or unsuitable, but also how that suitability affects growth and spread: Growth
and Spread must be interpreted as a function of habitat suitability as a continuous
variable, rather than a binary variable. Mathematical, population-dynamical models have
been historically used to describe how a population reproduces and migrates during the
growth and spread phase (Archer 1985; Franklin et al. 2017; Keeling et al. 2017;
Renshaw 1991; Robinet et al. 2016; Shigesada and Kawasaki 1997; Varley et al. 1973).
These models are discussed at length in Section 1.5.
Finally, after the invasive population has increased in number and expanded into
its new, more extensive range, it is necessary to consider the ecological and economic
impacts of the invasion, and if countermeasures have not yet been employed,
countermeasures must be considered to stop further losses and further growth and spread
of the invasive population. These calculations constitute the impact phase of the
biological invasion model (Sakai, et al. 2001).
At this time, there is no widely agreed upon way to quantify ecological impacts.
Much work has been done in recent years to integrate ecological concerns into economic

7

calculations (Gowdy and Erickson 2005). A considerable problem for ecological
economics is adapting ecological concepts to the assumptions of neoclassical economics:
neoclassical economics assumes value-monism, that all values in a system are reducible
to a single unit of account (to wit, everything can be assigned a currency value), and
assumes that consumers make rational choices based on self-interest. Gowdy and
Erickson (2005) propose making allowances for a plurality of valuations, and for the
consumer to be viewed as a citizen making responsible choices, but these augmentations
do nothing to improve the ease of calculation. There is not much literature on how
ecological-economic impact can be calculated. For example, Limnois et al. (2009)
provide one of the few examples of explicit calculation: the authors demonstrate a
method to calculate the ecological impacts of the production of goods. Regarding
invasive species specifically, Zhang and Boyle (2010) relate the impact of invasive
waterfowl to the decline in lakefront property values. In an exhaustive survey of the
ecological-economic impacts of invasive species, Pimentel et al. (2005) note that
calculating the ecological-economic impact of invasive species is nearly impossible, and
most of the impacts calculated are from losses to agriculture or removal cost. The
ecological economics of invasive species requires some mapping from some ecological
unit to a financial unit. Even if a mapping existed for V. velutina, data on ecological
impacts of V. velutina in Europe or Asia would be required to project those impacts onto
North America, and no such data on ecological impacts in Europe and Asia exist in the
literature. Fortunately, there is literature on the agricultural impacts of V. velutina,
making agricultural impact calculations possible.

8

Pollination services contributed $10.95 billion to US agriculture in 2009, the last
year for which there is data (Hein 2009). While pollination is doubtlessly important to
wild plants, the value of pollinators to the ecosystem is impossible to calculate precisely
(Monceau et al. 2014).
Surveys of beekeepers in invaded regions found a total honeybee hive loss
(complete destruction of the hive) of between 5.0-7.5% (Monceau et al. 2014). Colony
losses are usually calculated once a year in the spring, and lost colonies are replaced,
usually by brood splitting (Smith 2013). Apiaries in the United States produced $353
million in honey production in 2016, the most recent year for which there is data
(FAOSTAT 2020). Higher resolution on impacts of honey production is possible: forty
states have published honey production in those states for the year 2017 (Flottum 2017).
Finally, V. velutina has been responsible for three human deaths, but it is
impossible to calculate the probability of death by V. velutina sting due to a lack of
comprehensive envenomation statistics (Monceau et al. 2014).
These impacts must be mitigated with countermeasures. The primary
countermeasure used in both South Korea and France is nest
destruction. This countermeasure requires involvement from the general public: nest
sightings must be reported to authorities, who then investigate. In France, nearly a third
of reports are false alarms. Nest destruction is conducted by either government authorities
or private companies. The costs of nest removal ranged from €130-€500 per nest in 2013.
Trapping has also been employed, but trapping is optimally efficient when a trapped
wasp dosed with a pesticide returns to the nest, killing the nest. This requires a pesticide

9

sufficiently specific to kill the nest without killing other insects in the environment. Such
a pesticide has not been found in the case of the V. velutina (Monceau et al. 2014).
Sakai et al. (2001) observe that invasiveness is not merely a function of habitat
suitability and mechanical growth and spread. Invasiveness is fundamentally an
evolutionary question. Invasive species are thrust into new environments. How quickly
can the new species adapt? If invasive species begin with a small initial population, how
susceptible are those populations to the founder effect and inbreeding depression? How
does interspecies competition effect invasion, and how do pathogens effect
the invader? Studying the ecology and evolutionary natural history of V. velutina, and of
vespids generally, may provide insight into the V. velutina invasion.

1.3-Ecology and Natural History of the Asian Hornet

V. velutina has no known natural predators in the European or Asian ranges, and
no pathogens are known to effect V. velutina in the European range, though there have
been anecdotally observed instances of predation by the European Honey
Buzzard (Pernis apivorus), and the domestic chicken
(Gallus gallus domesticus) (Monceau et al. 2014). V. velutina sampled in China tested
positive for the Israeli Acute Paralysis Virus (IAPV), acquired from feeding on infected
A. melifera, though the virus has no known effect on the infected V. velutina (Yañez et al.
2012) While it is not possible to say what predators and pathogens will affect V. velutina
in North America, it is reasonable to assume the North American case will be analogous

10

to the European case: no predator or pathogen will have a substantial effect on V. velutina
in North America.
The main prey of V. velutina in its native range is the Asian honeybee
(Apis cerana,) (Tan et al. 2005). A. cerana has developed a robust system of defense
from V. velutina . V. velutina hunts primarily by sending scouts to identify prey items.
When a worker bee is identified by the scout, the scout follows the bee back to the hive,
and secretes a pheromone on the entrance of the hive. The scout then returns to her nest,
and the V. velutina nest assaults the marked beehive. This practice is known as bee
hawking (Tan et al. 2005). The beehive has little hope of surviving the assault. The hive’s
only hope is to take out the scout before she can recruit her sisters. When the worker bee
detects the V. velutina scout stalking her, the worker may send the scout an “I-See-You"
signal, for example a unique wingbeat, which may cause the scout to disengage from the
hunt (Tan et al. 2012). The worker bee’s physiology changes, releasing pheromones and
triggering a pheromone increase put out by guard bees, rallying the whole hive and
bringing reinforcements to the guard bee position. The bees begin raising their body
temperature by vibrating their wings, which also spreads alert pheromones (Tan et al.
2005). The physiology of all the bees in the hive changes. When the scout arrives at the
beehive, she is ambushed by the hive. The hive forms a ball around the scout, and the
bees begin vibrating their wings (Tan et al. 2005). The temperature inside the ball raises
to 46oc, and the CO2 rises to 4%, which kills the scout but not the bees, who are able to
survive the high temperatures. This behavior is known as heat balling (Sugahara 2012;
Tan et al. 2005).

11

While some strains of the European honeybee (Apis melifera ligustica) have
been known to exhibit similar behavior (though to a lesser degree) in areas with
the predatory European hornet (Vespa crabo), most strains of European honeybee are
unable to implement this defense, or have only a primitive ability to do so. It is possible
that all Apidae have the genetic basis to evolve this defense, as heat balling has also been
observed in Apis dorsata (Tan et al. 2005). This may account in part for the much faster
rate of spread of V. velutina in Europe compared to the Korean population: Korea has an
A. cerana population (Choi et al. 2012). It is reasonable to believe that the relative lack of
A. cerana in North America would similarly affect an invasive V. velutina population in
North America.
The evolutionary history of the Asian hornet is included here for completeness.
Hymenopterans first evolved in the Triassic period, with sawflies
(suborder Symphyta) being the most basal form. The suborder Apocrita, containing
wasps, bees and ants, arose between late Triassic and early Jurassic. Bees and ants split
from the wasp lineage in the early Cretaceous. (Ward 2014).
The most well-known and controversial issue in hymenopteran evolution is the
evolution of eusociality. Eusociality is an arrangement where adults in social organisms
are divided into reproductive castes: some members reproduce, while other members
raise the brood of the reproductive members, without undergoing reproduction (Nowak et
al.2010). Eusociality affords some flexibility in adapting to new environments through
social intelligence (Moller 1996), so an understanding of how eusociality evolved may
provide insight into this valuable technique for invasion survival. The classic model of
eusocial evolution is the Hamilton model, also called the inclusive fitness model (Nowak,

12

et al. 2010; Queller, 2011). According to this model, ancestral hymenopterans developed
an altruistic phenotype, which caused the hymenopterans who express the altruistic
phenotype to give up their reproductive fitness for their siblings. These closely related
siblings had a probability of carrying the allele for altruism, and as such the phenotype
survives according to Hamilton’s inequality, to wit: the product of the fitness benefit to
the beneficiary and the relatedness coefficient between the altruist and the beneficiary, is
greater than the fitness cost to the altruist. There is evidence for the accuracy of
Hamilton’s model. Waibel et al. (2011) simulated the evolution of altruism using
artificially intelligent robots, capable of foraging for food and given the choice to share
food or keep it to themselves. The authors found that, in every case (of 500
simulations) where altruism evolved, Hamilton’s Rule predicted it. However, even
among hymenopterans, relatedness is no guarantee of eusociality or even altruistic
behavior: for example, males of the fig wasp (family Agaonidae) compete for mates
aggressively regardless of relatedness (West et al. 2001).
Nowak, et al. (2010) propose an alternative model for the evolution of eusociality.
The authors –including the eminent E.O. Wilson- note that, in every known instance of
eusociality, the organism builds a defensible nest. If some of the offspring of the founder
develop a mutation that causes them to not leave the nest, the founder will have more
aide in defending and maintaining the nest, and rearing future young. The “eusociality”
gene emerges in some of the species, and the mutants help their peers without respect to
relatedness (Hughes, et al. 2008). . The authors concede that, while relatedness was
important, it becomes the enforcer and consequence of this behavior, rather than the
driver (Nowak, et al. 2010; Wilson and Wilson. 2007). This model has been extremely

13

controversial (Abbot, et al. 2011), and has been undermined experimentally: Genetic
analysis of hymenopteran lineages finds that that eight of the nine eusocial lineages
practiced monandry (females mating with only one male), a practice that maximizes
relatedness (Hughes et al. 2008).
A third hypothesis is developed by Wheeler (1986), Hunt and Amdam (2005),
Toth et al. (2007), and Jeanne and Suryanarayanan (2011). Caste determination is a
developmental question. It is believed that caste determination occurs by developmental
ques passed from mother to daughter during larval feeding, including chemical ques, food
quantity (Hunt and Amdam 2005), and vibrational cues (Toth et al. 2007). Many species
of hymenopterans practice bivoltinism, or the laying of two brood during a single season.
Many insects enter stages of diapause, or developmental delay. It may be that ancestral
wasps could suppress the reproductive potential of their daughters by inducing diapause
in the early brood. On this view, eusociality might have evolved as a form of social
parasitism by queens on their daughters, a “Bad Mother” hypothesis. Under social
parasitism, benefit accrue to the parasite by exploiting the social structure of a
community. Social parasitism has been observed in hymenopterans: Slave-maker ants
(e.g. Harpagoxenus sublaevis) drive off adults from a host colony, and use the host brood
to serve the queen of the slave-maker ants (D’Ettorre and Heinze 2001). Whatever the
ultimate cause of hymenopteran eusociality evolution was, hymenopteran capacity to
implement this strategy makes them formidable invaders.

14

1.4-Invasion as Habitat Distribution: Niche Modeling

The suitability of a habitat to an organism is easy to determine if the organism is
already living there. How does one determine the suitability of habitat where an organism
has never lived, but one day might?
Niche modeling attempts to quantify the suitability of habitat for an
organism. First, variables relevant to habitat suitability must be identified from the
literature: for example, rainfall, average temperature, flora and fauna, etc. Secondly,
habitats where the organism lives (and does not live) must be identified. Thirdly, a
method of comparing habitats based on the environmental variables must be developed.
Finally, variables from occurrence habitats and candidate habitats are compared using the
developed model (Villemant et al. 2011).
Statistical regression is the most common model of comparison. The relationship
between variables and habitat suitability is assumed to fit some function with
coefficients. These coefficients are then estimated computationally, finding the
coefficient values that minimize the error in the model. The function is then used to
project suitability of the new habitat (Villemant et al. 2011). For the sake of example, let
the relationship between habitat and n variables Vn, be linear: the probability of
occurrence increases directly to the sum of variables with coefficients (Equation 1):
𝑃(𝑂𝑐𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑒) = 𝐵 + 𝐶/ 𝑉/ + 𝐶1 𝑉1 + ⋯ + 𝐶3 𝑉3
where B is the y-intercept, the probability of occurrence when all values
V1,…,Vn =0, and C1,…,Cn are the regression coefficients. Relationships need not be

15

linear: the relationships between probability and variables may assume any function
(Villemant et al. 2011).

1.5-Invasion as Population Dynamics: Growth and Spread

The standard model of the growth and spread of invasive species is the FisherSkellam reaction-diffusion model (Shigesada and Kawasaki 1997), which has been wellsupported in the study of V. velutina in France (Robinet et al. 2017). Section 1.5.1
contains a derivation of the Fisher-Skellam model. There are limitations to the FisherSkellam model: the model is deterministic-the model says the population will definitely
be of this density at this time and place- while real organisms vary with some probability
(Renshaw 1991); and the model assumes continuous growth and spread, while vespids
spread during discrete times and grow in discrete generations (Archer 1985). To counter
the stochasticity objection, Keeling et al. (2017) and Franklin et al. (2017) develop
stochastic models of V. velutina growth and spread. The work of these authors is detailed
in section 1.5.2. In response to the discreteness objection, Archer (1985) develops a
discrete model of vespid growth, discussed in section 1.5.3. To model discrete spread of
vespids, this study develops a spread model using the mathematical object known as the
Markov Chain, a set of weighted nodes, and a set of paths weighted with the probability
of moving from one node to another (Hill et al. 2004), discussed in section 1.5.4. The
stochastic models developed by Keeling et al. (2017) and Franklin et al. (2017) (section
1.5.2) require positions of observed nests as inputs. In North America, there are no
observed nests. To use the Keeling and Frankel models in North America, it would be

16

necessary to lay down some initial probability distribution. The Fisher-Skellam model
can take a probability distribution as an input, meaning the output of a Fisher-Skellam
model taking a probability distribution as an input can itself be interpreted as a
probability distribution: thus, despite being a deterministic model, the Fisher-Skellam
model can account for stochasticity, given the proper input (Shigesada and Kawasaki
1997). The Markov Chain object contains a probability component, thereby also
accounting for stochasticity (Hill et al. 2004). Given the stochasticity implicit in the
Fisher-Skellam model and the Markov Chain model, the Keeling and Frankel models are
presented here for the sake of completeness: only the Fisher-Skellam model and the
Archer-Markov models were used in this study. All Equations described in this study are
summarized in Table 2.
1.5.1-Continuous Growth and Spread

The growth of a population over the time interval [t, t+1] will depend in part of
the population at time t: the bigger the population, the more reproduction to contribute to
the population at time t+1. The population will also depend in part on the average
reproductive contribution of each member of the population, the intrinsic rate of growth.
For eusocial organisms like V. velutina, it is sufficient to count the growth of nests, the
reproductive unit. If no other factors (e.g. death) affect the rate of growth over the time
interval [t,t+1], then the population N at time t+1 is given by (Equation 2):
𝑁56/ = 𝑁5 + 𝑟𝑁5
where N is the population, and r is the innate rate of growth. This sort of growth is
discrete. Growth is measured in discrete time units, often the time of whole generations.
17

If the time interval, rather than consisting of discrete time units, is the variable interval
[t, t+h], and h is allowed to approach zero, then the limit becomes (Equation 3):
𝑑𝑁
= 𝑟𝑁
𝑑𝑡
This differential equation describes the exponential (or Malthusian) growth curve.
No population experiences literal continuous growth, but for large, rapidly reproducing
populations for very small values of t, this curve is a useful model (Renshaw 1991).
As t increases, N tends to hit restrictions in its growth. This restriction, the
maximal population an environment can sustain, is known as carrying capacity K. For
these large values of t, the rate of growth is also proportional to the difference between
the current population and the carrying capacity. The resulting equation describes a
bound or logistic growth curve (Renshaw 1991) (Equation 4):
𝑁
𝑁 ∗ = 𝑟𝑁(1 − )
𝐾
This paper adopts the notation Y* to mean the derivative of Y with respect to
time, the complete derivative for univariate functions, and the partial derivative for
multivariate functions. Invasive populations do not merely grow. Invasive populations
also spread. Let U(x,y,t) be the concentration of the population at the point (x,y) at time t.
If the population is spreading only, then the rate of change in U is driven entirely the rate
of diffusion. If it is assumed that U at t=0 follows a Gaussian distribution around the
origin, then the rate of diffusion from the origin is given by the Heat
Equation (Equation 5):
𝑈 ∗ = 𝐷(

𝜕1𝑈 𝜕1𝑈
+
)
𝜕𝑥 1 𝜕𝑦 1

18

D is the innate rate of diffusion, in units of area per time (Shigesada and
Kawasaki 1997). If a population is both growing and spreading, then the rate of
concentration change will be the sum of the rate of diffusion and the rate of
growth (Equation 6):
𝜕1𝑈 𝜕1𝑈
𝑈∗ = 𝐷 B 1 + 1 C + 𝑁 ∗
𝜕𝑥
𝜕𝑦

Expanding this equation with the logistic growth equation (Equation 4), gives (Equation
7):
𝜕1𝑈 𝜕1𝑈
𝑁
𝑈 = 𝐷 B 1 + 1 C + 𝑟𝑁(1 − )
𝜕𝑥
𝜕𝑦
𝐾
∗

Equation 7 is known as the Fisher-Skellam equation (Shigesada and Kawasaki
1997). This model assumes continuous growth and continuous spread. A population may
grow only during a discrete mating season, and may spread only during a discrete
migratory season. Such a model would therefore be inaccurate for those populations. This
will be addressed in sections 1.5.3 and 1.5.4. There is another assumption which limits
the effectiveness of the Fisher-Skellam model: The population in this model is growing
and moving over a homogeneous, smooth environment. The population everywhere has
the same growth rate and the same rate of spread. Heterogeneous or patched models
assume a different value of r, D and K at each point (x,y) (Equation 8):
𝜕1𝑈 𝜕1𝑈
𝑁
𝑈 ∗ = 𝐷(𝑥, 𝑦) B 1 + 1 C + 𝑟(𝑥, 𝑦)𝑁(1 −
)
𝜕𝑥
𝜕𝑦
𝐾(𝑥, 𝑦)

19

The smooth version of Fisher-Skellam has algebraic solutions, but the patched
version requires numerical methods to solve. Numerical solutions to differential
equations require specifying starting conditions. The starting conditions are described
with the three-dimensional Gaussian distribution (Shigesada and Kawasaki 1997), the
general formula for which is given by (Equation 9):
/ HJLM
J BK
O
1
𝑃(𝑥, 𝑦) =
𝑒 1 NM
2𝜋𝜎H 𝜎I

P

6Q

IJLR P
S C
NR

where 𝜇H and 𝜎H are the mean and standard deviation in the x direction,
respectively, and 𝜇I and 𝜎I are the mean and standard deviation in the y direction,
respectively.
1.5.2- Stochastic Growth and Spread

It may be objected that the Fisher-Skellam model is too deterministic. The model
predicts that the population density must be some value at time t and point (x,y). Real
organisms, it might be argued, do not behave so deterministically. The growth and
movement of real organisms, it might be argued, should be measured stochastically.
Franklin et al. (2016) conducted a lengthy study on the V. velutina population in
the vicinity of the French seaside commune of Andernos-les-Bains. On the basis of these
data, the authors formulate a stochastic model for growth as a Poisson Distribution with a
mean, an expected population value, at the ratio of prior population growth to the prior
population’s density dependence, to wit (Equation 10):
𝑟𝑁5J/
𝑁5 = 𝑃𝑜𝑖𝑠𝑠𝑜𝑛 X
Y
𝑁5J/
1+ 𝐾
20

Keeling et al. (2017) extended this stochastic model to describe the stochastic
spread of the V. velutina population, and model the spread of the population into Great
Britain.
Let Pjk be the probability that a queen spawned at location j will establish a nest at
location k (Equation 11):
𝑃Z[ = 𝑒

J

\]^
L 𝑇𝑒𝑟𝑟𝑎𝑖𝑛

[

where ΔZ[ is the distance between the two locations, µ is the mean flight distance,
and Terraini is the suitability of the ith terrain. The suitability of the ith terrain is given by
Franklin et al. (2016), where terrain is defined by type: city, park, coniferous forest,
deciduous forest, and shrubland. This suitability varies between terrains, e.g. deciduous
forests are better than coniferous ones. The probability that a nest existed at
the ith location in year y, given that nests were discovered at locations r1 and r2 in year
y+1, and assuming there is no density dependent competition, is given by (Equation 12):
𝑃(𝑖, 𝑦) = 𝑛𝑟𝐸d 𝑓(𝑙𝑎𝑡d ) g𝑒

J

\hij
L 𝑇𝑒𝑟𝑟𝑎𝑖𝑛

kj l g𝑒

J

\hiP
L 𝑇𝑒𝑟𝑟𝑎𝑖𝑛

kP l

where n is a normalizing parameter, r is the growth rate, Ei is the effect of local
habitat as defined by habitat distribution modeling (see section IV of this introduction),
f(lati) is the effect of the position of the ith location (latitude, in this formulation), and e is
Euler’s constant (approximately 2.718).
The authors then define the probability that a nest exists at location q at time y+1
given that a nest existed at location j in year y given p environments (again, assuming no
density dependent competition) is (Equation 13):

21

g𝑒

J

\hp
L

𝑃(𝑞|𝑗, 𝑦 + 1) = 𝑛𝑟𝐸d 𝑓(𝑙𝑎𝑡d )
∑𝑒

J

𝑇𝑒𝑟𝑟𝑎𝑖𝑛q l

\hs
L 𝑇𝑒𝑟𝑟𝑎𝑖𝑛

t

The authors then compute the probability of finding a nest at location q and year
y+1 by integrating the above probabilities over all k nests, given the posterior probability
distribution of r, Post(r) (Equation 14):
𝑃(𝑞|𝑦 + 1) = u 𝑃𝑜𝑠𝑡(𝑟) vw 𝑝d I y 𝑝q|d I6/

While these stochastic models may provide useful insight, they are presented here
for the sake of completeness. These models require observations of actual nests (Keeling
et al. 2017), which would not be possible in North America, as there are presently no
nests in North America. The Gaussian nature of the initial conditions of the FisherSkellam model, and the stochastic nature of the Markov Chain discrete spread model
(Section 1.5.3; Section 1.5.4) already account for the randomness found in nature.

1.5.3-Discrete Growth

As discussed in Section 1.1, V. velutina undergoes discrete growth and spread. It
will be therefore necessary to refine the models further, in order to more
closely tailor them to the biology of the Asian hornet. Archer (1985) proposes a model
for the discrete growth of eusocial wasps in the related genus Vespula (Equation 15):
𝑁56/ = 𝑁5 𝑄𝑆

22

Where N is the number of nests, Q is the number of gynes produced per hive, and
S is the fraction of Q which survives to the spring. Because the population of the previous
generation has completely died off by time t+1, the generations do not sum.
Rome et al. (2015) offers the first experimental measure of Q.
Each V. velutina hive produces an average of 560 gynes. This measure of Q was obtained
by sampling and freezing V. velutina nests throughout the year, and dissecting the nests.
The value of S has not yet been determined for V. velutina, but Archer (1985) gives a
value of S for the related genus Vespula: S=0.02. The value of S=0.02 for Vespula was
confirmed by Plunkett et al. (1989). The literature is silent on values of S for the Vespa
genus.
The Archer model, like the Fisher-Skellam model, also assumes that populations
have a smooth growth rate. It is entirely possible that Asian hornets may produce
fewer gynes under austere conditions, and that fewer gynes survive overwintering in
austere conditions, but there is no literature to suggest that Q varies with environmental
conditions, while the work of Monceau et al. (2014) and Bessa, et al. (2015) implies that
overwintering survival S may vary with environmental conditions (Section 1.1). For
these reasons, and for simplicity of calculation, the Archer model must be patched: it may
be assumed that Q is a constant and all variation is due to S (Equation 16):
𝑁56/ = 𝑁5 𝑄𝑆(𝑥, 𝑦)

23

1.5.4-Discrete Spread: Markov Chains

The Archer Model offers a model of vespid growth rooted in the biology
of vespids, but hitherto there has been no proposed model of spread based on the biology
of vespids. This paper proposes the use of Markov Chains to model the spread of a
discretely growing, discretely spreading population.
A Markov Chain is a graph (a mathematical object comprising a set
of vertices and a set of edges) wherein the vertices (“nodes”), and their weights, represent
states, while the weight of the directional edges represent the probabilities of state
change. For example, the nodes of a Markov Chain can represent the nucleotide bases
(adenine, guanine, cytosine, thymine) and the edges of the graph represent the probability
of mutation from one base to another (Hill et al. 2004).
Consider a population that undergoes a distinct growth phase and a distinct spread
phase. Let E0 , E1 , E2 , … En be the discrete environments over which the population will
range, beginning at E0 and spreading to new environments during each spread
phase. Let ri be the growth rate of the population contained entirely within
the ith environment and, if j and k are environments, then let Ojk be the probability of a
member of the population at the jth environment will move to the kth environment during
the spread phase. Let Oii denote the probability that a member of the population in
the ith environment remains at the ith environment.
Finally, let Pjk denote the edge, the “path” from environments j to k. From these
definitions, the Markov Chain M may be formally defined (Equation 17):
𝑀 = [𝐸d ] ∪ [𝑟d ] ∪ €𝑃Z[ • ∪ €𝑂Z[ •

24

Where [𝐸d ] is the set of environments, [𝑟d ] is the set of growth rates at each
environment, €𝑃Z[ • is the set of paths between environments and [Ojk] is the set of the
probabilities of movement along the paths between the environments.
Let 𝑁(𝑒, 𝑡) be the population at environment e and at time t. This function may be
defined piecewise. If t falls during the growth phase, a modified version of equations 15
and 16 may be used (Equation 18):
𝑁 = 𝑁‚ 𝑟ƒ
where Ns is the population in environment e at the end of the last spread phase,
and re is the intrinsic growth rate at environment e. If t falls during the spread phase,
then (Equation 19):
[

[

𝑁(𝑒, 𝑡 + 1) = w 𝑁(𝑖, 𝑡)𝑂dƒ − w 𝑁(𝑒, 𝑡)𝑂ƒd (d„ƒ)
d

d

Where N(i,t) is the population in the ith environment at the end of the last growth
phase and Oie is the probability that a member of the ith population will enter environment
e.
This Markov Chain Model requires only one modification to make it applicable
to vespid biology: if t falls during the growth phase (Equation 20):
𝑁 = 𝑁‚ 𝑄𝑆ƒ
Growth is here defined according to the Archer Model: Se is the overwintering
survival in environment e. Moreover, let h be the interval tg + ts, where tg is the growth
phase and ts is the spread phase. As h approaches zero and the number of environments
per unit distance approach infinity, N(e,t) will approximate U(x,y,t), a Fisher-

25

Skellam model of any patching. Thus, the Archer-Markov model can itself be used as a
numerical approximation.

2-AIMS

The purpose of this study is to model the four stages of a hypothetical invasion of
North America, both to advance the field of invasion biology and to provide useful
information to authorities, that those authorities may plan countermeasures.
The transportation phase will be modeled by an analysis of transportation vectors
to determine the most-likely method by which V. velutina might make its way to North
America. These most-likely channels of invasion might warrant special attention from
management authorities.
The establishment phase will be modeled using niche analysis to determine the
suitability of habitat to V. velutina establishment. Such analysis may tell management
authorities what areas are at greatest risk of invasion, areas for managers to focus their
efforts, and what areas, being inhospitable, should be given lesser priority among
managers, making for the most efficient use of limited time and resources.
The Spread phase will be modeled using the continuous Fisher-Skellam model
and the discrete Archer-Markov model. The niche analysis will be used as the basis for
the patching on both models. If an invasion begun at one port were to produce much
greater nest density than others, this port would warrant extra attention from management
authorities. Further, if the more traditional Fisher-Skellam model and the more
biologically accurate Archer-Markov model produce statistically significantly different

26

predictions of nest density, it will be necessary to work out which model managers
should favor, but if the difference in predictions is not statistically significant, then
managers may use either model freely.
Finally, the impact phase will be modeled by examining impacts in the European
range and extrapolating impacts to the hypothetical North American range. It may then be
possible for managers to understand the magnitude of the danger, and prepare
accordingly. Managers may use these figures to raise awareness, for example. Beekeepers
may also use these data to plan financially for the loss resulting from invasion. The
conceptual model of invasion theory used in this study is summarized in Figure 2.

3-MATERIALS AND METHODS
This study is committed to the principles of the Open Source movement: When
possible, software used in this study were those distributed under the Creative Commons
License: the source code is freely available and free to be modified (Bonaccorsi and
Rossi 2006). Any software developed during this project will similarly be released under
the Creative Commons license. In the spirit of citizen science, this study was conducted
at no cost, using widely commercially available hardware: an HP laptop with an Intel ©
CORE i5 7th Gen processor with 4 GB of RAM and running a Windows 10 OS.
All scripts were programmed in Python 3.7.4 (Van Rossum et al. 2009), or R
3.6.2 (R Core Team 2019). Scripts for habitat distribution modeling, Fisher-Skellam
modeling, Archer-Markov modeling, and basic data processing were composed in Python
3.7.4 (Van Rossum et al. 2009). Arithmetic, statistical, and calculus functions were saved
27

in the module “funx” while matrix manipulation functions were saved in the module
“mfunx” (Appendix A). The only third-party Python module used was “random,” a
module packaged with base Python (Van Rossum et al. 2009). Additional data
processing, statistical tests, and graphics were done in R 3.6.2 (R Core Team 2019). R
packages used in this study were “dplyr” (Wickham et al. 2018) for data manipulation,
“ggplot2” (Wickham 2016) and “reshape” (Wickham 2007) for graph generation, and
“Stargazer” (Hlavac 2018) for table generation.

3.1-Transportation Phase

There is no solid information on what vectors will be favored by V. velutina. It
has been speculated that V. velutina came to France in a shipping container (Arca et al.
2015), but this is not known with certainty. Given that transport most likely occurs during
the hibernation state and given gynes can take advantage of human structures
(Monceau et al. 2014), it is entirely conceivable that a gyne could hibernate in some
compartment on an oil tanker. Any form of import could be a vector. As such, it is
impossible to define a formal vector: transoceanic shipping, airfreight, land travel, or
even the luggage of commercial airline passengers could be possible vectors. The
relevant factor is the amount of imports from infected sites during the ideal transport
phase (The first economic quarter, January through March. See Table 1, and Section 1.2
of the Introduction). Fortunately, the U.S. Census Bureau’s FT900 U.S.
International Trade in Goods and Services Report 2020 accounts for imports by value,
source, and time, for all potential vectors (transoceanic cargo, commercial air travel, etc.).
28

The FT900 U.S. International Trade in Goods and Services Report 2020 does not contain
data on when items were packed for shipping, so for example if a hibernating gyne were
packaged in November and not shipped until April, there would be no way to account for
it in this model.
U.S. Census Bureau statistic on imports were accessed from the FT900 U.S.
International Trade in Goods and Services Report 2020 for the first quarter (January
through March) from China, South Korea, and France for 2019. Canadian Trade statistics
were accessed from the Statistics Canada database (Accessed 2020) for yearly imports
from China and the European Union for 2018. Finer resolution on Canadian imports was
not available.
3.2-Establishment Phase
Occurrence Coordinates for V. velutina were extracted from the Global
Biodiversity Information Facility (GBIF) database (GBIF.org, 2019), while climactic
variables were extracted from rasters obtained from the WorldClim database (Hijmans et
al. 2005). The European Occurrence is presented in Figure 3, while the Asian Occurrence
is presented in Figure 4.
It was determined that the optimal algorithm for computing occurrence
probability would be a logistic regression test performed on the rainfall variable and a
temperature variable (Mdziniso, Bloomsburg University, Personal Communication).
Since overwinter survival is such an essential component of vespid population growth
(Archer 1985), mean yearly winter temperature was chosen for the temperature variable,
and aridity being such a critical factor affecting V. velutina habitat suitability (Bessa et
29

al. 2015), average yearly rainfall was chosen for the rainfall variable. Bessa et al. (2015)
find a minimal suitable amount of rainfall to be 410 mm per year, and a minimum
temperature of 15.2℃ , though this temperature was recorded while the colony was
active, and does not reflect overwintering temperature. Rainfall and winter temperature
values were sampled at the occurrence points using a script in Python (Appendix A) to
generate PRESENCE values. ABSENCE values were extracted by constructing the
smallest rectangle possible around the range, and values were sampled at random from
the regions of the rectangle containing no known V. velutina presence. The occurrence
range combined both the European, North Asian, and South Asian range. Owing to the
random sampling of the ABSENCE statistic, there will be some variation between
repeated samplings of ABSENCE.
Logistic coefficients were approximated using JMP Pro, Version 14.3 (SAS
Institute Inc., 1989-2019). The rainfall coefficient was 0.157869, the winter temperature
coefficient was 0.0158029, and the intercept coefficient was –5.45707014. These
coefficients were used to generate the logistic regression equation (Equation 21):
𝑃(𝑂𝑐𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑒) =

1
1+

𝑒 J….‡…ˆ‰ˆ‰/‡6‰.‰/…Š‰1‹Œ6‰./…ˆŠ•‹t

Where w is the mean winter temperature and p is the average yearly
precipitation. A Python script (Appendix A) was then used to extract the variable values
for all points, compute the probability of occurrence using Equation 20, and write those
values to a raster file (Figure 5). All probabilities are values between 0.0 (no probability
of occurrence) and 1.0 (100% probability of occurrence). All rasters in this paper are
standardized using QGIS 3.8.3 (QGIS Development Team 2019) to 1500 by 3600
pixels, each representing one 10th of a degree by one 10th of a degree square of Earth’s
30

surface, an area equal to 36 nautical miles2. See Section 3.3.3 for more information on
the standardization process. The program architecture of the Python Script is summarized
in Figure 6.
3.3-Growth and Spread Phase
The continuous population density U at point (x,y) and time t is given by
(Equation 22; from Equation 8):
5
𝜕1𝑈 𝜕1𝑈
𝑈
𝑈(𝑥, 𝑦, 𝑡) = u 𝐷(𝑥, 𝑦) B 1 + 1 C + 𝑟(𝑥, 𝑦)𝑈 Q1 −
S 𝜕𝑈
𝜕𝑥
𝜕𝑦
𝐾(𝑥, 𝑦)
‰

This equation requires numerical techniques to solve (Shigesada and Kawasaki
1997). Erdmann (2009) and Herman (2014) offer such numerical techniques. An initial
population of 1 nest is assumed. While the exact location of the nest is unknown, it is
assumed that the probability of finding a nest is a three-dimensional Gaussian distribution
with a mean at the point of introduction. A modified Gaussian distribution (from
Equation 9) describes these initial conditions (Equation 23):
P

/ HJ•
J BK
O
1
𝑈(𝑥, 𝑦, 0) =
𝑒 1 1.‡
11.52𝜋

IJ‘ P
6K
O C
1.‡

where [I,J] is the matrix index representing the starting location of the invasion. See
Section 3.3.1 for a calculation of σ. This probability is treated as the initial population
density. The values of the patching are calculated from the input of the environmental
rasters discussed in Section 3.2 above. An algorithm then cycles rapidly between a
growth phase and a spread phase according to the logistic growth equation and the
diffusion equation. Five cycles per annum were used, for a total of fifty cycles over a tenyear simulation. In testing the scripts, additional cycles did not produce meaningfully
different projections (varying only in decimal values, biologically meaningless for
31

discrete objects like nests) while occupying valuable computer time. The five cycles per
annum therefore represent a compromise between accuracy and efficiency. The Program
Architecture, sensu lato, of this Growth and Spread simulation is summarized in Figure 7.
While this model can account for multiple nests at the same origin (the initial probability
distribution is simply multiplied by the number of nests), the model cannot account for
nests introduced at two separate locations without specifying a new initial probability
distribution.
3.3.1-Refining the Model

To calculate the standard deviation, it is assumed that the edge of the invasion
wave in the first year (in this case, a radius of 60 km around the central point (Robinet et
al. 2017; Monceau et al. 2015;Franklin, et al. 2017) is three standard deviations away
from the source, so that 99.9% of the probability (to wit, nest density) lies within that
radius. Thus, one standard deviation is a third of that distance, equivalent to 2.4 map
units. This value is calculated by taking the square of 60 km, converting this value to map
unit area, taking the square root of that value, and dividing that value by three.
The diffusion equation itself requires the solution of a derivative of spatial change. A
very small amount of discrete spatial change (h) must be specified. This value is arbitrary
so long as it is very small (Erdmann 2009). A value of 0.000001 units was specified.
The French population data suggest that the front of the Asian hornet territory
expands by 60 km per year on average (Monceau et al. 2015: Franklin, et al. 2017). If the
population expands by 60 km in the x direction and 60 km in the y, then the area expands
at a rate of 3600 km2 per year, or 51.84 map units2, an experimental value for D. There is

32

no literature suggesting the rate of spread is patched, so D was assumed to be constant for
all patches (Robinet et al. 2017).
Carrying Capacity (K) was calculated from the European population (Robinet et
al. 2017) through unit conversion. A K of 7.397 nests per unit was calculated. In testing
the prototype draft of the script, after running the first continuous simulation and the first
discrete simulation, no population in any cell exceeded the calculated density of 7.397
nests per unit. Varying K would have provided insight into how reaching the maximum
population density in an environment would have changed the dynamics of growth and
spread, but as no population tested reached carrying capacity, patching K would have
offered no new insight while occupying valuable computer time, though studying how
varying K affects overall predictions of Fisher-Skellam models may make for interesting
future work. Thus, the only patched variable required is growth, r(x,y).
The rate of growth,r(x,y), when P(occurrence)=1 was assumed to be the same as
that projected by the Archer model, where S is assumed to be the same as in
the Vespula genus: 0.02. Logistic growth is approximately equal to Malthusian growth
for small values of t (Renshaw 1991). Assuming the continuous and discrete growth rates
are approximately equal, and approximately described by Malthusian growth, at least
between t0 and t1, r can be calculated as:
1𝑒 /k = 560 × 0.02 = 11.2
ln 𝑒 k = 𝑟 = ln(11.2) = 2.415
Solving for r by taking the natural logarithm of 11.2 gives a value of 2.415. This rvalue causes the number of nests to increase by an order of magnitude per generation.
This assumption is reasonable, as the European population increased by approximately an

33

order of magnitude each generation, until reaching carrying capacity (Robinet et al.
2017). This value of r is close to the May Threshold (r >2.692), the value for r at which a
logistic equation becomes chaotic. At 2.415, a logistic differential equation becomes
cyclical. However, this only applies to logistic differential equations where the
population of the previous generation is added to the new generation (May 1974): for V.
velutina, the prior population dies off (Monceau et al. 2014). For methods of calculating
r(x,y) for minor variables, see section 3.3.5, below. The Fisher-Skellam equation may
therefore be simplified to (Equation 24):
5

𝜕1𝑈 𝜕1𝑈
𝑈
𝑈(𝑥, 𝑦, 𝑡) = u 51.84 B 1 + 1 C + 2.415𝑃˜™™šk (𝑥, 𝑦)𝑈 Q1 −
S 𝜕𝑈
𝜕𝑥
𝜕𝑦
7.397
‰
The constant values of Equation 23, their method of calculation, and sources are
summarized in Table 3.
3.3.2-Minor Variables

In addition to the variables from the establishment analysis (rainfall and overwinter
temperature, here combined into the single “occurrence” variable), human population
density (Choi et al. 2015), the presence or absence of a major river (Bessa et al. 2015),
and elevation (Robinet et al. 2017) are reported as potentially
important secondary variables of habitat suitability. Urban and suburban
environments (Choi et al. 2015), and environments with a major river (Bessa et al.
2015) benefit V. velutina , while environments with elevation over 791 m are detrimental
to V. velutina (Robinet et al. 2017).
These secondary variables, henceforth minor variables, were left out of the logistic
regression because the literature (Choi et al. 2015; Bessa et al. 2015; Robinet et al. 2017)
34

does not suggest an equal importance to climatic variables in limiting the range of V.
velutina, but these variables are accounted for by additional model statements.
Elevation data was drawn from the U.S. Geological Survey National Map Digital
Elevation Model (Archuleta et al. 2017). River shapefiles were drawn from Natural Earth
1.2 (Kelso and Patterson 2009). Human Population Density will be drawn from NASA
Socioeconomic Data and Applications Center (SEDAC) (CIESIN, 2018). These raster
and vector files were then standardized to the standard raster format using QGIS
3.8.3 (QGIS Development Team 2019). Human Population Density is presented in
Figure 8. Major River Presence is presented in Figure 9. Elevation is presented in Figure
10.
3.3.3-Input Data and Processing

The details of the specific models will be discussed thoroughly, but it may be
useful to describe the general workflow here. For each model statement, environmental
data rasters were loaded into the program. The patching r(x,y) was calculated from these
rasters. The script then carried out the appropriate calculations, using Equations 19 and
20 for the discrete simulation, and Equation 22 for the continuous simulation. These
calculations output a raster file showing the population density at each point, and a
statistics file containing the total number nests after 10 years. This process was carried
out for each specified port, and the new model statement was specified.
Input rasters were of different dimensions, x by y. Dimensions need to be
standardized so that a single coordinate system of matrix indices can be used to pull data
from the same cell in multiple raster. If the dimensions of the rasters are too large, the
35

rasters exceed the 4 GB of RAM used in this study. Standardizing raster size to 3600 x by
/

1500y allows for each cell to be /‰žŸ of one degree. There is a downside to this
standardization: Decreasing the dimensions of a raster decreases the resolution. Consider
a raster of a map of a coastline. When the resolution is reduced, the QGIS algorithm must
make a choice as to whether a set of pixels containing land and water will now be
represented by a single land pixel or a single water pixel. Consequently, a GPS
coordinate pair that once represented a land pixel may now represent a water pixel.
Several matrix indices for ports represented water pixels after the rasters were
standardized. In the standardized rasters, water pixels are assigned NODATA values.
Points surrounding the indices were pulled to determine if they were land or water pixels.
In these cases, the nearest index representing a land point was used. GPS coordinates
were converted to matrix indices using the CoordConvert function in the Python Module
“funx” (Appendix A).
A Python script (Appendix A) was used to read in the standardized rasters. To
simplify the calculations, each raster combination was used to calculate a growth
raster, which was then written out and saved to an ASCII text file. These saved ASCII
text growth rasters were then loaded into the script, rather than recreating the growth
matrix each time. The simulation was then performed for each point in the raster, with a
mean at the test point. The resulting raster was then written out, along with a statistics file
containing the final nest density at the test point, and a sum of the total population density
within a search area of 121 square units (4,356 square nautical miles) centered at the test
point. While the script was being developed, Because it was possible for land area at
ports to effect nest projections, a control for land area was added.
36

For the discrete simulation, the process is the same as the continuous simulation,
except that the alternating growth and spread phases are taken for each year, and spread is
defined according to a matrix of distances between points. The probability that a member
from one population will emigrate to another is a Gaussian probability of the distance
between the first and the second, in standard deviations. More memory for a matrix of all
points to be computed was required than the hardware could access, so a smaller matrix
of points within 441 square units (15,876 square nautical miles) was constructed for this
purpose.
3.3.4-Trial Ports

Thirty-two sites were chosen for simulation, 24 test ports and 8 control sites (some of
which are not ports: See section 3.3.6). The test sites were chosen by studying a Google
Map of the United States and Canada for major port cities. GPS coordinates for these
locations were obtained from Google Maps. GPS coordinates were then converted to
matrix indices of the standardized raster matrix. The standardization process in QGIS
(QGIS Development Team 2019) assigned NODATA values to some of those
indices that are on coastal areas. In those cases, the nearest index containing a data
value was used instead. The test ports are summarized in Table 4, while control sites are
summarized in Table 5.

37

3.3.5-Methods of Calculating r(x,y)

Rate of growth for human population density was assumed to be maximal (2.415)
in the areas of highest population density, declining linearly as population declines.
“Urban” human population density was found to be favorable to V. velutina (Choi et al.
2012), but there is no literature suggesting that increased population density within an
urban site has an effect (e.g. between 2,000 people per km2 and 2,500 people per km2)
Here, urban populations were defined as those greater than or equal to 2,000 people.
Population was corrected so that maximal population density was 2,000 people per km2 .
The variable pop_val was defined as Human_Population_Densty(x,y) divided by 2,000.
The r-value, r(x,y) for the human population density model was calculated by multiplying
pop_val by 2.415.
The river presence raster contains binary values: 1 for presence, 0 for absence. V.
velutina can clearly grow in the absence of rivers (Bessa et al. 2015), these binary values
needed to be altered: a value of growth when river presence=0 needed to be assumed. It
was assumed that V. velutina grew half as well in areas without a river. The variable
riv_val was defined as 1 when river presence= 1, and riv_val=0.5 when river presence
=0. The r-value, r(x,y) for the river presence trial was calculated by multiplying riv_val
by 2.415.
Elevation acts as a governor, such that growth does not occur above 791 m. The
variable elev_val was defined as 1 when elevation(x,y) was less than 791 m, and 0 when
elevation was greater than or equal to 791 m. The r-value r(x,y) for the elevation trial was
calculated by multiplying elev_val by 2.415.

38

Growth values for trials combining multiple variables were calculated by
multiplying the trial variables, e.g. 2.415 * riv_val*elev_val for minor variables, and
2.415*Poccur(x,y)*riv_val*elev_val for trials combining major and minor variables.
Model Statements and methods of calculation are summarized in Table 6.

3.3.6-Measurements

Fifteen Continuous trials and fifteen Discrete trials were run for 24 test ports and
8 control sites, for a total of 960 simulations. The output of the simulation, for a single
port, is a raster representing nest density distribution after ten years, U(x,y,10). The
simulation could have been run for any number of years, but ten years was chosen for the
duration of the invasion in Europe (Robinet et al. 2017) and South Korea (Choi et al.
2012). Outputting a raster for every year was not feasible, given the amount of computing
time and storage required for constructing and saving these rasters. Nest density output is
a distribution of decimal values. This output is not useful for statistical analysis: one
value, or a small set of values, per port is needed to summarize the trial, and properly test
hypotheses. For this purpose, projected nest population after 10 years (N10) was extracted
instead. There is only one generation of V. velutina secondary nests per year (Monceau et
al. 2014). This extraction was done by summing up nest density within 121 square map
units (plus or minus ten map units in the x and y directions, centered at the point of
origin). This measurement may not represent the entire N10 population, but the
measurement represents the majority of the population, and the measurement allows for
quantitative comparisons. Means, standard deviations, minima, maxima, ranges, and z-

39

scores for each port were calculated with a Python script (Appendix A) from these N10
projections.
The number of map units, within the 121 square map unit search area, positive for
land (rather than ocean) were extracted, and the N10 projection was divided by the total
land area to calculate a Mean Nest Density per map unit for each site. Mean nest density
allows for comparisons between coastal sites and sites more inland. Statistical tests (see
Section 3.3.7) were done with an R (R Core Team 2019) script (Appendix B).

3.3.7-Experimental Controls and Statistical Tests

There are three sorts of controls in the growth and spread simulation: controls for
land topography, negative controls (sites Albuquerque, NM; Barry County, MI; St. Paul,
MN) and positive controls (sites Busan, SK; Montreal, QC; Nerac, FR; Tsushima City,
JP; Walhalla, SC). In testing the scripts, a much smaller set of ports, entirely within the
contiguous United States, variances in N10 were found that could not be explained by
differences in the Major Variable. Interestingly, ports set further inland along rivers, e.g.
the river port of Philadelphia, PA, had higher projections of N10 than oceanfront ports,
e.g. Charleston, SC. Intuitively, it was possible that more land around the initial invasion
point provided more opportunity for settlement and growth. To test this hypothesis, a
raster was created with an r(x,y) =1 assigned to each point, and the simulation was run
with the prototype draft of the script. Z-Scores were taken and compared. Land control
accounted for all this outstanding variance. For this reason, a control trial for land shape,
Land Control, was added to the slate of tests.

40

Negative controls denote sites where growth is expected to be much lower than
the test sites. Very arid sites and very cold sites are expected to very small N10 projections
(see Section 3.3.2), so Albuquerque, NM (very arid) and St. Paul, MN (very cold) were
added to negative controls. Sites which are not extremely cold nor extremely arid, but are
predicted by the Niche Analysis (see Section 3.2) to be habitat of intermediate quality for
V. velutina, are likely to produce less growth than a test site in a region identified by
Niche Analysis to be ideal habitat, so Barry County , MI was added to Negative controls
(see Section 4.2).
Positive controls denote sites where V. velutina is known to occur, or where
growth is likely to be very high. The V. velutina invasion in Korea began in Busan (Choi
et al. 2012). An invasion in Japan began in 2012 in Tsushima City, Nagasaki Provence
(Ueno 2014). While the precise location of the origin of the French invasion is unknown,
the first identified specimen was documented in the town of Nerac, Lot-et-Geronne,
France (Haxaire et al. 2006). Using these starting sites where an invasion was known to
begin, will provide a strong basis for comparison between these models and observed
nest populations. Every port except Anchorage, AK is located in highly suitable habitat
but abutting water. What might an invasion be like if the invasion began in highly
suitable habitat, but completely surrounded by land? For this reason, Walhalla, SC was
added to the positive control group. What might an invasion begun in a highly suitable
but completely inland port, far from the ocean, look like? Thus, Montreal, QC was added.
The addition of these Positive controls is to contextualize the results of the test, e.g. that
an invasion beginning at port A was a statistical outlier greater than the mean, but not
greater than the control population emanating from Walhalla, SC.

41

This context is useful for certain aspects of hypothesis testing: the hypotheses
being statistically tested are 1) that some ports will produce statistically greater or lesser
invasive populations; 2) that discrete and continuous simulations will produce statistically
similar predictions; 3) that the addition of the minor variables to model statements will
not significantly change projections of N10 ; and 4) that the test ports are similar to the
positive controls and statistically significantly different from the negative controls. The
first hypothesis was tested by examining the test data for statistical outliers. Sites
generating an outlier projection of N10 for a given trial were identified by manually
looking at z-score output tables (Appendix C) for a z-score of 3.0 or greater. If an outlier
was identified using z-score, that site’s outlier status was confirmed by a One-Way
ANOVA, conducted in R (R Core Team 2019), comparing that site to all other sites in
that site’s trial group, across all trials for both N10 and Mean Nest Density.. To test the
second hypothesis, the trial means for the fifteen continuous test trials, and the trial
means for the fifteen discrete trials (30 trial means in total) were compared using the
Unequal Variance T-Test in base R (R Core Team 2019). Then, the continuous N10
projections for all test sites were compared to the discrete N10 projections for all test sites
using an Unequal Variance T-Test, and finally all N10 projections (test group, negative
control group, positive control group) for continuous and discrete trials were compared
using an Unequal Variance T-Test. In this latter comparison, Walhalla, S.C. provides an
upper bound of the distribution of possible N10 projections (see Section 5).
To test the third hypothesis, if the minor variables in themselves, or in
combination with the major variable Occurrence, produce significantly different results
from the major variable alone, a One-Way ANOVA was conducted comparing

42

Occurrence other trial variables for all trial groups. Finally, to test hypothesis four, if the
assumptions of the model are valid (for more on model validation, see Section 3.4), the
projections of the test group should not differ, in a statistically significant way, from the
projections made for the positive control group, but should differ significantly from the
projections made for the negative control group. A One-Way ANOVA comparing the test
group to the control groups was conducted (R Core Team 2019).
By default, R (R Core Team 2019) regards a p-value of 0.05 or less to be
statistically significant. For this reason, this study adopts that a p-value of 0.05 or less is
statistically significant.
3.4-Impact Phase

The literature only provides a means of calculating values for two impacts: the
value of implementing nest destruction; and the value of economic loss to the agriculture
industry. Monceau (2014) gives a cost of nest destruction ranging from €130 to €500
($144-$555 in 2020 US Dollars) per nest. These values were multiplied by the range
of estimated population growth (from the Occurrence simulation) to arrive at a projected
cost range for the complete removal of these nests.
Total economic loss is the loss of economic productivity from the loss of
pollinator services, honey production, and the loss to beekeepers accrued from replacing
lost hives. Monceau et al. (2014) reports a rate of total hive loss from V. velutina attacks
at 5%. Heim (2009) estimates pollinator services are worth 5% of the total agricultural
production (which was $219 Billion in the US in 2009). The total value of honey
produced in 2009 was $147 Million, while production in 2016, the most recent year for
43

which there is data, was $162 million (FAOSTAT 2020). Statistics on the total number of
hives in the United States was acquired from the U.S. Department of Agriculture’s
National Agricultural Statistics Service (NASS) (2019). Multiplying total hives by 0.05
gives the total number of hives expected to be lost, a 5% loss in honey production, and a
5% loss of pollinator-generated agricultural value.
It is possible to calculate impacts on honey production at a finer resolution: forty
states have published the value of honey production in the state (Flottrum 2017). A vector
map of the United States was obtained from The National Weather Service (Accessed 15
June 2020). This map of the United States was overlaid on the heat map produced from
the Habitat Distribution modeling in the Establishment analysis (Figure 11). Whether a
state contained suitable habitat for V. velutina was determined by manually looking at
Figure 11, and states with suitable habitat were assigned a binary variable value of 1,
while states without suitable habitat were given a binary variable value of 0. Honey
production for states with a binary variable value of 1 were multiplied by 0.05, to obtain
the USD value of the loss. These results were summarized in Table 7.

3.5-Model Verification: The Case of the Centaurea Leafcutting Bee
(Megachile apicalis)

Megachile apicalis, known as the Centaurea leafcutting bee, or the apical
leafcutter bee, is an invasive solitary bee introduced in the area of Santa Barbara, CA in
the 1980’s. Since M. apicalis’s introduction, M. apicalis has become invasive throughout
the United States, and especially the west coast, making it as far as Washington state in
2003 (Barthell et al. 2003).
44

M. apicalis is trivoltine, laying three nests per season (Kim 1997). Each nest
contains approximately 12 brood, of which only 49% percent survive (Hranitz et al.
2009; Hranitz Personal Communication 2020); approximately 40% of offspring are
female, due to the greater nutritional need of females (Kim 1997). 102 nests were
observed in a field of 3.5 km2 (Kim 1997). M. apicalis may be a useful organism
to verify the V. velutina models used.
A maximal growth rate for M. apicalis of 1.954 was calculated from fecundity
rates (Kim 1997; Hranitz et al. 2009; Hranitz. Personal Communication. 2020). A
maximal carrying capacity of 2023.140 nests per map unit was calculated from data
provided by Kim (1997). A diffusion rate of 63.722 square map units was calculated from
Barthell et al. (2003).
Major bioclimactic variables were determined to be average yearly rainfall and
mean yearly temperature (Hranitz et al. 2009). A habitat distribution raster was obtained
using the open-source habitat distribution modeling software Wallace (Kass et al.
2018). Bioclimactic variables were automatically accessed from WorldClim (Hijmans et
al. 2005) by the Wallace package, and M. apicalis occurrence was automatically
accessed from GBIF (GBIF.org accessed 26 January 2020) by the Wallace software.
Wallace can only run a BioClim model at this time (Kass et al. 2018).
The output raster was standardized using QGIS 3.8.3 (QGIS Development Team
2019) as described in Section 3.2). A starting index representing Santa Barbara was
chosen at a matrix index of [555,603]. This standardized raster and the constants were
entered into the discrete and continuous model scripts.

45

4-RESULTS
4.1-Transportation Phase
105.973 billion US Dollars of commerce were imported from China in the first
quarter of 2019, while 19.883 billion were imported from South Korea and 14.139 billion
were imported from France during the same period, for a total of 542.791 billion US
Dollars in trade imported from countries with source populations of V. velutina during
the biologically appropriate period. 5.461% of all US imports by value are potential
vectors of transmission. This calculation is summarized in Table 8.
In Canada, 82.653 billion Canadian Dollars in goods and services were
imported from Europe and 128.300 billion Canadian Dollars were imported from Asia,
accounting for 37.383% of Canadian import values (Statistics Canada. Accessed 2019).
Assuming an even distribution of trade across months, potentially invasive trade would
occur during the first quarter, accounting for 0.25 of that import value, a value
of 52.783 billion Canadian Dollars, to wit 9.345% of Canadian import values could be
potential vectors of a V. velutina invasion. This calculation is summarized in Table 9.
The lack of reliable vectors in the literature prohibits the most
effective analyses of the risk of exposure, so these claims must be tempered by their
generality. An exposure of 5.461% of import value to the United States shows V. velutina
to be a strong candidate for invasion.
In Canada, 9.345% of trade import values are potential vectors, but this is less
likely to be accurate than the 5.461% for the United States. The Canadian measure
includes trade from “Asia” and “Europe” rather than the specific countries with host
populations (Statistics Canada. Accessed 2019), and it assumed an equal distribution of
46

trade across economic quarters, which is not necessarily the case. Therefore, it may not
be the case that Canada’s exposure is greater than the United States.

4.2-Establishment Phase

An occurrence raster was obtained with occurrence probability values were
obtained for the whole world, based on the regression performed on the mean yearly
rainfall and mean winter temperature. A QGIS projection of this raster can be found in
Figure 5 (QGIS Development Team 2019). Much of the west coast of North America is
suitable for invasion, and much of the east coast and Gulf of Mexico. The interior of the
Southern United States is also highly suitable for invasion, but the center of the continent
is not suitable for invasion. A QGIS projection a vector political map of the United
States (National Weather Service 2020) overlaid on this raster can be found in Figure 11
(QGIS Development Team 2019).
The raster output of the habitat shows that every port studied in the test group was
maximally suitable (p(occur)=1.0) for establishment of an invasive V. velutina
population, except for Anchorage, AK (p(occur)= 0.048), as a function of the occurrence
variable.
4.3-Growth and Spread Phase
The projected populations of nests after ten years, N10, the Mean Nest Density,
and the z-scores of these populations, for all trials and controls, are presented as Raw
Output in Appendix C. Summary statistics of N10 for all trials in the test group can be

47

found in Table 10. Summary statistics of N10 for all trials for the positive control sites ca
be found in Table 11. Summary Statistics of N10 for the negative control group can be
found in Table 12. Summary Statistics of the Mean Nest Density for the test group,
positive control group, and negative control group can be found in Tables 13, 14, and 15,
respectively. ANOVA outputs can be found in Table 16.
The Growth and Spread phase, in addition to generating predictions, statistically t
tested four hypotheses. The first hypothesis was that some of the test sites produce
statistically different N10 projections – outliers – from the rest of the test sites. These
outliers would then warrant special attention from managers, or could be eliminated as a
site of concern. Anchorage, AK was the only outlier from among the test sites (for
Continuous Occurrence, N10: 5.454 nests, Mean Nest Density: 0.07575 nests, Z-score: 3.29739), and differed significantly all sites in the test group except San Francisco CA,
St. Petersburg FL, and Vancouver BC, per the One-Way ANOVA (R Core Team 2019).
The Mean Nest Density ANOVA showed Anchorage, AK to be statistically different
from all test sites except San Francisco CA, Savannah GA, St. Petersburg FL, and
Vancouver BC.
The Second Hypothesis was that continuous and discrete trials would not produce
statistically significantly different results. If the two models do not produce different
results, it would not matter which model managers used to predict population. The trials
were marginally statistically significantly different (p-value= p= 0.02698 ) when
comparing just the test group, but that difference went away when all groups together
were compared (p-value= 0.1084).

48

The third hypothesis was that the major variable Occurrence would be different
from the minor variables. The results of the One-Way ANOVA (R Core Team)
Continuous Occurrence (O) differed significantly from all but Human Population Density
x River Presence (HR), Occurrence x Human Population Density x River Presence
(OHR), Occurrence x Human Population Density x Elevation (OHE) and All Variables
(ALL). Discrete Occurrence differed significantly from all discrete trials except Human
Population Density (DH), Occurrence x Elevation (DOE), and Occurrence x Human
Population Density x Elevation (DOHE).
The fourth hypothesis was that the test group would be significantly different
from the negative control group, but not the positive control group, tested by a One-Way
ANOVA (R Core Team 2019). The test group was not significantly different from the
positive control group (p-value=0.301), but did differ significantly from the negative
control group (p-value <2e-16).
4.3.1-Continuous Growth
The Simulation based on occurrence alone (O) had a mean total population (in the
search area) of 222.75 nests after ten years (N10), and a standard deviation of 64.5 nests.
Anchorage, AK is an outlier with a population of 5.47 nests (z score: -3.368). The rest
range from 164.2 nests (San Fransisco, CA) to 311.96 nests (Portland, OR).
Due to the mechanics of the model, in areas of low growth, it is possible for the
spread phase to overwhelm the growth phase and produce negative population densities.
An illustration of this distribution geometry can be found in Figure 12. This is the case
for Anchorage: -2.43 nests at the point of origin. The rest had 5.17 nests at the point of
origin. Figure 13 shows the means of all trials, together with the standard deviation.
49

Figure 14 contains the Boxplot distributions of all trials for the test group, positive
control group, and negative control group. Figure 15 summarizes the distribution of N10
projections across all sites.
Human Population Density produced wildly different results from those of
Occurrence, with a mean of 14.698 nests (compare Occurrence, mean: 222.75) and a
standard deviation of 29.809 (Occurrence: 64.5). The minimum population was –16.916
nests (Port Charlotte, FL) and the maximum population was 99.880 nests (Los Angeles,
CA). None of these values are outliers (z score > ±3.000). In the other trials where
Human Population Density is a variable (Trials: OH, HR, HE, OHR, OHE, HRE, ALL),
similarly low results were obtained. HR and HRE had identical means (-5.455 nests),
standard deviations (6.833 nests), minimum populations (-18.325 nests) both in PortCharlotte, and maximum populations (5.563 nests) in Portland, OR. OHR and ALL had
nearly identical means (-7.673 and –7.674 nests respectively), identical standard
deviations (4.893 nests), identical minimum populations (-18.453 nests), both at PortCharlotte, FL, and identical maximum populations (0.001 nests) both at San Fransisco,
CA. OH and HE also have very similar means (14.698 and 14.819 nests,
respectively), similar standard deviation (29.809 and 29.725 nests, respectively), identical
minimum populations (-16.916) both at Port Charlotte – Fort Meyers,
FL and identical maximum populations (99.869 nests) at Los Angeles, CA. Finally, OHE
is much lower than O, with a lower mean (4.689 to 222.75 nests, respectively).
Major River Presence also produces lower population projections than the
occurrence variable. The calculation based solely on river presence (R) had a mean of
37.702 nests (compared to a mean of 222.75 nests in O), a standard deviation of

50

22.415 nests (compared to a standard deviation of 64.5 nests in O), a minimum
population projection of 17.357 nests in Miami FL, and a maximum population
projection of 92.180 nests in New Orleans, LA. When river presence is combined with
occurrence (OR), the mean is reduced to 17.787 nests, a standard deviation of 13.586
nests, a minimum population of –1.684 nests in Anchorage, AK, and a maximum
population of 52.285 nests, also in New Orleans, LA.
Elevation had a mixed effect on population projections. Calculations based on
elevation alone (E) had a higher mean than O (237.367 to 222.75 nests, respectively), a
lower standard deviation (49.010 to 64.5 nests, respectively), a higher minimum
population (129.298 to 5.47 nests, respectively), in Vancouver, BC, and a nearly
identical maximum population (311.192 to 311.964), both in Portland, OR. The E
calculation assigns maximal growth rate (2.415) to all points except those over 791
meters in elevation, so Anchorage Ak is stronger in this trial than it is in O, accounting
for the higher mean, smaller standard deviation, and higher minimum
population. When occurrence is added to the elevation calculation (OE), the mean is
reduced (123.878 nests), the standard deviation is reduced (35.025 nests), the minimum
population is nearly identical (17.310 nests) at Anchorage AK, and a reduced maximum
population of 174.983 nests, also in Portland, OR.
The positive control sites showed a smaller mean (211.362 nests) and larger
standard deviation (124.719 nests) in the continuous major variable trial (O). This is
likely accounted for by the lower population projection from Tsushima City (27.357
nests). Human Population Density (H) had a low mean (-1.059) and standard deviation
(22.111 nests). River Presence (R) had a mean nest density of 53.94 nests with a standard

51

deviation of 39.453/ Elevation (E) had a mean of 220.9579 nests and a standard deviation
of 129.3804 nests. Occurrence and Elevation (OE) had a mean of 120.3965 nests and a
standard deviation of 70.64999 nests. The remaining combined trials continuous trials had
a mean no greater than 52.977 nests and a standard deviation no greater than 39.261
(RE).
The negative control sites showed a broader range of values than the test sites in
O, with a much smaller minimum projection (-9.400 nests in Albuquerque, NM
compared to 5.454 nests in Anchorage, AK), a much larger maximum projection (439.
680 nests in Barry County, MI compared to 311.91 nests in Portland, OR), and
a lower Mean (3.244 nests) and Standard Deviation (26.665 nests). The Controls in the
minor variables followed a similar pattern as the test sites.
The European population grew by approximately an order of magnitude each year
until reaching a population of 330 nests (Robinet et al. 2017), while the Korean
population grew to 453 nests after ten years of invasion (Choi et al. 2012) The precise
nest population near Tsushima City is unknown. (Ueno 2014). Only projections based on
Occurrence (O) and Occurrence with Elevation (OE) produced populations in the
hundreds. The elevation variable only acts as a cap on growth in OE. The multiplicative
proportionality assumption used to integrate the minor variables may account for the
failure of these trials to adequately add predictive power. It may be that the minor
variables need to be added to the regression model in future analysis.
Growth and spread based on a continuous model rooted in the major variable of
habitat suitability shows, if no countermeasures are implemented, populations of several
hundred nests are possible at all test locations (except Anchorage, AK) within ten

52

years. When Anchorage is removed, the mean prediction rises from 222.745 nests to
232.193 nests.
The variance in nest population (excluding Anchorage, which has inferior growth
conditions) may be accounted for by the land area surrounding the port. Intuitively, an
inland port has more land area and therefore more spaces for nests to colonize, relative to
a port located close to the water. Walhalla, SC was included as a control site because the
location, like all ports save Anchorage, have p(occur)=1.0, but unlike the ports, Walhalla
is landlocked, and the land that surrounds it also has a p(occur) of 1.0. Walhalla has
more land area than any port. The occurrence projection for Walhalla was 439.680
nests.
This pattern holds for nest density as well: Trial O had a mean of 2.949 nests per
unit, with a standard deviation of 0.613. while Trial H had a mean of 0.191 nests per unit,
with a standard deviation of 0.396. Trial E had a mean of 3.009 and a standard deviation
of 0.239. Occurrence with Elevation (OE) had a mean of 1.637 nests per unit, and a
standard deviation of 0.342. The combined continuous trials did not have a mean greater
than 0.484 (RE) or a standard deviation greater than 0.396 (HE).
4.3.2-Discrete Growth
The geometry the discrete model produces is a rectangle of homogeneously filled
cells with an even density of nests. An example of this geometry is provided by Figure
16. The discrete model does not produce negative nest densities: the model rather
produces very small nest density projections (e.g. on the order 1.0 * 10-31 nests) in the
same cases where the continuous model produces negative nest densities.

53

The discrete model produced similar results to the continuous trials. In the major
variable trial DO, the mean population was 289.823 nests, with a standard deviation
of 123.440 nests, a minimum projection of 0.138 nests (Anchorage, AK) and a maximal
projection of 439.821 nests (Portland, OR).
The minor variables, accounting for the difference in the way the models handle
cases where spread exceeds growth, showed the same pattern as the continuous variables:
trials containing the Human Population
Density variable (DH, DOH, DOHR, DOHE, DHRE, DALL) have means ranging
from 0.083 to 0.087 nests. Elevation acts as a control, DE reducing the mean to 262.715
nests from 289.823 nests in DO. The river presence variable reduces the mean further, to
3.506 nests in RO, 3.135 nests in RE, and 0.597 nests in OR.
The positive control sites showed a smaller mean (211.3624 nests; compare
289.823 nests) and larger standard deviation (124.719 nests) in the discrete major
variable trial (DO). This is likely accounted for by the lower population projection from
Tsushima City (33.684 nests). Human Population Density (DH) had a low mean (0.001
nests) and standard deviation (0.002 nests). Elevation (DE) had a mean of 291.142 nests
and a standard deviation of 170.714 nests. Occurrence and Elevation (DOE) had a mean
of 100.8953 nests and a standard deviation of 52.438 nests. The remaining combined trials
continuous trials had a mean no greater than 4.396 nests and a standard deviation no
greater than 1.252 nests (DRE).
The negative control projections in DO ranged from 5.079e-19 nests in St. Paul
MN to 439.680 nests in Barry County, MI. The Land Control Trial LC had a Standard

54

Deviation of 0.0, making z-scores impossible to calculate for the control populations.
Maps were very homogenous across all invasive territory.
The discrete model predicts a higher population and more homogeneous
distribution. The Discrete model is more biologically accurate than the
Continuous model, but adding more biological accuracy may not produce a
statistically significantly different prediction from the less biologically accurate
continuous model. An Unequal Variance T-Test was performed in R (R Core Team
2019). The script and outputs can be found in Appendix B. In the first test, the means of
the discrete and continuous trials (see Figure 12) were compared. The t-test showed no
statistically significant differences (p=.099) in the predictions made by both models.
Figure 17 represents the two datasets, continuous means and discrete means, as boxplots.
A second Unequal-Variance T-test was performed comparing the projections made by
trials O and DO, the most biologically relevant trials. The sets of data containing only the
test sites did generate statistically significant differences (p= 0.02698) at a 95%
confidence interval, but when the control groups were added –two sets of all sites – the
significance went away (p = 0.1084). Figure 18 represents the population projections of
O and DO with a boxplot.
This difference is unlikely to be biologically significant: whereas the continuous
model deals with spread exceeding growth by predicting negative nest densities, the
discrete model deals with these cases by generating very small nest densities. Both
models are also functions, generating geometries in three-dimensional space. The
geometry of the continuous model is a Gaussian surface expanding outward over a
circular base with a center at the starting point. The discrete model forms a cube centered

55

at the starting point. The search area is a square centered at the starting point. It may be
that the discrete model fills the search area more completely.
The mean projection of the discrete model in DO projects a mean which differs
from the continuous projection by only 67 nests (289.827 nests to 222.745 nests) and
while that is slightly more than one standard deviation greater (64.510 nests) than the
mean of the continuous model, both results are in the same order of magnitude.
The pattern holds for nest density in continuous trials as well: Trial DO had a
mean of 3.785 nests per unit, with a standard deviation of 1.461, while Trial DH had a
mean of 0.001 nests per unit, with a standard deviation of 0.005. Trial DE had a mean of
3.423 and a standard deviation of 1.533. Occurrence with Elevation (DOE) had a mean of
1.596 nests per unit, and a standard deviation of 0.949. The combined continuous trials
did not have a mean greater than 0.041 (DRE) or a standard deviation greater than 0.037
(DRE).
Regardless of which model – discrete or continuous – is ultimately more
accurate, both models project a substantial invasive population within ten years of
invasion.
4.3.3- Both Discrete and Control Trials

There was a significant difference (p-value <2e-16) between the negative control
group and the test group for all trials, while no significant difference (p-value=0.301)
exists between the test group and the control group for all trials. These groups are
summarized with boxplots in Figure 19.

56

Minor variables had the effect of dragging down N10 and Mean Nest Density. This
may have been caused by a failure to properly integrate these variables in the model. In
future analyses, it may be useful to find a way to bring the minor variables into the
logistic regression model. A visual inspection of the data suggests that Human Population
Density had the strongest effect in dragging down the nest projections and mean nest
density. This observation was confirmed by Principle Components Analysis in R (R Core
Team 2019). The analysis showed that Human Population Density had the largest effect
on the distribution of data. See Figure 20.
It might be asked if Human Population Density is a function of Land Area, as
ports tend to have high populations. A correlation analysis was run in R (R Core Team
2019). There was no statistically significant difference between Human Population
Density and Land Area (p-value=0.134, Correlation=0.314). See Figure 21.

4.4-Impact Phase
Based on a five percent loss to the beekeeping industry if the values of the most
recent years are taken as representative of any given year, and the cost of nest removal in
2020 dollars, the total potential cost of an V. velutina invasion is projected to range
from 565,181,398.135 USD to 565,307,127.539 USD, including a nest removal cost
ranging from 31,398.135 USD to 157,127.539 USD.
In Canada, a value for pollination services could not be found, but Canadian
honey production for the last year for which there is data, 2016, was $97,931,320 USD
(FAOSTAT 2019), equal to 129,504,377.57 CAD (Bank of Canada Accessed 2/21/2020).
A loss of five percent honey production would be a loss of 6,475,218. 878 CAD.
57

Converting estimated nest removal const from USD to CAD gives a range of 41,526.350207,397.338 CAD (Bank of Canada Accessed February 21st 2020), for a total range of
economic impact of 6,516,745.228 -6,682,616.216 CAD. Tables 17 and 18 summarize
these calculations for the United States and Canada, respectively.
Ecological and human health impacts, while probably significant, are not possible
to calculate due to lack of data. Economic impact was possible to estimate based on
some available data: five percent total loss to the main services provided by honeybees
(pollination and honey production) is possible to calculate, though it may be unlikely that
the kind of complete invasion assumed in the calculation would materialize. Nest
removal cost, ranging from 31,398.135 USD to 157127.539 USD, is more likely to be a
more accurate reflection, calculated from mean projected population and nest removal
cost in France, assuming a cost in line with 2020 exchange rates. In Canada, the full
measure of cost is less accessible than in the United States because pollinator values are
not available.
In the analysis of impacts of honey production by state revealed a total of
$9,904,350 USD in loss of honey production from all states with suitable habitats. Of the
potentially infected states, California had the greatest impact, with a loss of 1,435,300
USD. See Table 7.
A potential invasion cost of over half a billion USD to American agriculture, and
a loss of 6,475,218. 878 CAD to Canadian honey production, is nonetheless substantial,
and it demonstrates the value of countermeasures to a V. velutina invasion.

58

4.5-Model Validation
The heat map of M. apicalis occurrence, generated with the software package
Wallace, can be found in Figure 22. The continuous model projects a population of 4.219 nests within the search area, while the discrete model projects a
population of 2.308e-08 nests. In cases where the rate of spread eclipses the rate of
growth, the continuous model assigns negative nest projections while the discrete model
assigns very small nest projections. In the M. apicalis case, it is clear the rate of spread
exceeds the rate of growth in both the discrete and continuous model. The M. apicalis
invasion was therefore not an effective means of model validation.

5-DISCUSSION

The purpose of this study was to determine what a V. velutina invasion would
look like in quantitative terms: How likely was an invasion to occur? What habitats were
the hornets likely to occupy, and how many nests could be expected in these habitats?
What would the financial and ecological impacts of the invasion be?
This study was successful in generating a prediction of what habitats were likely
to support V. velutina, and that prediction raised an important insight: An invasion
beginning on the west coast, while potentially calamitous for ecology and agriculture on
the West Coast, is unlikely to cross the center of the continent and settle in the East. A
large band of inhospitable territory splits the continent between the two hospitable
coats. An invasion begun on the east coast would be significantly more devastating in
terms of its potential to spread, given suitable habitat from Florida to the Canadian
59

Maritimes, through the Midwest as far as Michigan. Habitats inhospitable to V. velutina
separate the coasts, so V. velutina will not migrate naturally. An additional transportation
event will be required for V. velutina to move from the invaded coast to the non-invaded
coast. Goods shipped from the invaded coast to the other could be screened for the
presence of V. velutina gynes.
This study was also successful in generating predictions of nest density
and nest populations (N10). In France, Robinet et al. (2017) report an observed nest
population N10 of 330 nests, while in South Korea, an observed N10 of 453 nests was
reported (Choi et al. 2012). The Positive control site Nerac had a projected N10 of
311.962 based on the major variable, within 5.4% of the observed value reported by
Robinet et al. (2017). The discrete trial based on the major variable at the same location
produced a projection of 440.829 nests, consistent to within 2.8% of the observed nest
population at Busan (Choi et al. 2012). Busan itself, however, was consistent only to
within order of magnitude, being less than half the population observed at Busan.
Projections of nest population (N10) in North America based on the major variable alone,
using both the continuous and discrete models, are consistent with the what has been
observed in Europe (Robinet et al. 2017) and Korea (Choi et al. 2012), save Anchorage.
Of note is Walhalla, SC, chosen to represent maximal land area, had the same continuous
and discrete projections as Nerac. Observed invasive populations range from 330 to 453
nests. For the major variable, continuous projections predict a value within 5.4% of the
lower bound, and discrete projections predict a value within 2.8% of the upper bound,
when land shape is not an issue. This result suggests that the main limitation of both the
discrete and continuous models is its inability to account for land shape. The model is
60

accurate when land shape is not an issue. This result also implies that the assumptions of
the model were justified: 2.415 is an appropriate value for r; the logistic growth model
was approximately equal to Malthusian growth, which was approximately equal to
Archer’s (1985) discrete growth model; the calculated model values from the French
population (Robinet et al. 2017) were accurate in the map unit basis coordinates; and the
discrete model laid out here is validated.
A second goal of the population simulation was to determine whether the
continuous and discrete models produced statistically significantly different population
projections. The two models did not produce statistically significantly different results.
This result implies that either model could be used for further predictions of nest density
and population, giving allowances for land shape. The tendency of the continuous model
to produce negative results, and of the discrete model to produce very small results, when
spread exceeds growth, also presents a problem for the future usage for the model.
Adding the minor variables took the N10 projections far from the observed values of 330
nests and 453 nests in France and Korea (Robinet et al. 2017; Choi et al. 2012),
respectively. This may be attributed to the failure of integrating the minor variables into
the model, something that may be fixed by including the minor variables into the habitat
suitability regression analysis.
This study was unsuccessful in validating the population models for other species.
The biology of M. apicalis was not compatible with the models used. This species
reproduces far too slowly relative to its rate of spread. This fact of M. apicalis generated
negative population densities. The continuous model used in this study has been validated

61

for V. velutina in Europe (Robinet et al. 2017), and these results suggest that both models
have been validated, giving allowances for land shape.
A major goal of the population projection study was to determine which port
would produce the highest nest population (N10) given an invasion beginning at that port.
This study was less successful in achieving this goal: all ports studied except Anchorage,
AK occurred in habitats that were highly hospitable to V. velutina. Variation in nest
population (N10) can be explained by the shape of the land surrounding it. More land
available to settle leads higher populations. It is therefore not possible, based on these
data, to say which port should be the focus of heightened attention from authorities. In
the continuous major variable trial, Anchorage AK is a statistical outlier (Z<-3.0, Z>3.0)
based on z-score, but only that trial. The results of the ANOVA indicate that all the
distributions are statistically significantly different from each other across all trials, but
not that any given port was worthy of any special attention from authorities. This
conclusion is supported by the Mean Nest Density results: the majority of the mean nest
density for ports in the continuous, major variable trials (25th-75th percentile) ranged from
2.935-3.123 nests per square unit.
This study was less successful in ascertaining the risk of V. velutina invasion
itself. The lack of literature on invasion vectors accounted for this lack of success. This
study was able to generate an estimate of the maximal share of goods that could be
potential vectors, but a more-refined estimate was not possible.
This study was also unsuccessful in quantifying ecological damage caused by a V.
velutina invasion. A lack of literature on the ecological impacts of V. velutina in Europe
and Northern Asia, and a lack of literature concerning methods for calculating ecological
62

impacts, accounted for this lack of success. This study was marginally more successful in
generating predictions of economic costs of a V. velutina invasion. Economic impact data
was available from Europe and Northern Asia (Monceau et al. 2014), and economic data
from the United States was available (Smith et al. 2009), enabling calculations of
economic impact. These calculations represent an estimate of the maximal economic
impact, assuming an invasion of the entire United States. A full invasion of the United
States is unlikely, given that several large regions of the United States are inhospitable to
V. velutina (See Figures 5, 7), so this value is necessarily an overestimate. Literature on
pollinator impact by state is not available, but Flottum (2017) provided a means of
calculating impacts to honey production by state.
A study of the efficacy of countermeasures would logically be the next step in
researching a biological invasion of North America. Such a study would likely want to
look at the effects of increasing the proportion of resistant strains of bees (A. cerana and
A. melifera ligustica) in North American apiaries, or selective breeding programs, both
on V. velutina resistance and the ecological impacts such organisms must have. More
research is also needed into potential vectors of V. velutina, and more research is needed
into ecological impacts of V. velutina.
The theoretical ecology techniques used in this study raise a very powerful
prospect for the future of invasive species management: species likely to become invasive
in new habitats can be studied by habitat distribution modeling and population-dynamic
modeling years in advance of them actually becoming invasive. Modelers can give these
data, and their recommendations, to management authorities years in advance of the

63

invasion. In cases where inhospitable habitat separates suitable habitat, such habitats
could serve as crucial lines of redoubt for containing invasions.
Given the volume of trade serving as potential vectors of V. velutina invasion, it is
not practical to screen every possible potential vector. It is also not practical to prioritize
a port for targeted enforcement. There is no evidence that one port above the others will
lead to a worse invasion. It is however possible to eliminate Anchorage, AK as a
potential port of invasion. The most practical techniques for containing a V. velutina
invasion are those implemented in Europe and Korea: nest documentation and
destruction. North American managers do have access to a strategy not available in
Europe and Asia: screening goods shipped from the invaded coast to the non-invaded
coast.

64

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70

TABLES

TABLE 1: Summary of analysis comparing transportation criteria (Hulme 2009) to the
known biology of V. velutina. Table contains the criteria, conclusions of the criteria, and
the reasoning for those conclusions.
Hulme’s (2009) Criterion
The strength of the
association between the
species and the vector at the
point of export.
Volume of vector imports at
the point of interest
Frequency of importation

V. velutina Biology
Unknown.

Reasoning
No literature on Potential
Vectors.

Unknown

Survivorship and growth
during transport
Suitability of the importing
point to species
establishment
Appropriateness of the time
of year for
the establishment of the
species
The ease of containing
the species within the vector
Effectiveness of
management measures
Distribution of the vector
post importation
The likelihood of postimportation transport
to suitable habitat

Survivorship Unknown;
Growth =0 in transit.
Warm, wet urban ports

No literature on Potential
Vectors.
No literature on Potential
Vectors.
Inferred from life cycle of V.
velutina
Choi et al. 2012; Bessa et al.
2015; Franklin et al. 2016.

Unknown

January through the end of
March

Inferred from life cycle of V.
velutina

Unknown

No literature on Potential
Vectors.
Monceau et al. 2014.

Limited to Nest Destruction
at present.
unknown
Very Likely, as most ports
studied are already in
suitable habitat.

No literature on Potential
Vectors.
Results of the Establishment
Phase Simulation.

71

TABLE 2: Table of Equations, together with legends of variable meanings.
Y*=derivative or partial derivative of Y with respect to time, for all Y. Unless otherwise
specified, e=2.718 (Euler’s Constant).
Equation
Number
1

Equation
𝑃(𝑂𝑐𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑒) = 𝐵 + 𝐶/ 𝑉/ + 𝐶1 𝑉1 + ⋯

Description

Variables

Example Linear
Regression

B=intercept
Cn=nth regression coefficient
Vn=nth variable

Malthusian
Difference
Equation
Malthusian
Differential
Equation
Logistic
Differential
Equation

Nt+1=population at t+1
Nt=population at time t
r=innate rate of growth
N=population
r= innate rate of growth

2D Heat
Equation

D=innate rate of
diffusion
U=population density
at point (x,y) and time
t.

2D Heat
Equation plus a
differential
equation of
Growth.

D=innate rate of
Diffusion
U=population density
at point (x,y) and time
t.
N=Population

2D Heat
Equation plus
Logistic
Growth

D=innate rate of
Diffusion
U=population density
at point (x,y) and time
t.
N=Population

+ 𝐶3 𝑉3

2

𝑁56/ = 𝑁5 + 𝑟𝑁5

3

𝑁 ∗= 𝑟𝑁

4

𝑁
𝑁 ∗ = 𝑟𝑁(1 − )
𝐾

5

𝜕1𝑈 𝜕1𝑈
𝑈 = 𝐷( 1 + 1 )
𝜕𝑥
𝜕𝑦

6

7

8

9

∗

𝑈∗ = 𝐷 B

𝜕1𝑈 𝜕1𝑈
+
C + 𝑁∗
𝜕𝑥 1 𝜕𝑦 1

𝜕1𝑈 𝜕1𝑈
𝑁
𝑈 ∗ = 𝐷 B 1 + 1 C + 𝑟𝑁(1 − )
𝜕𝑥
𝜕𝑦
𝐾

𝑈 ∗ = 𝐷(𝑥, 𝑦) B

𝜕1𝑈 𝜕1𝑈
𝑁
+
C + 𝑟(𝑥, 𝑦)𝑁(1 −
)
𝜕𝑥 1 𝜕𝑦 1
𝐾(𝑥, 𝑦)

P

/ HJLM
J BK
O
1
𝑃(𝑥, 𝑦) =
𝑒 1 NM
2𝜋𝜎H 𝜎I

6Q

IJLR P
S C
NR

N=Population
r= innate rate of growth
K=Carrying Capacity

r= innate rate of growth
K=Carrying Capacity

Patched
FisherSkellam
Differential
Equation
3D Gaussian
Curve

D=innate rate of
Diffusion
U=population density at
point (x,y) and time t.
N=Population
r= innate rate of growth
K=Carrying Capacity

𝜎H =Standard deviation
of x
𝜎I =standard Deviation
of y
𝜇H =Mean of x
𝜇I =Mean of y

72

Equation
Number
10

Equation

𝑟𝑁5J/
𝑁5 = 𝑃𝑜𝑖𝑠𝑠𝑜𝑛 X
Y
𝑁5J/
1+ 𝐾

11

12

𝑃Z[ = 𝑒

J

\]^
L 𝑇𝑒𝑟𝑟𝑎𝑖𝑛

[

𝑃(𝑖, 𝑦)
= 𝑛𝑟𝐸d 𝑓(𝑙𝑎𝑡d ) g𝑒

\hi
J j
L 𝑇𝑒𝑟𝑟𝑎𝑖𝑛

kj l g𝑒

13

g𝑒

\hi
J P
L 𝑇𝑒𝑟𝑟𝑎𝑖𝑛

\hp
J L

𝑃(𝑞|𝑗, 𝑦 + 1) = 𝑛𝑟𝐸d 𝑓(𝑙𝑎𝑡d )
∑𝑒

kP l

𝑇𝑒𝑟𝑟𝑎𝑖𝑛q l

\hs
J L
𝑇𝑒𝑟𝑟𝑎𝑖𝑛

Description

Variables

Franklin et al.
(2016)
Equation

Nt-1=population at t-1
Nr=population at time t
r=innate rate of growth
K=Carrying Capacity

Keeling et al.
(2017) equation
1

µ=mean flying Distane
∆jk=distance between
both sites.
Terraink=quality of kth
terrain.

Keeling et al.
(2017) equation
2

N=normalizing coefficient
r=innate rate of growth
Ei=Suitability of ith
environment
f(lati)=position function
µ=mean flying Distane
∆jk=distance between both
sites.

Keeling et al.
(2017) equation
3

N=normalizing coefficient
r=innate rate of growth
Ei=Suitability of ith
environment
f(lati)=position function
µ=mean flying Distane
∆jk=distance between both
sites.

t

14

𝑃(𝑞|𝑦 + 1) = u 𝑃𝑜𝑠𝑡(𝑟) vw 𝑝d I y 𝑝q|d I6/

Keeling et al.
(2017) equation
4

Post(r)=Posterior
Distribution

15

𝑁56/ = 𝑁5 𝑄𝑆

Archer (1985)
equation

16

𝑁56/ = 𝑁5 𝑄𝑆(𝑥, 𝑦)

Patched
Archer (1985)
equation

17

𝑀 = [𝐸d ] ∪ [𝑟d ] ∪ €𝑃Z[ • ∪ €𝑂Z[ •

Formal
Definition of
a Markov
Chain

18

𝑁 = 𝑁‚ 𝑟ƒ

Discrete
Growth Phase

Nt+1=population at t+1
Nt=population at time t
Q=number of gynes
produced per hive
S=overwinter survival rates.
Nt+1=population at t+1
Nt=population at time t
Q=number of gynes
produced per hive
S=overwinter survival rates.
[Ei]=set of environments
[ri]=set of growth rates
[pjk]=set of paths connecting
environments j and k.
[Ojk]=set of probabilities of
transmission from j to k.
Ns=Population at the end of
the Spread Phase
re=rate of growth at
environment e.

19

[

[

𝑁(𝑒, 𝑡 + 1) = w 𝑁(𝑖, 𝑡)𝑂dƒ − w 𝑁(𝑒, 𝑡)𝑂ƒd (d„ƒ)
d

d

Discrete
Spread Phase

N(e,t+1)=Population at
environment e at time t+1
N(I,t)=Population at the ith
environment at time t.
Oie=probability of a member
of a population at I migrating
to e.
N(e,t) =population at e at
time t.

73

Oei=probability that a
member of the population at
e will leave e.

Equation
Number
20
21

Equation

𝑁 = 𝑁‚ 𝑄𝑆ƒ
𝑃(𝑂𝑐𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑒)
=

22

1
1+

𝑒 J….‡…ˆ‰ˆ‰/‡6‰.‰/…Š‰1‹Œ6‰./…ˆŠ•‹t
5

𝑈(𝑥, 𝑦, 𝑡) = u 𝐷(𝑥, 𝑦) B
‰

𝜕1𝑈 𝜕1𝑈
+
C
𝜕𝑥 1 𝜕𝑦 1

+ 𝑟(𝑥, 𝑦)𝑈 Q1 −

23

𝑈(𝑥, 𝑦, 0)
P

/ HJ•
J BK
O
1
=
𝑒 1 1.‡
11.52𝜋

24

𝑈
S 𝜕𝑈
𝐾(𝑥, 𝑦)

IJ‘ P
6K
O C
1.‡

5
𝜕1𝑈 𝜕1𝑈
𝑈(𝑥, 𝑦, 𝑡) = u 51.84 B 1 + 1 C
𝜕𝑥
𝜕𝑦
‰

+ 2.415𝑃˜™™šk (𝑥, 𝑦)𝑈 Q1
−

Description

Variables

Combination
of equations
15 and 18
Logistic
Regression
Equation

Ns=Population at the end of
the Spread Phase
Se=Overwinter survival at
environment e.

Integral of the
restatement of
equation 8 in
terms of U

D=innate rate of
Diffusion
U=population density at
point (x,y) and time t.
N=Population
r= innate rate of growth
K=Carrying Capacity

Restatement
of Equation 9
with values

[J,K]=mean located
at the point (J,K)

W=mean winter
temperature
P=Mean yearly
rainfall

Restatement
of Equation
22 with
values.

𝑈
S 𝜕𝑈
7.397

74

TABLE 3: Summary of the constants and their values used in the Growth and Spread
Simulation, together with their units, the method of their calculation, and the sources of
the value.
Constant
D

Value
51.84

Unit
Unit/Year

K

7.397

Nests/Unit

Max. r

2.415

NA

t
Standard
Deviation
h
Max Pop.
Density
Elevation above
which AH
habitation
is unlikely
River Presence
and Absence

10
2.4

years
Units

0.000001
2000

Square Units
humans/unit

791

meters

1,0

NA

Calculation
Source
Unit Conversion Robinet et
al. 2017
Unit Conversion Robinet et
al. 2017
Archer 1985;
Rome 2015
From max yearly Robinet et al.
invasion wave 2017
Definition
Definition
Robinet et al.
2017
Definition

75

TABLE 4: Sites in the Test Group, together with GPS coordinates and the Matrix indices
used to represent the port.
Site #

Site

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

Anchorage AK
Baltimore MD
Biloxi MS
Boston MA
Charleston SC
Houston TX
Jacksonville FL
Los Angeles CA
Miami FL
Mobile AL
New Orleans LA
New York NY
Pensacola FL
Philadelphia PA
Port Charlotte-Ft. Myers
FL
Portland ME
Portland OR
Providence RI
San Francisco CA
Savannah GA
Saint John NB
St. Petersburg-Tampa FL
Seattle WA
Vancouver BC

16
17
18
19
20
21
22
23
24

GPS Coordinates
Long,Lat
-148.9, 61.216
- 76.6122, 39.2904
- 88.8853, 30.3960
-71.0589, 42.3601
- 79.9311, 32.7765
- 95.3698, 29.7604
- 81.6557, 30.3322
- 118.2437, 34.0522
- 80.1918, 25.7617
- 88.0399, 30.6954
- 90.0715, 29.9511
- 74.0060, 40.7128
- 87.2169, 30.4213
- 75.1652, 39.9526
- 81.8606, 26.6031

Matrix Index
Used [Row, Column]
[287, 301]
[506, 1033]
[595, 911]
[476, 1089]
[572, 1000]
[602, 846]
[596, 983]
[559, 617]
[642, 997]
[593, 918]
[600, 899]
[492, 1059]
[595, 927]
[500, 1048]
[632, 981]

- 70.2568, 43.6591
-122.6750, 45.5051
- 71.4128, 41.8240
-122.4194, 37.7749
- 81.0912, 32.0809
- 66.0633, 45.2733
- 82.6403, 27.7676
- 122.3321, 47.6062
- 123.1207, 49.2827

[463, 1097]
[444, 573]
[481, 1085]
[522, 575]
[578, 989]
[447, 1139]
[620, 975]
[422, 576]
[407,568]

76

TABLE 4: A) Sites in the Positive Control Group, together with their GPS coordinates
and the Matrix Index used to represent it. B) Sites in the Negative Control Group,
together with their GPS coordinates and the Matrix Index used to represent it.
A)
Site #

Site

GPS Coordinate
Used
Long., Lat.

Index Used
[Row, Column]

25

Montreal, QC

- 73.5673, 45.5017

[ 448,1068]

26

Walhalla SC

- 83.0640, 34.7648

[555,966]

27

Busan, South Korea 179.0667,35.1667

[548,3090]

28

Nerac, France

0.3342, 44.1316

[458,1803]

29

Tsushima City,

129.2833, 34.200

[558,3092]

Japan

B)
Site #

Site

Index Used
[Row, Column]

Albuquerque NM

GPS Coordinate
Used
Long., Lat.
- 106.6504, 35.0844

30
31

Barry County MI

- 85.3550, 42.5354

[475, 946]

32

St Paul MN

- 93.0900, 44.9537

[450,869]

[549, 734]

77

TABLE 6: Model Statements with Trial Codes, Trial Numbers, and the Method each
Model uses to calculate r(x,y). Trial codes presented are for continuous trials. Discrete
trials add D to the beginning of the continuous trial code. Odd trial numbers represent the
continuous version of the model statement, while even numbers represent the discrete
version of the model statement. These trial numbers are represented by the x-axis of
Figure 13.
Trial #

Trial
Code

Model Statement

Formula for Calculating r(x,y)

1,2

C

Land Control

=1 for all cells

3,4

O

Occurrence Probability Only

Poccur(x,y) *2.415

5,6

H

Human Population Density Only

7,8

R

River Presence Only

Riv(x,y)*2.415

9,10

E

Elevation Only

Elev(x,y)*2.415

11,12

OH

Occurrence x Human Population Density

Poccur(x,y)*Pop(x,y)*2.415

13,14

OR

Occurrence x River Presence

Poccur(x,y)*Riv(x,y)*2.415

15,16

OE

Occurrence x Elevation

Poccur(x,y)*Elev(x,y)*2.415

17,18

HR

Human Population Density x River Presence Pop(x,y)*Riv(x,y)*2.415

19,20

HE

Human Population Density x Elevation

Pop(x,y)*Elev(x,y)*2.415

21,22

RE

River Presence x Elevation

Riv(x,y)*Elev(x,y)*2.415

23,24

OHR

Occurrence x Human Population
Density x Rivers

Poccur(x,y)*Pop(x,y)*Riv(x,y)*2.415

25,26

OHE

Occurrence x Human Population
Density x Elevation

Poccur(x,y)*Pop(x,y)*Elev(x,y)*2.415

27,28

HRE

Human Population Density x Rivers x
Elevation

Pop(x,y)*Riv(x,y)*Elev(x,y)*2.415

29,30

ALL

Occurrence x Human Population
Density x Rivers x Elevation

Poccur(x,y)*Pop(x,y)*Riv(x,y)*Elev(x,y)*2.415

˜t(H,I)
1‰‰‰

*2.415

78

TABLE 7: Impact on Honeybee production by State. The “State” column contains the sta
ndard abbreviations for the U.S. State. “Product” is the Honey Production by State in 1,0
00 USD (Flottum 2017). “Suitable” is =1 if there is suitable habitat in that state, and =0 if
there is no suitable habitat in that state (See Figure 7) Total impact from these states is $9
,904,350 USD. Table Generated by R Package “Stargazer” (Hlavac 2018).
Impact
State #

State

Product 1000 USD

Suitable

1000
USD

1

AL

873

1

43.650

2

AZ

1,725

1

86.250

3

AR

4,265

1

213.250

4

CA

28,706

1

1,435.300

5

CO

2,923

1

146.150

6

FL

21,156

1

1,057.800

7

GA

9,377

1

468.850

8

HI

2,374

1

118.700

9

ID

7,482

1

374.100

10

IL

2,409

1

120.450

11

IN

1,324

1

66.200

12

IA

4,507

1

225.350

13

Ks

2,312

1

115.600

14

KY

775

1

38.750

15

LA

6,548

1

327.400

16

ME

2,158

1

107.900

17

MI

9,435

1

471.750

18

MN

4,530

0

0

19

MS

1,882

1

94.100

20

MO

1,836

1

91.800

21

MT

24,012

1

1,200.600

22

NE

5,266

0

0

23

NJ

2,861

1

143.050

79

Impact
State #

State

Product 1000 USD

Suitable

1000
USD

24

NY

9,608

1

480.400

25

NC

1,957

1

97.850

26

ND

63,636

0

0

27

OH

3,416

1

170.800

28

OR

5,897

1

294.850

29

PA

2,502

1

125.100

30

SC

1,665

1

83.250

31

SD

27,762

0

0

32

TN

1,343

1

67.150

33

TX

16,711

1

835.550

34

UT

1,724

1

86.200

35

VT

1,314

1

65.700

36

VA

1,003

1

50.150

37

WA

7,796

1

389.800

38

WV

924

1

46.200

39

WI

8,221

0

0

40

WY

3,287

1

164.350

80

TABLE 8: Summary of the calculations of the risk of transportation of V. velutina into
the United States.
Source
Population
China
Korea
France
Total:

1st Quarter
Total Yearly
Trade 2019 (BillionsTrade 2019
of US Dollars)
(Billions of US
Dollars)
105.9739
418.575
19.8839
70.7191
14.1397
53.4974
139.995
542.791

% of Total
Yearly Trade
25.32
28.11
26.43
N/A

% of Total US
Imports 2018
(2563.651 Billion
US Dollars)
4.134
0.775
0.552
5.461

81

TABLE 9: Summary of the calculations of the risk of transportation of V. velutina into
Canada.
Import Values
from Europe
(1000 Canadian
Dollars)
82,653,655

Total
Imports
¼
20,663,413.75
of imports

Import Values
from Asia
(1000 Canadian
Dollars)
128,300,426

Total
% of Total Imports
(1000 Canadian (564,297,051,000 CD)
Dollars)
210,954,081

37.383%

32075106.50

52,738,520.25

9.345%

82

TABLE 10: Summary Statistics of Nest Projections after 10 years (N10) of the test
groups. All units are in Nests. Table Generated by R Package “Stargazer” (Hlavac 2018).
Trial
C
DC
O
DO
H
DH
R
DR
E
DE
OH
DOH
OR
DOR
OE
DOE
HR
DHR
HE
DHE
RE
DRE
OHR
DOHR
OHE
DOHE
HRE
DHRE
ALL
DALL

Means
St.Dev
Min
Max
Range
9.206083
2.647439
2.647439
12.845
10.19756
0.299113
0.218101
0.173784
1
0.826216
222.7439
65.89757
5.454
311.964
306.51
289.8275
126.1021
0.138655
439.8218
439.6832
14.82025
30.36555
-16.916
99.88
116.796
0.087967
0.281478
1.19E-14
1
1
37.7025
22.89726
17.357
92.18
74.823
3.506447
2.658928
1
11.7447
10.7447
227.3673
50.06505
50.06505
311.192
261.1269
262.7155
129.0834
1
431.9165
430.9165
14.69858
30.45055
-16.916
99.88
116.796
0.087938
0.281485
8.32E-32
1
1
17.78671
13.87871
-1.684
52.285
53.969
0.597163
0.434697
0.004421
1.84934
1.844919
123.8779
35.77859
17.31
174.983
157.673
120.5644
71.20098
0.155001
204.2721
204.1171
37.20604
23.1366
14.707
92.18
77.473
0.083338
0.282328
1.17E-17
1
1
14.81967
30.36432
-16.916
99.869
116.785
0.087906
0.281492
1.19E-14
1
1
37.20604
23.1366
14.707
92.18
77.473
3.135698
2.932463
0.122799
11.7447
11.6219
-7.67393
4.998902
-18.4536
4.998902
23.45247
0.083338
0.282328
8.12E-35
1
1
4.689659
18.45213
-17.5556
53.96497
71.52054
0.083334
0.28233
2.09E-21
1
1
-5.456
6.518497
-18.3252
6.518497
24.84371
0.083338
0.282328
1.17E-17
1
1
-7.67407
4.998869
-18.4536
4.998869
23.45244
0.083334
0.28233
2.09E-21
1
1

83

TABLE 11: Summary Statistics of Nest Projections after 10 years (N10) of the positive
control group. All units are in Nests.
Trial

Means

St.Dev

Min

Max

Range

C

8.686036

6.296198

-1.35245

12.84592 14.19837

DC

0.324116

0.21772

0.21489

0.711775 0.496885

O

211.3624

124.7196

27.357

311.9645 284.6075

DO

295.4947

182.0664

33.68451

440.829 407.1445

H

-1.05997

22.11139

-14.6894

37.73063 52.42006

DH

0.000944

0.002111

0

0.004721 0.004721

R

53.09421

39.45305

0.46196

DR

5.171332

2.540185

2.540185

9.296599 6.756414

E

220.9579

129.3804

27.357

311.9617 284.6047

DE

291.142

170.714

33.68451

440.829 407.1445

OH

-1.0921

22.12406

-14.6894

37.72569 52.41512

DOH

0.000761

0.001703

0

0.003807 0.003807

OR

26.59586

21.64653

-1.35245

54.58461 55.93706

DOR

0.716341

0.419361

0.419361

1.437427 1.018066

OE

120.3965

70.64999

14.84971

175.389 160.5393

DOE

100.8953

52.43802

26.60819

166.0678 139.4596

HR

-5.99571

12.21505

-14.7538

14.46248

29.2163

DHR

8.64E-06

1.93E-05

0

4.32E-05

4.32E-05

HE

-1.05997

22.11139

-14.6894

37.73063 52.42006

DHE

0.000944

0.002111

0

0.004721 0.004721

RE

52.97759

39.26183

0.46196

104.3679 103.9059

DRE

4.396096

1.25215

1.25215

5.778534 4.526384

OHR

-7.94798

9.247058

-14.7757

9.247058 24.02272

DOHR

7.37E-06

1.65E-05

0

OHE

-4.98596

14.99171

-14.7266

20.71365 35.44024

DOHE

0.000128

0.000286

0

0.000639 0.000639

104.951

3.68E-05

104.489

3.68E-05

84

Trial

Means

St.Dev

Min

Max

Range

HRE

-5.99571

12.21505

-14.7538

14.46248

29.2163

DHRE

8.64E-06

1.93E-05

0

4.32E-05

4.32E-05

ALL

-7.94798

9.247058

-14.7757

DALL

1.20E-06

2.69E-06

0

9.247058 24.02272
6.02E-06

6.02E-06

85

TABLE 12: Summary Statistics of Nest Projections after 10 years (N10) of the negative
groups. All units are in Nests. Table made with “Stargazer” (Hlavac 2018).
Trial

Means

C

12.84592

0

0 12.84592 12.84592

0.21489

0

0

DC

St.Dev

Min

Max

0.21489

Range

0.21489

O

3.244912 26.66573

-14.7457 33.88079 48.62649

DO

6.733086 11.66205

5.08E-19 20.19926 20.19926

H

-0.24212

12.0827

-13.1205

12.0827

25.2032

DH

5.09E-09

8.81E-09

0

1.53E-08

1.53E-08

R

70.26567 35.22918

30.389

97.167

66.778

DR

3.472664 2.062487 1.971025 5.824315 3.853291

E

203.0277 188.6841

-14.8459 311.9645 326.8105

DE

293.1201 253.8495

0 439.6802 439.6802

OH

-14.6566 0.297953

DOH

2.61E-29

OR

-2.63198 1.259693

DOR

0.010769 0.017208 0.000719 0.030638 0.029919

OE

21.54878

41.0471

-14.8459 66.04125 80.88719

DOE

7.569119 12.91092

0 22.47677 22.47677

HR

-6.42195 10.49922

-14.4772 10.49922 24.97647

DHR

2.05E-10

HE

-5.70718 14.36045

DHE

5.09E-09

RE

37.57046 56.35099

-14.8459 97.16766 112.0136

DRE

2.598447 2.962416

0 5.824315 5.824315

OHR

-13.7749

1.13904

-14.6694

DOHR

1.39E-30

2.40E-30

0

-13.633

1.57345

-14.8459

OHE

4.51E-29

3.55E-10

8.81E-09

-14.8328 0.297953
0

7.82E-29

15.1308
7.82E-29

-3.66749 1.259693 4.927183

0

6.15E-10

6.15E-10

-14.8459 14.36045 29.20639
0

1.53E-08

1.53E-08

1.13904 15.80844
4.16E-30

4.16E-30

1.57345 16.41939

86

Trial

Means

St.Dev

Min

Max

Range

DOHE

3.35E-14

5.80E-14

0

1.00E-13

1.00E-13

HRE

-7.95699 11.61418

DHRE

2.05E-10

ALL

-14.0026 1.310719

DALL

3.35E-14

3.55E-10

5.80E-14

-14.8459 11.61418 26.46011
0

6.15E-10

6.15E-10

-14.8459 1.310719 16.15666
0

1.00E-13

1.00E-13

87

TABLE 13: Summary Statistics for Mean Nest Density of the Test Groups. All units are
in nests. Table was made with “Stargazer” (Hlavac 2018).
Trial

Means

St.Dev

Min

Max

Range

C

0.124029 0.035277 0.035277 0.192892 0.157615

DC

0.004235 0.003688 0.002165 0.016667 0.014502

O

2.948504 0.631156

DO

3.784934

H

0.190696 0.395825

-0.21687 1.280513 1.497385

DH

0.001394 0.004516

1.66E-16 0.016667 0.016667

R

0.491018 0.261401 0.253051 1.197143 0.944092

DR

0.046413 0.033197 0.015385 0.152529 0.137144

E

3.008939 0.239235 0.239235 3.512986

DE

3.423084 1.532854 0.015385 4.407311 4.391926

OH

0.189006 0.397015

-0.21687 1.280513 1.497385

DOH

0.001394 0.004516

1.16E-33 0.016667 0.016667

OR

0.231173 0.165216

-0.02339 0.679026 0.702415

DOR

0.008095 0.005791

6.14E-05 0.024017 0.023956

OE

1.637377 0.323778 0.240417 1.959986 1.719569

DOE

1.596143 0.948873 0.002153 2.726958 2.724806

HR

0.483616 0.262584 0.188551 1.197143 1.008592

DHR

0.001336 0.004528

1.62E-19 0.016667 0.016667

HE

0.190688

0.39581

-0.21687 1.280372 1.497244

DHE

0.001394 0.004516

1.66E-16 0.016667 0.016667

RE

0.483616 0.262584 0.188551 1.197143 1.008592

DRE

0.041268 0.036909 0.001574 0.152529 0.150954

OHR

-0.10154 0.063072

-0.23658 0.063072 0.299657

OHE

0.059322 0.242268

-0.22507 0.691859

DOHE

0.001335 0.004528

2.91E-23 0.016667 0.016667

HRE

-0.07329 0.084532

-0.23494 0.084532

0.07575 3.512986 3.437236

1.46112 0.001926 4.407311 4.405385

3.27375

0.91693

0.31947
88

Trial

Means

St.Dev

Min

Max

Range

DHRE

0.001336 0.004528

1.62E-19 0.016667 0.016667

ALL

-0.10154 0.063072

-0.23658 0.063072 0.299656

DALL

0.001335 0.004528

2.91E-23 0.016667 0.016667

89

TABLE 14: Summary Statistics for Mean Nest Density of the Positive Controls. All units
are in nests. Table was made with “Stargazer” (Hlavac 2018).
Trial

Means

St.Dev

Min

Max

Range

C

0.067765 0.132411

DC

0.020118 0.038512 0.002149 0.088972 0.086823

O

3.011135 0.311897 0.311897 3.419625 3.107727

DO

4.070482 0.398905 0.398905

H

-0.03591

0.46782

DH

1.85E-05

4.14E-05

R

0.63314

0.41144 0.057745

-0.16906 0.132411 0.301467

4.40829 4.009386

-0.53158 0.739816 1.271401
0

9.26E-05

9.26E-05

1.04951 0.991765

DR

0.148674 0.181153 0.028427 0.466614 0.438187

E

3.120518 0.195267 0.195267 3.419625 3.224358

DE

4.101137 0.454023 0.454023

OH

-0.03624 0.467829

DOH

1.49E-05

OR

0.284958 0.298709

DOR

3.34E-05

4.40829 3.954268

-0.53158 0.739719 1.271304
0

7.47E-05

7.47E-05

-0.16906 0.545846 0.714902

0.02436 0.036324 0.004349 0.088972 0.084623

OE

1.699962 0.118569 0.118569 1.856214 1.737645

DOE

1.797211 0.925386 0.878765 3.326024 2.447259

HR

-0.12999 0.288762

DHR

1.69E-07

3.79E-07

HE

-0.03591

0.46782

DHE

1.85E-05

4.14E-05

RE

0.631974

0.40997 0.057745 1.043679 0.985934

DRE

0.140922 0.184952 0.028427 0.466614 0.438187

OHR

-0.1645 0.236645

OHE

-0.10787 0.334293

DOHE

2.51E-06

HRE

-0.12999 0.288762

5.60E-06

-0.53168 0.288762 0.820439
0

8.47E-07

8.47E-07

-0.53158 0.739816 1.271401
0

9.26E-05

9.26E-05

-0.53169 0.236645 0.768336
-0.53162
0

0.40615 0.937769
1.25E-05

1.25E-05

-0.53168 0.288762 0.820439
90

Trial
DHRE
ALL
DALL

Means

St.Dev

Min

Max

Range

1.69E-07

3.79E-07

0

8.47E-07

8.47E-07

-0.1645 0.236645
2.36E-08

5.28E-08

-0.53169 0.236645 0.768336
0

1.18E-07

1.18E-07

91

TABLE 15: Summary Statistics for Mean Nest Density of the Negative Controls. All
units are in nests. Table was made with “Stargazer” (Hlavac 2018).
Trial

Means

St.Dev

Min

Max

Range

C

0.128459

0

0 0.128459 0.128459

DC

0.002149

0

0 0.002149 0.002149

O

0.032449 0.266657

0.14746 0.338808 0.486265

DO

0.067331

0.11662

5.08E21 0.201993 0.201993

H

-0.00242 0.120827

-0.1312 0.120827 0.252032

DH

5.09E-11

8.81E-11

0

1.53E-10

1.53E-10

R

0.702657 0.352292

0.30389

0.97167

0.66778

DR

0.034727 0.020625

0.01971 0.058243 0.038533

E

2.030277 1.886841

0.14846 3.119645 3.268105

DE

2.931201 2.538495

0 4.396802 4.396802

OH

-0.14657

0.00298

0.14833

DOH

2.61E-31

4.51E-31

0

0.00298 0.151308
7.82E-31

7.82E-31

OR

-0.02632 0.012597

0.03667 0.012597 0.049272

DOR

0.000108 0.000172

7.19E06 0.000306 0.000299

OE

0.215488 0.410471

0.14846 0.660413 0.808872

DOE

0.075691 0.129109

0 0.224768 0.224768

HR

-0.06422 0.104992

0.14477 0.104992 0.249765

DHR

2.05E-12

HE

-0.05707 0.143605

DHE

5.09E-11

3.55E-12

8.81E-11

0

6.15E-12

6.15E-12

0.14846 0.143605 0.292064
0

1.53E-10

1.53E-10
92

Trial

Means

St.Dev

Min

Max

Range

RE

0.375705

0.56351

0.14846 0.971677 1.120136

DRE

0.025984 0.029624

0 0.058243 0.058243

OHR

-0.13775

0.01139

OHE

-0.13633 0.015734

DOHE

3.35E-16

5.80E-16

HRE

-0.07957 0.116142

DHRE

2.05E-12

3.55E-12

ALL

-0.14003 0.013107

DALL

3.35E-16

5.80E-16

0.14669

0.01139 0.158084

0.14846 0.015734 0.164194
0

1.00E-15

1.00E-15

0.14846 0.116142 0.264601
0

6.15E-12

6.15E-12

0.14846 0.013107 0.161567
0

1.00E-15

1.00E-15

93

TABLE 16: Outputs of the three One-Way ANOVAs. The first ANOVA compares N10
for Trial O to the other continuous trials, while comparing N10 for Trial DO to all other
discrete trials. The second ANOVA compares N10 and Mean Nest Density of Anchorage,
AK, to the N10 and Mean Nest Density to all other sites in the test group. The third
ANOVA compares N10 of the test group for all trials to N10 of the positive and negative
control groups. The One-Way ANOVA model (R Core Team) requires one variable
designated for comparison. The p-values indicate that Alaska is significantly different
than the other ports for all trials. Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’
1

Trial

P-Value –
N10
Projections

Site

1.08e-13 ***
C

Anchorage
1.47e-06 ***

DC

P-Value –
N10
Projections

P-Value Mean Nest
Density

Trial Group

P-value

N/A

N/A

Positive
Control

0.301

< 2e-16 ***

3.15e-15 ***

Negative
Control

<2e-16 ***

Baltimore

O

N/A

Biloxi

5.25e-07 ***

9.38e-09 ***

DO

N/A

Boston

9.93e-08 ***

7.72e-10 ***

0.000454
***

4.24e-13 ***

Charleston

1.85e-10 ***

4.10e-09 ***

9.69e-15 ***
H
0.963430
DH

Houston

R

8.28e-13 ***

Jacksonville

3.27e-09 ***

4.79e-08 ***

DR

0.024648 *

Los Angeles

< 2e-16 ***

8.31e-15 ***

E

< 2e-16 ***

Miami

0.967191

0.385207

3.82e-07 ***

2.80e-06 ***

DE

0.000194
***

Mobile

OH

< 2e-16 ***

New Orleans

1.71e-08 ***

2.05e-07 ***

DOH

0.860158

New York

5.25e-07 ***

4.09e-06 ***

OR

1.27e-14 ***

Pensacola

9.93e-08 ***

8.41e-07 ***

Philadelphia

0.000454
***

0.000685
***

2.00e-11 ***

6.04e-10 ***

2.23e-08 ***
DOR
< 2e-16 ***
OE

Port Charlotte

DOE

0.571501

Portland ME

1.22e-13 ***

7.72e-12 ***

HR

0.949

Portland OR

< 2e-16 ***

1.56e-14 ***

DHR

0.744362

Providence

5.81e-07 ***

4.73e-06 ***

94

Site

Trial

P-Value –
N10
Projections

P-Value –
N10
Projections

P-Value Mean Nest
Density

HE

2.87e-07 ***

San Francisco

0.115240

0.146754

DHE

0.568416

Savannah

0.093864

0.124283

1.13e-11 ***

3.73e-10 ***

0.08795

0.08043

0.000123
***

0.000403
***

0.882858

0.901461

1.66e-10 ***
RE
DRE

Trial Group

P-value

SaintJohn
0.002876 **

St Petersburg

0.177
OHR

Seattle
0.0124 *

DOHR

Vancouver

OHE

0.276

DOHE

0.521720

HRE

6.70e-05 ***

DHRE

4.983e11***

ALL

0.858

DALL

4.983e11***

95

TABLE 17: Summary of Economic Impact Cost Calculations in the United States.
Calculations are based on trial means from O and DO, being the highest trial means.
Calculation Steps Pollinator
Services
(U.S.D.)
Total Value
10.95 billion
Means
ContinuousDiscrete
Low Estimate
ContinuousDiscrete
High Estimate
[
5% of the value
Total Impact

Honey
Production
(U.S.D)
353 million

Removal Cost
(U.S.D)
140.96-542.15 (accessed 2.21.20,
Bloomberg.com)
222.745-289.823
31,398.135 – 40,853.450
120,761.202- 157,127.539

547,500,000.0 17,650,000.0
565,150,000.0

565,181,398.135 – 565190853.539
565,270,761.202
– 565,307,127.539

96

TABLE 18: Summary of Economic Impact Cost Calculations in the Canada. Calculations
are based on trial means from O and DO, being the highest trial means.
Calculation Steps
Total Value
Means
Continuous-Discrete
Low Estimate
Continuous-Discrete
High Estimate
[
5% of the value
Total Impact

Honey
Production
(C.A.D)
129.5 million

Removal Cost
(C.A.D.)
186.429-694.04 (accessed 2.21.20,
Bank of Canada)
222.745-289.823
41,526.350- 54,031.701
154,593.9398- 207,397.338

6,475,218. 878
6,475,218. 878

6,516,745.228 – 6,529,250.579
6,629,812.816 – 6,682,616.216

97

FIGURES

FIGURE 1: Diagram of V. velutina life cycle (Monceau et al. 2014).

98

FIGURE 2: An illustration of the phases of biological invasions, sensu lato (Sakai et al.
2001). Phases were modeled for a hypothetical biological invasion by V. velutina:
Transportation from importation records, Establishment in an ecological niche model,
Spread predicted by FisherSkellam and Archer-Markov simulations, and invasive species
impact estimated using estimated economic values.

99

FIGURE 3: V. velutina Occurrence in Europe (GBIF.org. Accessed 2019). Dark Red is
positive for an V. velutina nests. Map created in QGIS (QGIS Development Team 2019).

100

FIGURE 4: V. velutina Occurrence in Europe (GBIF.org. Accessed 2019). Dark Red is
positive for an V. velutina nests. Map created in QGIS (QGIS Development Team 2019).

101

FIGURE 5: Heat map of V. velutina habitat suitability, defined as the probability of
occurrence. Map was generated in QGIS (QGIS Development Team 2019) from the
output raster of the Niche Analysis, Darkest red indicates the probability of occurrence
=1, to wit highly suitable habitat, while light pink indicates probability of occurrence=0,
highly inhospitable habitat.

102

FIGURE 6: Program Architecture for the Niche Analysis script.

103

FIGURE 7: Program Architecture of the Continuous Growth and Spread Simulation. The
Discrete Simulation differs only in that the Main Algorithm carries out the Markov Chain
Calculation rather than solving a differential equation.

104

FIGURE 8: Human Population Density in the North America. (CIESIN, 2018). Darkest
Red have the maximum Hunan Population Density (> 2000 people per km). Original map
contained population density for the entire world. This map was clipped from the larger
one. Map created in QGIS (QGIS Development Team 2019).

105

FIGURE 9: Major River Courses in North America. (Kelso and Patterson 2009). Dark
red indicates River Presence =1.while pink indicates River Presence=0. Map was of the
entire world. This map was clipped from that larger map. Map created in QGIS. (QGIS
Development Team 2019).

106

FIGURE 10: Elevation (m) in North America. (Archuleta et al. 2017). The input raster
contained elevation data from the entire world. This map was clipped from a portion of
that map. Darkest red has the highest elevation. Map created in QGIS (QGIS
Development Team 2019)..

107

FIGURE 11: Habitat suitability of V. velutina by US State. US vector shapefile obtained
from the National Weather Service (Accessed 15 June 2020). Map generated in QGIS
3.8.3 (QGIS Development Team 2019).

108

FIGURE 12: Geometry of a distribution of a Continuous Trial with negative nest density
at the point of origin. Map was created from the output raster of trial O beginning in St.
Paul, MN. Map was created in QGIS (QGIS Development Team 2019).

109

FIGURE 13: Nest Projection (N10) Means for Each Trial with Standard Error. Character
denotes whether the trial was Continuous or Discrete. Trial Number is listed in Table 5.
Graph was generated using the “ggplot2” package (Wickham 2016) in R (R Core Team
2019).

110

FIGURE 14: A) Boxplot of N10 Distributions for all trials for the Test Group; B)
Boxplot of N10 Distributions for all trials for the Positive Control Group; C) Boxplot of
N10 Distributions for all trials for the Negative Control Group. All Boxplots were made
with ggplot2 (Wickham 2016) and reshape (Wickham 2007).

111

A)

B)

FIGURE 15: A) Boxplots of N10 projections for all sites across all trials. B) N10
projections by site for Trials O (teal) , DO (red), Mean Nest Density for Trial O (purple),
and Mean Nest Density for Trial DO (Green). Site numbers can be found in Tables 4 and
5. All Boxplots were made with ggplot2 (Wickham 2016) and reshape (Wickham 2007).

112

A) Continuous Geometry

B) Discrete Geometry

FIGURE 16: A comparison of the geometries of the distributions produced by (A) the
continuous simulation and (B) the discrete simulation. Both maps were generated in
QGIS (QGIS Development Team 2019) from the output rasters of the trials O and DO
respectively.

113

FIGURE 17: Boxplots of distributions of the means of the continuous trials (Column1)
and the discrete trials (Column 2). The y-axis represents population projections after ten
years, N10, in nests. The boxplots was generated using the “boxplot” command (R Core
Team 2019) in base R.

114

A-Test Sites

B-All Sites

FIGURE 18: Boxplots of distributions of the continuous trial O (Column1) and the
discrete trial DO (Column 2). The y-axis represents population projections after ten years,
N10, in nests. (A) Comparison of the distributions of the test groups between the two
trials. (B) Comparison of the distributions of all sites, test group and control group
together. Boxplots were generated using the “boxplot” command (R Core Team 2019) in
base R.

115

FIGURE 19: Boxplot of N10 Population Projections for the Test Group, Negative Control
Group, and Positive Control Group across all Trials. All Boxplots were made with
ggplot2 (Wickham 2016) and reshape (Wickham 2007).

116

A)

B)

C)

FIGURE 20: A) Biplot of the Principle Components Analysis (PCA) of the Nest
Projections after 10 years (N10) for the test group. PCA and Biplot performed in R (R
Core Team 2019). B) Elbow Plot of the variances explained by Principle Components.
Elbow plot created in R (R Core Team 2019). C) Plot of Principle Component 1 by
Principle Component 2, colored for Human Population Density. PCA showed Human
Population Density (variable name: “hpop”) the major driver of PC1. Plot made with
ggplot2 (Wickham 2016).
117

FIGURE 21: Correlation plot with Linear Regression Line, Land Area by Human
Population Density at the Starting Point. Plot created with ggplot2 (Wickham 2016).
Correlation= 0.314, p-value=0.134.

118

FIGURE 22: Heat map of M. apicalis suitability, defined as the probability of occurrence.
Probability was calculated with Wallace (Kass et al. 2018). The map image was
generated using QGIS (QGIS Development Team 2019). Darkest red areas have the
highest occurrence probability, to wit the highest environmental suitability.

119

APPENDIX A
PYTHON SOURCE CODE

A.1 Script 1-Habitat distribution modeling
## Modules ##
import funx as f #Stats and Calculus Library
import mfunx as m #Matrix Manipulation Library

## Data ##
#Header for the Output Raster
120onca=”ncols
3600\nnrows
1500\nxllcorner -180.000000000000\nyllcorner
-60.000000000000\ncellsize 0.100000000000\nNODATA_value 3.4028234663852885981e+38\n”

## Extract Occurance Data ##

#Open I Data(.csv)
tfile=open(“test_extract_form.csv”,”r”,errors=”ignore”)
rfile=tfile.readlines()

#Open Empty List of Coords
coordlist=[]

#Make List of Ordered Points
#Make Sure to Check Indices
for I in rfile:
coordcell=[] #open new cell
120

coordline=i.split(“,”)#split line at comma
coordcell.append(coordline[17])#latitude string to cell
coordcell.append(coordline[18])#longitude string to cell
coordlist.append(coordcell) #add cell to list

#Clip First Entry – Pulled From the Header – From List
del coordlist[0]

#Close .csv File
tfile.close()

## Write I Points Out ##
# Write the raw points to a .txt file for quick access if needed later
extractfile=open(“extracted_coordinates.txt”,”w”)
extractfile.write(“Latitude

Longitude\n”)

extractfile.write(“\n”)
for I in coordlist:
extractfile.write(i[0]+”

“+i[1]+”\n”)

extractfile.close()

## Clean Up I Points ##
#Convert Matrix of Strings to Matrix of Floats
#Filter Out And Report Corrupted Data
coord_fl=[] #float matrix opened
for I in coordlist:
coordcell=[] #open new cell
ecount=0 #initiate error count
errorlist=[] #open list of corrupted cells
121

e_index_list=[] #open list of corrupted indicies
try:
x=float(i[0])
y=float(i[1])
coordcell.append(x)
coordcell.append(y)
coord_fl.append(coordcell)
except:
ecount=ecount+1 #increase error counter by 1
errorlist.append(i)#add corrupted cell to list
e=coordlist.index(i) #index of corruption
e_index_list.appendI #add index to list

## Write Error Report ##
#Write an Error Report
#Error defined as an invalid [x,y] point
##efile=open(“Occurance_Error_Report.txt”,”w”)
##efile.write(“Occurance Points Error Report: “)
##er_count=”Number of Errors: “+str(ecount)+” “
##efile.write(er_count)
##if ecount!=0:
## for I in e_index_list:
##

efile.write(“Index of Errors: “+str(i)+” “)

## for j in errorlist:
##

efile.write(“Error Cells: “+j[0]+” “+j[1]+” “)

##efile.close()

## Convert GPS to Matrix Indicies ##
122

##Convert GPS points to Matrix indicies
#Open Empty List Of Coordinates
coord_index=[]

#Create Points
for I in coord_fl:
coord_index.append(f.CoordConvert(i))

## Eliminate Duplicate Points ##
#Get Rid of Duplicate indicies
ucoords=m.NoDupRows(coord_index)

## Read In Rasters ##
#Build Matrix of Minimum Temperature Values
tmin_file=open(“raster_library_avg_min_temp.txt”,”r”) #open avg min temp data
tmin_mat=m.RasterToMat(tmin_file)#convert raster to matrix of floats from “mfunx”
tmin_file.close()#close File

#Build Matrix of Precip Values
precip_file=open(“raster_library_avg_precip_mm.asc”,”r”) #open avg precip
precip_mat=m.RasterToMat(precip_file) #convert raster to matrix of floats
precip_file.close() #close file

## Extract Values at Occurance Points ##
tmin_occur_list=[] #Initialize list of temperatures
for I in ucoords:#iterate through points
123

tmin_occur_list.append(m.valxy(tmin_mat,i[0],i[1])) #append val at (x,y) to list.

Precip_occur_list=[] #initialize list of temperatures
for I in ucoords:
precip_occur_list.append(m.valxy(precip_mat,i[0],i[1]))
##
#### Process NODATA values ##
#filter out NODATA error points from tmin
nu_o_list_tmin=[]
for I in tmin_occur_list:
if i!=-3.4028234663852886e+38:
nu_o_list_tmin.append(i)

#filter out NODATA errors from precip
nu_o_list_precip=[]
for I in precip_occur_list:
if i!=-3.4028234663852886e+38:
nu_o_list_precip.append(i)

## Write Out Raw Data ##
###Write Values at Points to Report
##raw_precip=open(“raw_precip_data.txt”,”w”)
##raw_precip.write(“Raw Total Yearly Precipitation Data (mm): \n”)
##raw_precip.write(“\n”)
##for I in nu_o_list_precip:
##

raw_precip.write(str(i)+”\n”)

##
##raw_precip.close()
124

##
##raw_tmin=open(“raw_tmin_data.txt”,”w”)
##raw_tmin.write(“Raw Avg Minimun Temperature (degrees C*10):\n”)
##raw_tmin.write(“\n”)
##for I in nu_o_list_tmin:
##

raw_tmin.write(str(i)+”\n”)

##
##raw_precip.close()
##
#### Compute Statistics ##
###tmin
##mu=f.Mu(nu_o_list_tmin)
##me=f.Median(nu_o_list_tmin)
##sd=f.SD(mu,nu_o_list_tmin)
##range_list=f.MaxMinRange(nu_o_list_tmin)
##occur_dis_tmin=f.DistroMat(nu_o_list_tmin)
##mode_l=f.Mode(occur_dis_tmin)
##
###precip
##mu_p=f.Mu(nu_o_list_precip)
##me_p=f.Median(nu_o_list_precip)
##sd_p=f.SD(mu,nu_o_list_precip)
##range_list_p=f.MaxMinRange(nu_o_list_precip)
##occur_dis_precip=f.DistroMat(nu_o_list_precip)
##mode_l_precip=f.Mode(occur_dis_precip)
##
#### Write Stats Report ##
##
125

###Write tmin Stats to Report
##tmin_stats=open(“Occurance_Statistics_Min_Temp.txt”,”w”)
##tmin_stats.write(“Occurance Statistics: \n”)
##tmin_stats.write(“Average Minimum Temperature (degrees c*10): \n”)
##tmin_stats.write(“\n”)
##tmin_stats.write(“Mean:

“+str(mu)+”\n”)

##tmin_stats.write(“Median:

“+str(me)+”\n”)

##tmin_stats.write(“Mode:

“+str(mode_l)+”\n”)

##tmin_stats.write(“Standard Deviation: “+str(sd)+”\n”)
##tmin_stats.write(“Range:

“+str(range_list)+”\n”)

##tmin_stats.write(“\n”)
##tmin_stats.write(“Minimum Temperature Frequency\n”)
##tmin_stats.write(“\n”)
##
##for I in occur_dis_tmin:
##

tmin_stats.write(str(i[0])+”

“+str(i[1])+”\n”)

##
##tmin_stats.close()
##
##
###Write Precip Stats to Report
##precip_stats=open(“Occurance_Statistics_Precip.txt”,”w”)
##precip_stats.write(“Occurance Statistics: \n”)
##precip_stats.write(“Total Yearly mm Precipitation: \n”)
##precip_stats.write(“\n”)
##precip_stats.write(“Mean:

“+str(mu_p)+”\n”)

##precip_stats.write(“Median:

“+str(me_p)+”\n”)

##precip_stats.write(“Mode:

“+str(mode_l_precip)+”\n”)
126

##precip_stats.write(“Standard Deviation: “+str(sd_p)+”\n”)
##precip_stats.write(“Range:

“+str(range_list_p)+”\n”)

##precip_stats.write(“\n”)
##precip_stats.write(“Minimum Temperature Frequency\n”)
##precip_stats.write(“\n”)
##
##for I in occur_dis_precip:
##

precip_stats.write(str(i[0])+”

“+str(i[1])+”\n”)

##
##precip_stats.close()

## Create Output Rasters ##

#Open a Matrix with 1500 r0ws and 3600 columns
n_mat=m.NbyOMat(1500,3600)

#Add NODATA Value -3.4028234663852886e+38 to every cell
niche_mat=m.AddMat(n_mat,-3.4028234663852886e+38)

#Unique Points
pz=m.ListOfPoints(1500,3600)#total list of points
pre_pz=[]
land_pz=[]
for I in pz:
if m.valxy(precip_mat,i[0],i[1])!= -3.4028234663852886e+38:
pre_pz.append(i)#append all points with precip vals
for I in pre_pz:
if m.valxy(tmin_mat,i[0],i[1])!=-3.4028234663852886e+38:
127

land_pz.append(i)

#Compute the Final Matrix
##for I in land_pz:
##

tm=m.valxy(tmin_mat,i[0],i[1])

##

pc=m.valxy(precip_mat,i[0],i[1])

##

pval=f.LogOdds(tm,pc)

##

if pval>2.0:

##

pval=2

##

m.ChangeMat(niche_mat,i[0],i[1],pval)

#Compute occurrence matrix
for I in land_pz:
m.ChangeMat(niche_mat,i[0],i[1],0)
for I in ucoords:
m.ChangeMat(niche_mat,i[0],i[1],1)

#Write the Matrix to the Output Raster
##mout=open(“Niche_Analysis_Output_Raster”,”w”)
##mout.write(128onca)
##moutstr=m.MatToString(niche_mat)
##mout.write(moutstr)
##mout.close()

#Write occurrence raster to out
mout=open(“Vespa_Occurrence”,”w”)
mout.write(128onca)
moutstr=m.MatToString(niche_mat)
128

mout.write(moutstr)
mout.close()

##Write land points to .txt file
##need it for Growth / Spread
##pzout=open(“Land_Point_Values_Output_List.txt”,”w”)
##for I in land_pz:
## pzout.write(str(i[0])+” “+str(i[1])+”\n”)
##pzout.close()
##
A.2 Script 2-Continuous Growth and Spread Simulation

# Import Modules #
import funx as f # Stats, Arithmatic, and Calculus Library
import mfunx as m # Matrix Manipulation Library

## Header ##
#Header for the Output Rasters
129onca=”ncols
3600\nnrows
1500\nxllcorner -180.000000000000\nyllcorner
-60.000000000000\ncellsize 0.100000000000\nNODATA_value 3.4028234663852885981e+38\n”

### Read in Rasters #
#####Niche Model Output
##nish=open(“Niche_Analysis_Output_Raster.asc”,”r”)
##nish_f=m.RasterToMat(nish)
##nish.close()
#######Population Density
129

##popfile=open(“Population_Density_Adjusted.asc”,”r”)
##pop_mat=m.RasterToMat(popfile)
##popfile.close()
#####River Course
##rivfile=open(“World_River_Raster.asc”,”r”)
##riv_mat=m.RasterToMat(rivfile)
##rivfile.close()
###Elevation
##elevfile=open(“World_Elevation_Raster.asc”,”r”)
##elev_mat=m.RasterToMat(elevfile)
##elevfile.close
#M apicalis
##nish=open(“Bee_Niche_Processed.asc”,”r”)
##nish_f=m.RasterToMat(nish)
##nish.close()

## Growth Matrices ##
#Growth Matrix Control
##growfile=open(“Growth Matrix Control.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix – niche only
##growfile=open(“Growth Matrix Occur Only.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix – pop only
130

##growfile=open(“Growth Matrix Pop.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix – rivers only
##growfile=open(“Growth Matrix Rivers.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix -Elevation only
##growfile=open(“Growth Matrix Elev Only.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix-Occur and Pop
##growfile=open(“Growth Matrix Occur and Pop v3.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix-Occur and River
##growfile=open(“Growth Matrix Occur River.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix-Occur and Elevation
##growfile=open(“Growth Matrix Occur Elev.asc”,”r”)
##rlist=m.RasterToMat(growfile)
131

##growfile.close()

#Growth Matrix -Pop and Rivers
##growfile=open(“Growth Matrix Pop River.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix-Pop and Elevation
##growfile=open(“Growth Matrix Pop Elev.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix-River and Elevation *******
##growfile=open(“Growth Matrix River Elev.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix-Occur Pop River
##growfile=open(“Growth Matrix Occur Pop River.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix-Occur Pop Elev*
##growfile=open(“Growth Matrix Occur Pop Elev.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

132

#Growth Matrix-Occur River Elevation
##growfile=open(“Growth Matrix Occur River Elev.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix-Pop River Elev
##growfile=open(“Growth Matrix Pop River Elev.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix-Occur River Pop Elevation *Done*
##growfile=open(“Growth Matrix Occur Pop River Elev.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix Bee
growfile=open(“Growth Matrix Bee.asc”,”r”)
rlist=m.RasterToMat(growfile)
growfile.close()

#### Read in List Of Points ##
###open list of points
pz=open(“Land_Point_Values_Output_List.txt”,”r”)
pzlist=pz.readlines()
pointmat=[]
for I in pzlist:
p=i.split(“ “)
p[0]=int(p[0])
133

p[1]=int(p[1])
pointmat.append(p)

pz.close()
##
#### Growth Matrix ##
###Ideal Growth Rate
###e^r = 560*.02 = 11.2
###r=ln(11.2)=2.415
###r=(p-1)*x
###r=2-1)x=2.415
###x=2.415

#for M apicalis
#r=1.954

##grow_mat=m.NbyOMat(1500,3600)
##rlist=m.AddMat(grow_mat,-3.4028234663852886e+38)
##for p in pointmat:
## pval=m.valxy(nish_f,p[0],p[1])
## growval=pval*1.954
########

proval=pval-1.0

#### popdenval=m.valxy(pop_mat,p[0],p[1])
#### popval=float(popdenval/2000)
######

g_val=m.valxy(nish_f,p[0],p[1])

#### 134onca=m.valxy(riv_mat,p[0],p[1])
#### if 134onca==0:
####

134onca=.5
134

##########

growval=g_val*135onca

#### e_val=m.valxy(elev_mat,p[0],p[1])
#### if e_val>791.5:
####

egval=0

#### if e_val<=791.5:
####

egval=1

##########

growval=g_val

#### growval=egval*135onca*popval*2.415
######

growval=1

## m.ChangeMat(rlist,p[0],p[1],growval)

###### Write Out Growth Raster ##
#####Do this only once
#######then comment out
grow_out=open(“Growth Matrix Bee.asc”,”w”)
grow_out.write(135onca)
growstr=m.MatToString(rlist)
grow_out.write(growstr)
grow_out.close()

#### Initial Parameters ##
# k=0.06 per square km.
#Must Convert to Square Nautical Models
#.205/nautical_mile^2 * 36 = 7.397
#k=7.397

#m apicalis
k=2023.140
135

#Rate of Spread
#D=km^2/year
#D=7.2^2
#D=51.84

#D for M. Apicalis
#7.982 ^2
D=63.722

#Standard Deviation
# 3 standard deviations in any direction contains >99% of data
#sd_x=2.4
#sd_y=2.4

#7.982/3 = 2.650871
sd_x=2.650871
sd_y=2.650871

#Number of Years Running the Simulation
#t=10

#M. apicalis
t=20

#Spacial Change
h=.000001
136

# Run Scripts for All Points #
#port_list=[[506,1033],[595,911],[476,1089],[600,899],[602,846],[578,989],[559,617],[5
72,1000],[596,983],[642,997],[593,918],[492,1059],[595,927],[500,1048],[632,981],[463
,1097],[444,573],[481,1085],[522,575],[422,576],[620,975],[407, 568],[287, 301],[447,
1139]]
port_list=[[555,603]]
for I in port_list:
#set starting point
po=i
mu_x=po[0]
mu_y=po[1]
###########################
###### Initialize Matrix ##
###########################
#Define the Size of the Rows and Columns
col_val=1500
row_val=3600
# Open a col*row Matrix with All Vals =0
emptym=m.NbyOMat(col_val,row_val)
#add nodata to every cell
emptymat=m.AddMat(emptym,-3.4028234663852886e+38)
#Change Each Value in “emptymat” to the 3D Gaussian
#Value at that Position.
For p in pointmat:
gval=f.Gauss3D(mu_x,mu_y,sd_x,sd_y,p[0],p[1])
emptymat[p[0]][p[1]]=gval
###############################
###### Growth and Spread Loop #
137

###############################
#Compute Fisher Value at Each Point P after t years
for p in pointmat:
rval=m.valxy(rlist,p[0],p[1]) #pull r from list at point p
fval=f.Fisher(mu_x,mu_y,sd_x,sd_y,p[0],p[1],D,h,5,rval,k)
emptymat[p[0]][p[1]]=fval
###############################
## Compute Growth Statistics ##
###############################
#Sum of Population within +/- 5 units
mincol=po[0]-5
maxcol=po[0]+5
minrow=po[1]-5
maxrow=po[1]+5
nsum=m.MatSubSum(emptymat,mincol,maxcol,minrow,maxrow,3.4028234663852885981e+38)
centerval=m.valxy(emptymat,po[0],po[1])
###########################
##### Write to Raster Out #
###########################
#Write the Result of the Growth/Spread Loop to an Output Raster
#Make a String of the Final Matrix
Final_Val_String=m.MatToString(emptymat)
#Create a File Name
outfile_name=”Bee_Fin_cond_mu_x_”+str(mu_x)+”_mu_y_”+str(mu_y)+”_D_”+str(D)
+”_t_”+str(t)+”Pop_River_Elev.txt”
#Open a Writable File
fil=open(outfile_name,”w”)
138

#Write Header to File
fil.write(139onca)
#Write Final Value String to File
fil.write(Final_Val_String)
#Close the File
fil.close()
###############################
## Append Statistics to File ##
###############################
statfile=open(“Statistics_Data_Bee.asc”,”a”)
statfile.write(outfile_name+”\n”)
statfile.write(str(nsum)+”\n”)
statfile.write(str(centerval)+”\n”)
statfile.close()

## Run Script for All Control Locations ##
##control_list=[[450, 869],[555,966],[448, 1068],[549, 734],[475, 946]]
##for I in control_list:
## #set starting point
## po=i
## mu_x=po[0]
## mu_y=po[1]
## ###########################
## ###### Initialize Matrix ##
## ###########################
## #Define the Size of the Rows and Columns
## col_val=1500
139

## row_val=3600
## # Open a col*row Matrix with All Vals =0
## emptym=m.NbyOMat(col_val,row_val)
## #add nodata to every cell
## emptymat=m.AddMat(emptym,-3.4028234663852886e+38)
## #Change Each Value in “emptymat” to the 3D Gaussian
## #Value at that Position.
## for p in pointmat:
##

gval=f.Gauss3D(mu_x,mu_y,sd_x,sd_y,p[0],p[1])

##

emptymat[p[0]][p[1]]=gval

## ###############################
## ###### Growth and Spread Loop #
## ###############################
## #Compute Fisher Value at Each Point P after t years
## for p in pointmat:
##

rval=m.valxy(rlist,p[0],p[1]) #pull r from list at point p

##

fval=f.Fisher(mu_x,mu_y,sd_x,sd_y,p[0],p[1],D,h,5,rval,k)

##

emptymat[p[0]][p[1]]=fval

## ###############################
## ## Compute Growth Statistics ##
## ###############################
## #Sum of Population within +/- 5 units
## mincol=po[0]-5
## maxcol=po[0]+5
## minrow=po[1]-5
## maxrow=po[1]+5
## nsum=m.MatSubSum(emptymat,mincol,maxcol,minrow,maxrow,3.4028234663852885981e+38)
## centerval=m.valxy(emptymat,po[0],po[1])
140

## ###########################
## ##### Write to Raster Out #
## ###########################
## #Write the Result of the Growth/Spread Loop to an Output Raster
## #Make a String of the Final Matrix
## Final_Val_String=m.MatToString(emptymat)
## #Create a File Name
##
outfile_name=”Contr_cond_mu_x_”+str(mu_x)+”_mu_y_”+str(mu_y)+”_D_”+str(D)+”
_t_”+str(t)+”Control.txt”
## #Open a Writable File
#### fil=open(outfile_name,”w”)
#### #Write Header to File
#### fil.write(141onca)
#### #Write Final Value String to File
#### fil.write(Final_Val_String)
#### #Close the File
#### fil.close()
#### ###############################
## ## Append Statistics to File ##
## ###############################
## statfile=open(“Control_Statistics_Control.asc”,”a”)
## statfile.write(outfile_name+”\n”)
## statfile.write(str(nsum)+”\n”)
## statfile.write(str(centerval)+”\n”)
## statfile.close()

141

A.3 Script 3 – Discrete Growth and Spread Simulation

# Import Modules #
import funx as f # Stats, Arithmatic, and Calculus Library
import mfunx as m # Matrix Manipulation Library

## Header ##
#Header for the Output Rasters
142onca=”ncols
3600\nnrows
1500\nxllcorner -180.000000000000\nyllcorner
-60.000000000000\ncellsize 0.100000000000\nNODATA_value 3.4028234663852885981e+38\n”

## Initialize Constants ##
K=7.319
gen_num=10

### Read in Rasters #
#Growth Matrix Control
##growfile=open(“Growth Matrix Control.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix – niche only
142

##growfile=open(“Growth Matrix Occur Only.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix – pop only
##growfile=open(“Growth Matrix Pop.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix – rivers only
##growfile=open(“Growth Matrix Rivers.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix -Elevation only
##growfile=open(“Growth Matrix Elev Only.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix-Occur and Pop
##growfile=open(“Growth Matrix Occur and Pop v3.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix-Occur and River
##growfile=open(“Growth Matrix Occur River.asc”,”r”)
##rlist=m.RasterToMat(growfile)
143

##growfile.close()

#Growth Matrix-Occur and Elevation
growfile=open(“Growth Matrix Occur Elev.asc”,”r”)
rlist=m.RasterToMat(growfile)
growfile.close()

#Growth Matrix -Pop and Rivers
##growfile=open(“Growth Matrix Pop River.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix-Pop and Elevation
##growfile=open(“Growth Matrix Pop Elev.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix-River and Elevation
##growfile=open(“Growth Matrix River Elev.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix-Occur River Pop
##growfile=open(“Growth Matrix Occur River Pop.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix-Occur Pop Elev*
144

##growfile=open(“Growth Matrix Occur Pop Elev.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

###Growth Matrix-Occur Pop River *Ignore This one
##growfile=open(“Growth Matrix Occur Pop River.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix-Occur River Elevation
##growfile=open(“Growth Matrix Occur River Elev.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix-Pop River Elev
##growfile=open(“Growth Matrix Pop River Elev.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix-Occur River Pop Elevation
##growfile=open(“Growth Matrix Occur Pop River Elev.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()

#Growth Matrix Bee
##growfile=open(“Growth Matrix Bee.asc”,”r”)
##rlist=m.RasterToMat(growfile)
##growfile.close()
145

#### Read in List Of Points ##
###open list of points
pz=open(“Land_Point_Values_Output_List.txt”,”r”)
pzlist=pz.readlines()
pointmat=[]
for I in pzlist:
p=i.split(“ “)
p[0]=int(p[0])
p[1]=int(p[1])
pointmat.append(p)

pz.close()

# Run Scripts for All Points #
#port_list=[[506,1033],[595,911],[476,1089],[600,899],[602,846],[578,989],[559,617],[5
72,1000],[596,983],[642,997],[593,918],[492,1059],[595,927],[500,1048],[632,981],[463
,1097],[444,573],[481,1085],[522,575],[422,576],[620,975],[407,568],[287,301],[447,11
39]]
#port_list=[[506,1033]]#diagnostic to run one trial
#port_list=[[600,899]]
for I in port_list:

#set starting point#
####################
146

po=i#itial point
mu_x=po[0]#x of initial point
mu_y=po[1]#y of initial points

#set region around starting point
#MemmoryError occurs for all pointmat
#A smaller zone is required
#This defines that smaller zonw
mincol=po[0]-10
maxcol=po[0]+10
minrow=po[1]-10
maxrow=po[1]+10

################################
## Generate Pobability Matrix ##
################################
small_pz=m.SubListOfPoints(mincol,maxcol,minrow,maxrow)#define smaller search
area
small_pointmat=[]
for I in small_pz:#eliminate water units
for j in pointmat:
if i==j:
small_pointmat.append(i)

meta_pz=m.MetaMat(small_pointmat,small_pointmat)#all combinations of points
for j in meta_pz:
147

dval=f.PointDist(j[0],j[1])#distance between points in combinations
if dval>6.0:
probval=0.0#w/o this, spread is too large.
If dval<=6.0:
probval=f.gauss(0,2.4,dval)#gauss. Prob. Of distance
j.append(probval)#add probability to the combination

###########################
###### Initialize Matrix ##
###########################
#Define the Size of the Rows and Columns
col_val=1500
row_val=3600
# Open a col*row Matrix with All Vals =0
emptym=m.NbyOMat(col_val,row_val)
#add nodata to every cell
emptymat=m.AddMat(emptym,-3.4028234663852886e+38)
#Change Each Value in “emptymat” to the 3D Gaussian
#Value at that Position.
For p in pointmat:
emptymat[p[0]][p[1]]=0
#make the starting square =1
emptymat[mu_x][mu_y]=1

############################
## Growth and Spread Loop ##
148

############################
it_num=0#initialize iterator
while it_num #growth Loop
for k in pointmat:
rval=m.valxy(rlist,k[0],k[1])#pull growth val from mat
N=emptymat[k[0]][k[1]]#pull pop val from mat
nval=rval*N*(1.0-(N/K))#compute new pop: growth only
emptymat[k[0]][k[1]]=nval#write to pop mat
#it_num=it_num+1
#print(m.valxy(emptymat,i[0],i[1]))#diagnostic control
#spread loop
for h in meta_pz:
meta1=m.valxy(emptymat,h[0][0],h[0][1])#pop val: 1st point in combo
meta2=m.valxy(emptymat,h[1][0],h[1][1])#pop val: 2nd point in combo
pval=h[2]#pull probability appended to combo
if meta1==-3.4028234663852885981e+38:
meta1=0.0
if meta2==-3.4028234663852885981e+38:#otherwise it snags the nodata val
meta2=0.0
nuv1=meta1-(pval*meta1)+(pval*meta2)#subtract outgoing, add incoming
nuv2=meta2-(pval*meta2)+(pval*meta1)
emptymat[h[0][0]][h[0][1]]=nuv1#write new val to mat
emptymat[h[1][0]][h[1][1]]=nuv2
it_num=it_num+1#increase iterator
#print(m.valxy(emptymat,i[0],i[1]))#diagnostic out

###############################
149

## Compute Growth Statistics ##
###############################
#Sum of Population within +/- 5 units
mincol=po[0]-5
maxcol=po[0]+5
minrow=po[1]-5
maxrow=po[1]+5
nsum=m.MatSubSum(emptymat,mincol,maxcol,minrow,maxrow,3.4028234663852885981e+38)
centerval=m.valxy(emptymat,po[0],po[1])
###########################
##### Write to Raster Out #
###########################
#Write the Result of the Growth/Spread Loop to an Output Raster
#Make a String of the Final Matrix
Final_Val_String=m.MatToString(emptymat)
#Create a File Name
outfile_name=”New_Orleans_Graph”+str(mu_x)+”_mu_y_”+str(mu_y)+”_D_NA_t_”+s
tr(gen_num)+”Occur_Pop_River_Elev.txt”
#Open a Writable File
fil=open(outfile_name,”w”)
#Write Header to File
fil.write(150onca)
#Write Final Value String to File
fil.write(Final_Val_String)
#Close the File
fil.close()
## ###############################
150

## ## Append Statistics to File ##
## ###############################
## statfile=open(“Discrete_Statistics_Bee.asc”,”a”)
## statfile.write(outfile_name+”\n”)
## statfile.write(str(nsum)+”\n”)
## statfile.write(str(centerval)+”\n”)
## statfile.close()
##
#### Run Simulation for Control Groups ##
##contr_list=[[450, 869],[555,966],[448, 1068],[549, 734],[475, 946]]
##for I in contr_list:
##
## ####################
## #set starting point#
## ####################
## po=i
## mu_x=po[0]
## mu_y=po[1]
##
## #set region around starting point
## mincol=po[0]-10
## maxcol=po[0]+10
## minrow=po[1]-10
## maxrow=po[1]+10
##
## ################################
## ## Generate Pobability Matrix ##
## ################################
151

## small_pointmat=m.SubListOfPoints(mincol,maxcol,minrow,maxrow)#define
smaller search area
## meta_pz=m.MetaMat(small_pointmat,small_pointmat)
## for j in meta_pz:
##

dval=f.PointDist(j[0],j[1])

##

if dval>6.0:

##
##
##
##

probval=0.0
if dval<=6.0:
probval=f.gauss(0,2.4,dval)
j.append(probval)

##
##
##
## ###########################
## ###### Initialize Matrix ##
## ###########################
## #Define the Size of the Rows and Columns
## col_val=1500
## row_val=3600
## # Open a col*row Matrix with All Vals =0
## emptym=m.NbyOMat(col_val,row_val)
## #add nodata to every cell
## emptymat=m.AddMat(emptym,-3.4028234663852886e+38)
## #Change Each Value in “emptymat” to the 3D Gaussian
## #Value at that Position.
## for p in pointmat:
##

emptymat[p[0]][p[1]]=0

## #make the starting square =1
## emptymat[mu_x][mu_y]=1
152

##
## ############################
## ## Growth and Spread Loop ##
## ############################
## it_num=0
## while it_num ##

#growth Loop

##

for k in pointmat:

##

rval=m.valxy(rlist,k[0],k[1])

##

N=emptymat[k[0]][k[1]]

##

nval=rval*N*(1.0-(N/K))

##

emptymat[k[0]][k[1]]=nval

##

#it_num=it_num+1

##

#print(m.valxy(emptymat,i[0],i[1]))

##

#spread loop

##

for h in meta_pz:

##

meta1=m.valxy(emptymat,h[0][0],h[0][1])

##

meta2=m.valxy(emptymat,h[1][0],h[1][1])

##

pval=h[2]

##

if meta1==-3.4028234663852885981e+38:

##
##
##

meta1=0.0
if meta2==-3.4028234663852885981e+38:#otherwise it snags the nodata val
meta2=0.0

##

nuv1=meta1-(pval*meta1)+(pval*meta2)

##

nuv2=meta2-(pval*meta2)+(pval*meta1)

##

emptymat[h[0][0]][h[0][1]]=nuv1

##

emptymat[h[1][0]][h[1][1]]=nuv2

##

it_num=it_num+1
153

##

#print(m.valxy(emptymat,i[0],i[1]))

##
## ###############################
## ## Compute Growth Statistics ##
## ###############################
## #Sum of Population within +/- 5 units
## mincol=po[0]-5
## maxcol=po[0]+5
## minrow=po[1]-5
## maxrow=po[1]+5
## nsum=m.MatSubSum(emptymat,mincol,maxcol,minrow,maxrow,3.4028234663852885981e+38)
## centerval=m.valxy(emptymat,po[0],po[1])
## ###########################
## ##### Write to Raster Out #
## ###########################
## #Write the Result of the Growth/Spread Loop to an Output Raster
## #Make a String of the Final Matrix
## Final_Val_String=m.MatToString(emptymat)
## #Create a File Name
##
outfile_name=”Discrete_Contr_Fin_cond_mu_x_”+str(mu_x)+”_mu_y_”+str(mu_y)+”_
D_NA_t_”+str(gen_num)+”Occur_Pop_River_Elev.txt”
## #Open a Writable File
#### fil=open(outfile_name,”w”)
#### #Write Header to File
#### fil.write(154onca)
#### #Write Final Value String to File
#### fil.write(Final_Val_String)
154

#### #Close the File
#### fil.close()
## ###############################
## ## Append Statistics to File ##
## ###############################
## statfile=open(“Discrete_Contr_Statistics_Data_Occur_Pop_Elev.asc”,”a”)
## statfile.write(outfile_name+”\n”)
## statfile.write(str(nsum)+”\n”)
## statfile.write(str(centerval)+”\n”)
## statfile.close()

A.4 Script 4 -Function Library “Funx”

## Coordinate Conversion ##
#Convert from GPS 155onca to indices
###Matrix 3600*1500
def CoordConvert(p):
“Convert point ‘p’ from GPS to index”
lat=p[0] #old latitude
long=p[1] #old longitude
new_lat=90.0-lat #Apply Latitude correction
new_long=180+long#apply longitude corrections
new_lat=int(new_lat*10)#multiply by 10 and convert to float
155

new_long=int(new_long*10)
newp=[new_lat,new_long] #concatenate to new cell
return newp #new point

## Basic Arithmetic ##
#Distance Formula
def PointDist(p,q):
“Compute distance between points p and q”
x1=p[0]
x2=q[0]
y1=p[1]
y2=q[1]
xdif=x1-x2
ydif=y1-y2
xs=xdif**2
ys=ydif**2
dissum=xs+ys
dist=dissum**.5
return dist

## Basic Statistics Functions ##
#Find the Average
def Mu(L):
“Return the mean of list L”
lang=len(L)# number of entries in L
l_tot=0 #initialize sum
for I in L:
l_tot=l_tot+i#sum up values
156

mu=l_tot/lang #mean formula: sum of vals/# of vals
return mu #statistical mean

#Find The Standard Deviation
def SD(m,L):
“Find the Standard Deviation of list L with mean m”
sq_count=0 #initialize sum
lang=len(L) # # of values
for I in L:
d=i-m #difference between each point and the mean
sq=d**2 #difference squared
sq_count=sq_count+sq #sum of squared differences
var=sq_count/lang #Variance: mean of squared differences
sd=var**(1/2)#Standard Deviation: square root of Variance
return sd #return Standard Deviation.

#Find Median
def Median(L):
“Find the Median of the list L”
lang=len(L)
if lang%2==1:
mindex=int(round(lang/2))-1
if lang%2==0:
mindex=int(lang/2)-1
medi=L[mindex]
return medi

157

#Convert every element of a list to its z score
def Z_Score(LL):
“Convert Every Element of LL to Z Score”
mm=Mu(LL)
ss=SD(mm,LL)
z_list=[]
for I in LL:
dd=i-mm
z=dd/ss
z_list.append(z)
return z_list

#Convert every element of a list to a z score for any mean and SD
def raw_z(L,m,sd):
“Compute z score of list L by any mean m and sd”
z_list=[]
for I in L:
dd=i-m
z=dd/sd
z_list.append(z)
return z_list

#Build the Distribution Matrix
def DistroMat(L):
“Compute the Distribution Matrix of List L”
lang=len(L)# # of elements in list L
l_minus=lang-1#greatest index in L
L.sort()#order elements of L from least to greatest
158

l_min=int(L[0])#Int of minimum val in data range
l_max=L[l_minus]#max value in range
l_max_plus=int(l_max+1)#int of max val in range +1
range_list=[]#initiate list of values in range
for I in range(l_min,l_max_plus):#define range
range_list.append(i)#build list
dis_mat=[]#empty matrix
for I in range_list:#values for distribution
i_count=0#initialize count
i_cell=[i]#initialize matrix
for j in L:#if value in list=val in index
if i==j:
i_count=i_count+1#increase count by one
i_cell.append(i_count)#add frequency to cell
dis_mat.append(i_cell)#add cell to matrix
return dis_mat#return matrix

#Compute the Mode of A Distribution Matix
def Mode(distro):
“Compute the List of Modes of Distribution Matrix ‘distro’”
mode_val=[]#initialize list of distro freq. vals
for I in distro:
mode_val.append(i[1])#append freq. valsto list
mode_val.sort()#order the frequency vals least to greatest
l_max=len(mode_val)-1 #index of the largest value
big_val=mode_val[l_max]#biggest freq.
mode_list=[]#initialized list of modes
for I in distro:
159

if i[1]==big_val:#if frequency = the biggest frequency
mode_list.append(i[0])#add the first value to mode list
return mode_list

#Find the Range
def MaxMinRange(L):
“Find the min, max, and range”
lang=len(L)
l_end=lang-1 #last index
L.sort()#arrange from least to greatest
l_min=L[0]#min is the 0th entry
l_max=L[l_end] #max is the last index
l_range=l_max-l_min#difference between the max and min
return [l_min,l_max,l_range] #list of these values

# Statistical Distribution Functions #

#Simple Gaussian Normal Function
##Gaussian Normal Function in 3 Dimensions
##Assumes Bivariate with Pearson Correspondance Coefficient=0
160

##((1/2pi*s_x*s_y))e^[-1/2((x-mu_x)/s_x)^2)+((y-mu_y)/s_y)^2))]
def Gauss3D(mx,my,sx,sy,x,y):
“3D Gaussian assuming bivariate rho=0”
twopi=6.28 #constant: 2*pi
denom=twopi*sx*sy #constant: 2*pi*sx*sy
coef=1.0/denom #constant: 1/s*pi*sx*sy
e=2.718 #Euler’s Constant
xdif=x-mx #diff. between x coordinant and mean x
ydif=y-my #diff. between y coordinant and mean y
xquot=xdif/sx #x diff. divided by the standard dev. Of x vals
yquot=ydif/sy #y diff. divided by the standard dev. Of y vals
xsqr=xquot**2 #x diff/s.d._x squared
ysqr=yquot**2 #y diff/s.d._y squared
exp1=xsqr+ysqr #sum of squared normalized diffs
exp2=-(1/2)*exp1 #sum times constant
exp3=e**exp2 #Euler’s constant to exponent
pro=coef*exp3 #coefficient times exponential ter,
return pro #gaussian probability

# Spread Functions #

#Initial Gaussian-Distributed Population
# U(x,0)
def unaught(m,s,x):
“Bell curve. M=mean,s=standard deviation.”
V=s**2
p=3.14159
161

denom=2*p*v
dsqr=(denom)**(1/2)
c=1.0/dsqr
dnm=x-m
dnms=dnm/s
df_sqr=dnms**2
e=(1/2)*df_sqr
f=c*(2.718**-e)
return f

##2D Heat Equation – Numeric
##H(x,y,t+dt)=H(x,y,t)+dt*D*
#(H(x+h,y,t)+H(x,y+h,t)-4H(x,y,t)+H(x-h,y,t)+H(x,y-h,t))
# --------------------------------------------------#

h^2

#h=dx=dy

def heat(mx,my,sx,sy,x,y,D,h,dt):
“numeric (h) solution to 2D heat equation”
heat0=Gauss3D(mx,my,sx,sy,x,y)#initial conditions
alpha=dt*D #diffusion per time * time
four0=-4*heat0 #f *constant
minusy=Gauss3D(mx,my,sx,sy,x,y-h)#change in the -dy direction
minusx=Gauss3D(mx,my,sx,sy,x-h,y)#change in the -dx direction
plusx=Gauss3D(mx,my,sx,sy,x+h,y)#change in the +dx direction
plusy=Gauss3D(mx,my,sx,sy,x,y+h)#change in the +dy direction
162

hsqr=h**2 #constant in the denominator
num=four0+minusx+minusy+plusx+plusy #numerator sum
quot=num/hsqr #quotient: sum/constant
prod=alpha*quot #quotient * constant
hot=heat0+prod #initial conditions+change in conditions
return hot #new distribution.

# Fisher-Skellam Model #

def Fisher(mx,my,sx,sy,x,y,D,h,dt,r,k):
n0=Gauss3D(mx,my,sx,sy,x,y)
U=heat(mx,my,sx,sy,x,y,D,h,dt)+dislog(dt,r,n0,k)
return U

## Niche Analysis Functions ##
#Compute the Probability of Occurance given Minimum Temp and Precip
#HARDCODED
def LogOdds(t,p):
“The P(Occur) Given Min Temp ‘t’ and precip ‘p’”
tco=0.0158029*t
pco=0.156869*p
b=-5.35707014
esum=tco+pco+b
e=2.718
ex=e**esum
denom=1+ex
numer=1/denom
return denom
163

A.5 Script 5-Matrix function library “mfunx”

## Raster to Matrix ##

#Store Header as a String
def ExtractHeader(fil):
fi=fil.readlines()#turn read file into list of strings
#concatinate header (first six lines) to a single string
headrstr=fi[0]+fi[1]+fi[2]+fi[3]+fi[4]+fi[5]
return headrstr

#Function to Strip Header from Raster File
def RemoveHeader(fil):
fi=fil.readlines() #turn read file to list of strings
fi.remove(fi[0]) #remove header line 1
fi.remove(fi[0]) #remove header line 2
fi.remove(fi[0]) #remove header line 3
fi.remove(fi[0]) #remove header line 4
fi.remove(fi[0]) #remove header line 5
fi.remove(fi[0]) #remove header line 6
#fi.remove(fi[0]) #Remove line 7 only in hum_pop
return fi

#return list of strings w/o header

#Function to Convert a List of Strings to a Matrix of Strings
def StrMat(fil):
outmat=[] #New matrix for output
for I in fil:
outmat.append(i.split())#append a splitstring
164

return outmat #output

#Function to Convert Matrix of Strings to Matrix of Floats
def FloatMat(fil):
floatmat=[] #open output matrix
for I in fil: #difine column iterator
floatcell=[] #output cell
for j in i: #define row iterator
floatcell.append(float(j))#convert to float and append
floatmat.append(floatcell)#append cell to matrix
return floatmat #return matrix

#Function to do the above three in one step
def RasterToMat(fil):
fi=RemoveHeader(fil)
fispl=StrMat(fi)
fifl=FloatMat(fispl)
return fifl

## Matrix Manipulation ##
#Create a New n*o Matrix
#All Cells = 0
def NbyOMat(n,o):
165

“Generate n*o Matrix: all cells =0”
newmat=[] #new matrix: repository for cells
for I in range(n): #define column size
newcell=[] #create new empty row
for j in range(o): #define row size
newcell.append(0)# write value to row
newmat.append(newcell) #write row to matrix
return newmat #output matrix

#Create a List of Ordered Points in an nxm field
def ListOfPoints(x_max,y_max):
“List of all ordered pair points in x by y”
pointlist=[] #open list: repository for ordered pairs
for I in range(x_max): #define iter through x-max
for j in range(y_max): #define iter through y-max
xpoint=I #x-value
ypoint=j #y-value
pointcell=[xpoint,ypoint]#ordered pair (x,y)
pointlist.append(pointcell) #write ordered pair to list of points
return pointlist #list or ordered points

#Create a SubList of Ordered Points from (a-b)*(y-z)
def SubListOfPoints(x_min,x_max,y_min,y_max):
“List of all ordered pair points in (a to b) by (x to y)”
pointlist=[] #open list: repository for ordered pairs
for I in range(x_min,x_max): #define iter through x-max
for j in range(y_min,y_max): #define iter through y-max
xpoint=I #x-value
166

ypoint=j #y-value
pointcell=[xpoint,ypoint]#ordered pair (x,y)
pointlist.append(pointcell) #write ordered pair to list of points
return pointlist #list or ordered points

#Given two lists of objects, create matrix of all possible binary combinations
def MetaMat(M,N):
“Create a Matrix of combinations of elements in Lists M and N”
metmat=[]
for I in M:
for j in N:
metcell=[]
metcell.append(i)
metcell.append(j)
metmat.append(metcell)
return metmat

# Call a Value from a Matrix
def valxy(M,I,j):
“call value at [I,j] from matrix M”
vel=M[i][j] #ith volumn jth row
return vel #value at that location

#MuLtiply Every Element in a Matrix by the Constant “C”
def MultiMat(M,c):
“Multiply Every Element of Matrix M by Constant ‘c’”
newmat=[] #new matrix: repository for new values
for I in M: #Define column iterator
167

newcell=[] #create new row
for j in i: #define row iterator
newcell.append(j*c)#multiply M[I,j] by c, and add to row
newmat.append(newcell) #add row to new matrix
return newmat #New Matrix

##Given two Matrices, M and N, of Equal Size,
##multiply M[I,j] by N[I,j]
def MergeMat(M,N):
“Multiply M[I,j] by N[I,j]”#”where N and M are equal in size
newmat=[] #new matrix: repository for new values.
Lmat=len(M) #number of columns
lcel=len(M[0])#number of rows
for I in range(lmat): #define iterator over columns
newcell=[] #create new row
for j in range(lcel):#define iterator over rows
newcell.append(M[i][j]*N[i][j])#multiply and add to row
newmat.append(newcell)#add row to matrix
return newmat #new matrix

##invert Matrix
def InvertMat(M):
“Convert M[I,j] => 1/M[I,j]”
newmat=[] #open matrix
for I in M: #column iterator
newcell=[] #open row
for j in i: #row iterator
if j!=0: #avoid “Divide by Zero” Error
168

newcell.append(1/j)
if j==0:
newcell.append(0)#make =0 when “div. by Zero error”
newmat.append(newcell)#append row to matrix
return newmat #Matrix of inverted values

#Add constant “c” to every element in the matrix
def AddMat(M,c):
“Add constant ‘c’ to Every Element of Matrix M”
newmat=[] #open new matrix
for I in M:
newcell=[] #open new cell
for j in i:
newcell.append(j+c)#add c to j
newmat.append(newcell)#add row to matrix
return newmat

#Replace the entry in a specific cell [I,j] with constant c
def ChangeMat(M,I,j,c):
“Replace the entry at [I,j] in Matrix ‘M’ with ‘c’”
M[i][j]=c
return M

#Make every element of a matrix <=0 Positive
def MakePositiveMat(M,c):
“If M[I,j] >=0, replace with Constant ‘c’”
newmat=[]
169

for I in M:
newcell=[]
for j in i:
if j>0: #leave this value alone
newcell.append(j)
if j<=0:#write new value
newcell.appendI
newmat.append(newcell)
return newmat

## Matrix to Raster ##

##Matrix to String
def MatToString(M):
“Convert Matrix ‘M’ to Writable Raster String”
mastr=”” #New String: Repository for substrings
for I in M: #define column iterator
linstr=”” #open substring
for j in i: #define row iterator
linstr=linstr+str(j)+” “ #add matrix element to substringstring
linstr=linstr+” \n” #add line break to substring
mastr=mastr+linstr #add substring to master string
return mastr #master string

## Matrix Statistics ##

170

##Delete Dublicate Rows From Matrix
def NoDupRows(M):
“Return Matrix ‘m’ with Duplicate Rows Removed”
uniq_rows=[[0,0]] #repository for unigue rows
for I in M:
row_count=0#counts the number of occurances of a point
for j in uniq_rows:#compare I to unique vals list
if i==j:#if I has I already,
row_count=row_count+1#add one to the occur counter
if row_count==0: #ie if the row is unique
uniq_rows.append(i)#add the row to the list
del uniq_rows[0]#get rid of dummy row
return uniq_rows#list of unique rows

#Compute Mean of All Elements in a Matrix
def MeanMat(M):
“Find the Mean of All Values in a Matrix ‘M’ “
ent_count=0
val_count=0
for I in M:
ent_count=ent_count+len(i)
for j in i:
val_count=val_count+j
mu=val_count/ent_count
return mu

## Matrix Analysis ##
#sum up a specific subset of a matrix
171

#used for data analysis in growth/spread
def MatSubSum(M,min_col,max_col,min_row,max_row,no_data):
“sum of all entries in matrix ‘M’ bound by four vals. Ignore NODATA val”
subsum=0
for I in range(min_col,max_col):
for j in range(min_row,max_row):
if M[i][j]!=no_data:
subsum=subsum+M[i][j]
return subsum

#Pull All Indicies Containing Specific Values
def MatIndex(M,val):
“return the index [I,j] of the occurrances of ‘val’ in matrix ‘M’ “
oclist=[]
i_count=0
for I in M:
i_count=i_count+1
j_count=0
for j in i:
j_count=j_count+1
if j==val:
occell=[]
i_val=i_count-1
j_val=j_count-1
occell.append(i_val)
occell.append(j_val)
oclist.append(occell)
return oclist
172

A.6 Script 6-String Functions from my Useful Function Library “ufunx”

## String Functions ##

#Given a string of mixed letters and numbers
#pull numbers, decimals, and any other specified
#symbols “exceptors” to a new string

def NumbersFromString(s,*args):
“pull numbers and excepted symbols to new string”
new_s=”” #open new string
base_float=[“0”,”1”,”2”,”3”,”4”,”5”,”6”,”7”,”8”,”9”,”.”]#numbers/decimals
for arg in args:
base_float.append(str(arg))#add exceptors to list
for e in s:
for f in base_float:
if e==f:#if element in string is in exceptor list
new_s=new_s+e#add to new list
return new_s

#Replace Every Instance of one character in a string with another
#the same as s.replace(c1,c2), but I like this version better.

Def ReplaceAllInstances(s,c1,c2):
“Replace every instance of c1 in string s w/ c2”
new_s=””#open new string
173

for e in s:
if e!=c1:
new_s=new_s+e
if e==c1:
new_s=new_s+c2
return new_s

#Better Split Function
#split can be tempermental. I like this version better.
Def RobustSplit(s,c):
“split strings at c. better than s.splitI”
new_list=[]#repository of strings
#find out how many c’s.
split_counter=0#Initialize counter.
For e in s:
if e==c:#if element is splitter
split_counter=split_counter+1#raise split_count by +1
#open as many cells in new_list to I strings
for I in range(split_counter+1):#number of splits
new_cell=[]#open new cell
new_list.append(new_cell)#add to repository
#Sort string elements into lists
cell_num=0#cell the text goes in
for e in s:
if e!=c:
new_list[cell_num].appendI#add to the cell_num cell
if e==c:
cell_num=cell_num+1#move to next cell
174

#Eliminate empty cells
short_list=[]#list containing only full cells
for cell in new_list:
if len(cell)>0:#empty cells have len=0
short_list.append(cell)#add to new matrix
#Concatinate strings in cells to one string
string_list=[]#list containing only 175oncatenated strings
for cell in short_list:
string_cell=[]#new cell
cell_str=””#open new string
for e in cell:
cell_str=cell_str+e#add elements to one string
string_cell.append(cell_str)#append string to cell
string_list.append(string_cell)#append cell to list
str_list=[]
for I in string_list:
for k in i:
str_list.append(k)
return str_list

175

APPENDIX B
STATISTICAL CALCULATIONS AND SCRIPTS

B.1 R Script for Growth and Spread Analysis
##################
#Import Libraries#
##################
library(dplyr) #Data Mannipulation
library(ggplot2)#graphs
library(stargazer)#tables
library(readxl)#for Excel sheets
library(reshape)#need for boxplot
#############
#Import Data#
#############
#Test Data
test_sites<-c("Anchorage AK","Baltimore MD","Biloxi MS","Boston MA","Charleston
SC","Houston TX","Jacksonville FL","Los Angeles CA","Miami FL","Mobile
AL","New Orleans LA","New York NY","Pensacola FL","Philadelphia PA","Port
Charlotte FL","Portland ME","Portland OR","Providence RI","San Francisco
CA","Savannah GA","Saint John NB","St. Petersburg FL","Seattle WA","Vancouver
BC")
O 63,235.295,177.869,309.190,255.058,180.079,311.964,295.090,164.212,240.058,178.757
,242.396,218.730,167.332)
H<-c(-4.137,14.627,-9.25,32.642,-5.488,45.560,-13.660,99.880,42.727,-10.050,4.105,85.861,-5.255,32.625,-16.916,-2.317,21.505,1.810,26.827,-13.494,3.734,1.818,16.415,21.795)
R 83,19.218,57.463,19.738,22.176,85.550,27.553,19.789,59.584,43.142,21.251,23.257,39.4
38)
E 224.563,235.295,177.869,309.190,255.058,180.079,311.192,295.090,164.212,240.058,17
8.757,242.396,218.730,129.298)
OH<-c(-7.054,14.627,-9.253,32.642,-5.488,45.560,-13.660,99.880,42.727,-10.050,4.105,85.861,-5.255,32.625,-16.916,-2.317,21.505,1.810,26.827,-13.494,3.734,1.818,16.415,21.795)

176

OR<-c(1.684,11.570,7.649,21.199,7.685,22.583,42.234,5.363,6.920,26.522,52.285,10.943,9.394,
27.993,4.814,12.538,45.994,10.818,10.972,29.985,22.941,7.452,11.200,19.511)
OE 6.919,132.760,100.665,173.624,141.966,102.696,174.983,165.587,93.438,134.173,100.8
40,135.239,123.439,72.276)
HR 83,19.218,57.463,19.738,22.176,85.462,27.553,19.789,59.584,43.142,21.251,23.257,34.4
57)
HE<-c(-4.137,14.627,-9.253,32.642,-5.488,45.560,-13.660,99.869,42.727,-10.050,4.105,85.861,-5.255,32.625,-16.916,-2.317,21.505,1.810,26.827,-13.494,3.734,1.818,16.415,21.795)
RE 83,19.218,57.463,19.738,22.176,85.462,27.553,19.789,59.584,43.142,21.251,23.257,34.4
57)
OHE<-c(-6.602672026343643,3.5473022165695487,9.451363275607221,16.869262128791107,-6.456536789829549,21.859239215884706,15.497447772756113,53.96496842006372,22.656900172298645,10.262346182298577,-5.88074609076872,48.435232836008566,5.502110888134635,14.459029833686573,-17.555569135107337,2.400320914281212,7.695108212668095,-4.736516271284581,15.026394595369695,14.462588193436575,-5.178104917901807,4.571583936130664,7.208964317603426,9.387321068147479)
OHR<-c(-6.910388125498896,-11.120731479137902,-9.770112524590493,4.603990544452197,-7.752071462951866,-8.685588843342193,-16.453906817201926,6.606251736853167,-4.375376464500835,-10.600111259866129,-5.954957661850827,0.44600274530388717,-5.8962086072771,-5.642800291550419,-18.45356800718459,2.5414813645019945,-2.2334992594543706,13.579996504241207,0.000849115526033839,-15.697037704495493,6.963616296785915,-12.377810819908,-5.103184313957667,-2.4064218660195333)
HRE<-c(-6.432654460918969,-8.995653420653632,-9.71922552224005,1.4166661114194783,-7.575743921547813,-4.833080701504038,15.179671978570223,0.26719173542274444,-1.2615908434193188,10.542249413201331,-4.211499049597847,5.127729697379468,5.833702699340029,0.2574528200577711,-18.325213791767347,2.517844123594497,5.563812605819724,-12.518537734025406,1.7034004421128346,15.508923285764574,-6.7502117115771885,-11.434927770273957,3.639268146924278,2.8330532107512556)
ALL<-c(-6.910388125498896,-11.120731479137902,-9.770112524590493,4.603990544452197,-7.752071462951866,-8.685588843342193,-16.453906817201926,6.60978598935022,-4.375376464500835,-10.600111259866129,-5.954957661850827,0.44600274530388717,-5.8962086072771,-5.642800291550419,-18.45356800718459,2.5414813645019945,-2.2334992594543706,177

13.579996504241207,0.000849115526033839,-15.697037704495493,6.963616296785915,-12.377810819908,-5.103184313957667,-2.4064218660195333)
DC 962847,0.23172589431435012,0.24737457687492456,0.25467084411150465,0.2509155
39051507,0.29733404050572576,0.2611545506126562,0.2273859357718029,0.2246069
3491565534,0.2437540395324593,0.23642311841183888,0.259630457885826,1.0,0.216
5026966713416,0.3019899683251199,0.21438174768425822,0.2385959424156151,1.0,
0.25615951128468967,0.1845437368348254,0.18222665262355311)
DO 5,252.74088335089925,431.69932655938777,352.9639052201521,300.5638580045394,
258.0899334367345,347.65534688022643,336.97334071406243,346.4655111126585,26
0.97389396873314,431.916485144801,338.44077487278304,1.0,439.82182718578474,4
08.9963809402848,244.97832716943594,340.5484108730364,1.0,296.8565879484672,3
07.97034829069423,247.1131013994907)
DH<-c(1.1935813031183049e-14,2.5296920122289775e-05,3.33858144030868e13,2.9302571252850018e-05,1.6505352064337345e-12,6.4356570218971255e06,1.6992904736590298e-10,0.025086654211754544,8.527255996699707e05,4.388513763568611e-12,2.4974429983460152e12,0.08588160811218754,2.0645659001261818e-11,1.072827721990476e05,1.7228064424929038e-07,1.0,3.2941305463665304e-09,2.04542184339186e05,2.1478105631345254e-05,1.6127278138157145e-12,1.0,8.490773932639344e07,1.217540396164684e-05,1.7439777274427253e-05)
DR .064217827289194,7.6902200572471,9.713703653490919,1.6410030425725373,1.9369
184135779245,3.8780286716089565,11.744702332083387,3.4273490503013813,2.9928
999387073407,2.721083205841386,1.6975712844508704,1.0,2.6734650114893355,2.90
50028794840714,2.0689725916733943,4.253358720579881,1.0,1.6733548234755788,1.
8976947371966315,2.7042442846270554)
DE 52.74088335089925,431.69932655938777,352.9639052201521,88.19749437972507,258
.0899334367345,347.65534688022643,336.97334071406243,346.4655111126585,260.9
7389396873314,431.916485144801,338.44077487278304,1.0,225.5075407130646,408.9
963809402848,245.23567586068123,340.5484108730364,1.0,296.8565879484672,113.0
6373800180376,74.47553948767103)
DOH<-c(8.317238095334914e-32,2.5296920122289775e-05,3.33858144030868e13,2.9302571252850018e-05,1.6505352064337345e-12,6.4356570218971255e06,1.6992904736590298e-10,0.02439129961400149,8.527255996699707e05,4.388513763568611e-12,2.4974429983460152e12,0.08588160811218754,2.0645659001261818e-11,1.072827721990476e05,1.7228064424929038e-07,1.0,3.2941305463665304e-09,2.04542184339186e05,2.1478105631345254e-05,1.6127278138157145e-12,1.0,8.490773932639344e07,1.217540396164684e-05,1.7439777274427253e-05)
178

DOR 15046,0.7852099152822706,1.1875440347896222,1.5190885071850302,0.16900380117
839206,0.29733404050572576,0.5965302038827953,1.8493395939683508,0.526275018
3207965,0.46073622117039537,0.41639791691842964,0.259630457885826,1.0,0.40890
69582113834,0.4451282108543901,0.31765480256907824,0.6547157844686945,1.0,0.2
5615951128468967,0.2906496331808893,0.4163734002441647)
DOE 83,144.15163575036985,181.93933451565906,173.70941496840595,16.9350977459746
98,166.34446680361788,175.57763362722721,158.62456406544604,158.815438673027
78,150.45543294193186,176.30954770225307,173.2532514585469,1.0,48.51785116055
293,204.27210933999834,126.9236073121352,164.40334734241802,1.0,163.375879708
36034,21.92372266176627,16.16719018131519)
DHE<-c(1.1935813031183049e-14,2.5296920122289775e-05,3.33858144030868e13,2.9302571252850018e-05,1.6505352064337345e-12,6.4356570218971255e06,1.6992904736590298e-10,0.02364185650128657,8.527255996699707e05,4.388513763568611e-12,2.4974429983460152e12,0.08588160811218754,2.0645659001261818e-11,1.072827721990476e05,1.7228064424929038e-07,1.0,3.2941305463665304e-09,2.04542184339186e05,2.1478105631345254e-05,1.6127278138157145e-12,1.0,8.490773932639344e07,1.217540396164684e-05,1.7439777274427253e-05)
DRE .064217827289194,7.6902200572471,9.713703653490919,0.12279924479295377,1.936
9184135779245,3.8780286716089565,11.744702332083387,3.4273490503013813,2.992
8999387073407,2.721083205841386,1.6975712844508704,1.0,0.6762252369970749,2.9
050028794840714,1.906816913814253,4.253358720579881,1.0,1.6733548234755788,0.
23329346926335684,0.5086646120551801)
DOHR<-c(8.122329270806341e-35,6.983156284103863e-08,4.051214423530638e16,7.127696762476258e-08,1.6638251025141827e-15,9.267610364591808e09,1.0106653660138302e-11,2.3921695995864074e-05,8.363753014817754e08,4.573799551137005e-15,4.136465540711139e-13,9.20925519110769e05,2.090762363835089e-14,2.905466738004236e-08,1.6829246175409221e10,1.0,5.85211928372714e-11,5.625020173319869e-08,2.120616578589003e08,2.6931939329651388e-15,1.0,8.292828804439594e-10,1.2261912848256108e08,3.772460479669804e-07)
DOHE<-c(2.092870502615127e-21,1.059837536328187e-08,6.147974582466766e17,1.0819839549339828e-08,2.524913627489437e-16,1.4066444924438385e09,1.5340771764748047e-12,3.5159082182699088e-06,1.2699475406694296e08,6.941022398262186e-16,6.279422797604742e-14,1.3982199195976919e05,3.1729990908523e-15,4.409269138688792e-09,2.5539625465683925e11,1.0,8.881998913671988e-12,8.53766459449659e-09,3.2190575994461235e09,4.087411303319893e-16,1.0,1.258458990510788e-10,1.860997161239437e09,5.7268625054573424e-08)

179

DHRE<-c(1.1659043826972843e-17,6.983156284103863e-08,4.051214423530638e16,7.127696762476258e-08,1.6638251025141827e-15,9.267610364591808e09,1.0106653660138302e-11,2.318605601127585e-05,8.363753014817754e08,4.573799551137005e-15,4.136465540711139e-13,9.20925519110769e05,2.090762363835089e-14,2.905466738004236e-08,1.6829246175409221e10,1.0,5.85211928372714e-11,5.625020173319869e-08,2.120616578589003e08,2.6931939329651388e-15,1.0,8.292828804439594e-10,1.2261912848256108e08,3.772460479669804e-07)
DALL<-c(2.092870502615127e-21,1.059837536328187e-08,6.147974582466766e17,1.0819839549339828e-08,2.524913627489437e-16,1.4066444924438385e09,1.5340771764748047e-12,3.5159082182699088e-06,1.2699475406694296e08,6.941022398262186e-16,6.279422797604742e-14,1.3982199195976919e05,3.1729990908523e-15,4.409269138688792e-09,2.5539625465683925e11,1.0,8.881998913671988e-12,8.53766459449659e-09,3.2190575994461235e09,4.087411303319893e-16,1.0,1.258458990510788e-10,1.860997161239437e09,5.7268625054573424e-08)
DHR<-c(1.1659043826972843e-17,6.983156284103863e-08,4.051214423530638e16,7.127696762476258e-08,1.6638251025141827e-15,9.267610364591808e09,1.0106653660138302e-11,2.460408041669884e-05,8.363753014817754e08,4.573799551137005e-15,4.136465540711139e-13,9.20925519110769e05,2.090762363835089e-14,2.905466738004236e-08,1.6829246175409221e10,1.0,5.85211928372714e-11,5.625020173319869e-08,2.120616578589003e08,2.6931939329651388e-15,1.0,8.292828804439594e-10,1.2261912848256108e08,3.772460479669804e-07)
C 4,12.074,4.814,12.538,12.845,10.818,10.972,5.918,8.360,7.452,11.200,4.717)
#Positive Controls
#Positive Control Data
PC_Test_Sites<-c("Busan SK","Nerac FR","Tsushima City JP")
PC_C<-c(6.25062453064149, 12.84304130622685, -1.3524476116352573)
PC_DC<-c(0.26351537118660595, 0.21550878503616386, 0.7117752781871834)
PC_O<-c(139.6253864962005, 311.9616554970186, 27.356997716780082)
PC_DO<-c(177.35032000381526, 440.8290413545197, 33.684510628788836)
PC_H<-c(37.73062788344313, -14.659669241415443, -4.252677668983866)
PC_DH<-c(0.004721100033204433, 0.0, 0.0)
PC_R<-c(47.655399346743415, 75.14869001687674, 0.4619595018979659)
PC_DR<-c(5.778533941406178, 2.8426904715327175, 3.732911253200097)
PC_E<-c(146.61332872179383, 311.9616554970186, 27.356997716780082)
PC_DE<-c(215.9555894157436, 440.8290413545197, 33.684510628788836)
PC_OH<-c(37.7256874603262, -14.659669241415443, -4.252677668983866)
PC_DOH<-c(0.003807322036782975, 0.0, 0.0)
PC_OR<-c(26.075530795249044, 39.2741467408066, -1.3524476116352573)
PC_DOR<-c(0.4294737866407845, 0.4349004009617833, 0.7117752781871834)
PC_OE<-c(80.3790656206309, 175.38897249024424, 14.849709267069363)
180

PC_DOE<-c(91.73192856655375, 166.06778214101618, 26.608188507493416)
PC_HR<-c(14.462476659002851, -14.753820255533594, -4.25341265550077)
PC_DHR<-c(4.321512248255386e-05, 0.0, 0.0)
PC_HE<-c(37.73062788344313, -14.659669241415443, -4.252677668983866)
PC_DHE<-c(0.004721100033204433, 0.0, 0.0)
PC_RE<-c(47.655399346743415, 75.14869001687674, 0.4619595018979659)
PC_DRE<-c(5.778533941406178, 2.8426904715327175, 3.732911253200097)
PC_OHR<-c(6.665105635691452, -14.775664966081571, -4.253523195196977)
PC_DOHR<-c(3.6835318098856475e-05, 0.0, 0.0)
PC_OHE<-c(20.713648778486743, -14.71154493737744, -4.252948755769891)
PC_DOHE<-c(0.0006391796316063654, 0.0, 0.0)
PC_DHRE<-c(4.321512248255386e-05, 0.0, 0.0)
PC_HRE<-c(14.462476659002851, -14.753820255533594, -4.25341265550077)
PC_ALL<-c(6.665105635691452, -14.775664966081571, -4.253523195196977)
PC_DALL<-c(6.021020356286677e-06, 0.0, 0.0)
#Negative Control
NC_Test_Sites<-c("Albuquerque NM","Barry County MI","Montreal QC","St Paul
MN","Walhalla SC")
NC_C 9,12.845921814558709)
NC_DC 259884,0.21489017981259884)
NC_O<-c(-9.400355841705922,33.88079241989488,265.90332365892965,14.745700191326074,311.96453600535045)
NC_DO<-c(2.626994069466892e07,20.199258982007265,385.9297073145402,5.079264514609942e19,439.68015996791206)
NC_H<-c(1.549252209012889,-13.120496590247619,9.428721005564782,10.844889232306969,-14.689434492879961)
NC_DH<-c(0.0,0.0,0.0,1.5257009428266057e-08,0.0)
NC_E<-c(14.845936797434707,311.96453600535045,311.9616554970186,311.96453600535045,3
06.8959646421496)
NC_DE 7426)
NC_OH<-c(-14.83284436020131,-14.312559701465315,-9.584421456309158,14.824307255939768,-14.689434492879961)
NC_DOH<-c(0.0,0.0,0.0,7.817203751850384e-29,0.0)
NC_OR<-c(-3.667489737150706,-1.229569554108275,14.397482963551576,2.9988815970183516,54.58461145208383)

181

NC_DOR 3073603589,1.437427370088975)
NC_OE<-c(14.845936797434707,66.04125002308855,158.66874562850225,13.451027139292606,1
72.6958953679718)
NC_DOE 9532)
NC_HR<-c(-10.24082408557326,-14.47724388974438,10.691534486524121,5.452216837112796,-14.742249407718448)
NC_DHR<-c(0.0,0.0,0.0,6.154163134583662e-10,0.0)
NC_HE<-c(-14.845936797434707,-13.120496590247619,9.428721005564782,10.844889232306969,-14.689434492879961)
NC_DHE<-c(0.0,0.0,0.0,1.5257009428266057e-08,0.0)
NC_RE<-c(14.845936797434707,30.389656603021827,37.254067033776984,97.16766347420034,1
04.36785898400126)
NC_DRE 46)
NC_OHR<-c(-14.16267962279138,-14.669403239417253,-12.608523711061123,12.492590961850143,-14.76729698402048)
NC_DOHR<-c(0.0,0.0,0.0,4.1626170883016256e-30,0.0)
NC_OHE<-c(-14.845936797434707,-14.198015687614351,-11.952381017244415,11.855071221476226,-14.726590284246456)
NC_DOHE<-c(0.0,0.0,0.0,1.0041899245369854e-13,0.0)
NC_HRE<-c(-14.845936797434707,-14.47724388974438,10.691534486524121,5.452216837112796,-14.742249407718448)
NC_DHRE<-c(0.0,0.0,0.0,6.154163134583662e-10,0.0)
NC_ALL<-c(-14.845936797434707,-14.669403239417253,-12.608523711061123,12.492590961850143,-14.76729698402048)
NC_DALL<-c(0.0,0.0,0.0,1.0041899245369854e-13,0.0)
###########################
#Bind Data into Dataframes#
###########################
#Bind Test data vectors into single dataframe
trials E,DHE,RE,DRE,OHR,DOHR,OHE,DOHE,HRE,DHRE,ALL,DALL)
#Bind Positive Cotrols into single dataframe
P_Controls C_OH,PC_DOH,PC_OR,PC_DOR,PC_OE,PC_DOE,PC_HR,PC_DHR,PC_HE,PC_DH
182

E,PC_RE,PC_DRE,PC_OHR,PC_DOHR,PC_OHE,PC_DOHE,PC_HRE,PC_DHRE,PC
_ALL,PC_DALL)
#Bind negative controls
N_Controls E,NC_OH,NC_DOH,NC_OR,NC_DOR,NC_OE,NC_DOE,NC_HR,NC_DHR,NC_HE,
NC_DHE,NC_RE,NC_DRE,NC_OHR,NC_DOHR,NC_OHE,NC_DOHE,NC_HRE,NC
_DHRE,NC_ALL,NC_DALL)
##############################
#Write Data to Summary Tables#
##############################
#summary of Test Sites
stargazer(trials,digits = 3,type="html", out = "Test Sites Summary Table.doc")
#Summary of Positive Sites
stargazer(P_Controls,digits = 3,type="html", out = "Positive Controls Summary
Table.doc")
#Summary of Negative Sites
stargazer(N_Controls,digits = 3,type="html", out = "Negative Controls Summary
Table.doc")
##############################################
#Split Data Frames into Several and Write Out#
##############################################
#Trials
trials1<-select(trials,test_sites:DOH)
trials2<-select(trials,test_sites,OR:DRE)
trials3<-select(trials,test_sites,OHR:DALL)
#Positive Controls
pcon1<-select(P_Controls,PC_Test_Sites:PC_DOH)
pcon2<-select(P_Controls,PC_Test_Sites,PC_OR:PC_DRE)
pcon3<-select(P_Controls,PC_Test_Sites,PC_OHR:PC_DALL)
#Negative Controls
ncon1<-select(N_Controls,NC_Test_Sites:NC_DOH)
ncon2<-select(N_Controls,NC_Test_Sites,NC_OR:NC_DRE)
ncon3<-select(N_Controls,NC_Test_Sites,NC_OHR:NC_DALL)
#write out trials
stargazer(trials1,digits = 3,summary=FALSE,type="html", out = "Trials Table 1.doc")
stargazer(trials2,digits = 3,summary=FALSE,type="html", out = "Trials Table 2.doc")
stargazer(trials3,digits = 3,summary=FALSE,type="html", out = "Trials Table 3.doc")
183

#write out Positive Controls
stargazer(pcon1,digits = 3,summary=FALSE,type="html", out = "Pcon Table 1.doc")
stargazer(pcon2,digits = 3,summary=FALSE,type="html", out = "Pcon Table 2.doc")
stargazer(pcon3,digits = 3,summary=FALSE,type="html", out = "pcon Table 3.doc")
#Write out negative controls
stargazer(ncon1,digits = 3,summary=FALSE,type="html", out = "Ncon Table 1.doc")
stargazer(ncon2,digits = 3,summary=FALSE,type="html", out = "Ncon Table 2.doc")
stargazer(ncon3,digits = 3,summary=FALSE,type="html", out = "Ncon Table 3.doc")
#################################
#Organize Data by Site for ANOVA#
#################################
#Test Sites
Anchorage<-as.vector(unlist(trials[1,2:29]))
Baltimore<-as.vector(unlist(trials[2,2:29]))
Biloxi<-as.vector(unlist(trials[3,2:29]))
Boston<-as.vector(unlist(trials[4,2:29]))
Charleston<-as.vector(unlist(trials[5,2:29]))
Houston<-as.vector(unlist(trials[6,2:29]))
Jacksonville<-as.vector(unlist(trials[7,2:29]))
Los_Angeles<-as.vector(unlist(trials[8,2:29]))
Miami<-as.vector(unlist(trials[9,2:29]))
Mobile<-as.vector(unlist(trials[10,2:29]))
New_Orleans<-as.vector(unlist(trials[11,2:29]))
New_York<-as.vector(unlist(trials[12,2:29]))
Pensacola<-as.vector(unlist(trials[13,2:29]))
Philadelphia<-as.vector(unlist(trials[14,2:29]))
Port_Charlotte<-as.vector(unlist(trials[15,2:29]))
Portland_ME<-as.vector(unlist(trials[16,2:29]))
Portland_OR<-as.vector(unlist(trials[17,2:29]))
Providence<-as.vector(unlist(trials[18,2:29]))
San_Francisco<-as.vector(unlist(trials[19,2:29]))
Savannnah<-as.vector(unlist(trials[20,2:29]))
SaintJohn<-as.vector(unlist(trials[21,2:29]))
St_Petersurg<-as.vector(unlist(trials[22,2:29]))
Seattle<-as.vector(unlist(trials[23,2:29]))
Vancouver<-as.vector(unlist(trials[24,2:29]))
trials_by_site geles,Miami,Mobile,New_Orleans,New_York,Pensacola,Philadelphia,Port_Charlotte,Por
tland_ME,Portland_OR,Providence,San_Francisco,Savannnah,SaintJohn,St_Petersurg,Se
attle,Vancouver)

184

#Positive Controls
Busan<-as.vector(unlist(P_Controls[1,2:29]))
Nerac<-as.vector(unlist(P_Controls[2,2:29]))
Tsushima<-as.vector(unlist(P_Controls[3,2:29]))
pcon_by_site<-data.frame(Busan,Nerac,Tsushima)
#Negative Controls
Albuquerque<-as.vector(unlist(N_Controls[1,2:29]))
Barry<-as.vector(unlist(N_Controls[2,2:29]))
Montreal<-as.vector(unlist(N_Controls[3,2:29]))
StPaul<-as.vector(unlist(N_Controls[4,2:29]))
Walhalla<-as.vector(unlist(N_Controls[4,2:29]))
ncon_by_site<-data.frame(Albuquerque,Barry,Montreal,StPaul,Walhalla)
#######################
#Trials without Alaska#
#######################
#Pull trials without alaska
trials_no_alaska<-filter(trials,test_sites!="Anchorage AK"&test_sites!="Saint John
NB"&test_sites!="Vancouver BC")
#Write out
trials_na1<-select(trials_no_alaska,test_sites:DOH)
trials_na2<-select(trials_no_alaska,test_sites,OR:DRE)
trials_na3<-select(trials_no_alaska,test_sites,OHR:DALL)
stargazer(trials_na1,digits = 3,summary=FALSE,type="html", out = "Trials No Alaska
Table 1.doc")
stargazer(trials_na2,digits = 3,summary=FALSE,type="html", out = "Trials No Alaska
Table 2.doc")
stargazer(trials_na3,digits = 3,summary=FALSE,type="html", out = "Trials No Alaska
Table 3.doc")
###########################
#Add Values for Statistics#
###########################
#Add vector of land area
trials$L_Area #Add vector of occurrence
trials$p_occur .0,1.0)

185

#add Vector of Human Population Density
trials$hpop 0.0,500.0,500.0,300.0,2000.0,2000.0,2000.0,1000.0,0.0,100.0,2000.0,2000.0)
#add vector of River presence
trials$riv_pres .0)
#add vector of elevation
trials$Elev<-c(36.0,97.0,0.0,10.0,-3.0,20.0,-1.0,55.0,10.0,46.0,3.0,15.0,2.0,3.0,10.0,0.0,18.0,31.0,104.0,1.0,0.0,-4.0,-122.0,1.0)
#Add Land Area to Positive Controls
P_Controls$L_Area<-c(51, 100, 8)
#Add Land Area for Negative Controls
N_Controls$L_Area<-c(100,100,100,100,100)
###########################
#Compute Mean Nest Density#
###########################
#Trials
trials<-mutate(trials,mu_C=C/L_Area)
trials<-mutate(trials,mu_DC=DC/L_Area)
trials<-mutate(trials,mu_O=O/L_Area)
trials<-mutate(trials,mu_DO=DO/L_Area)
trials<-mutate(trials,mu_H=H/L_Area)
trials<-mutate(trials,mu_DH=DH/L_Area)
trials<-mutate(trials,mu_E=E/L_Area)
trials<-mutate(trials,mu_DE=DE/L_Area)
trials<-mutate(trials,mu_OH=OH/L_Area)
trials<-mutate(trials,mu_DOH=DOH/L_Area)
trials<-mutate(trials,mu_OR=OR/L_Area)
trials<-mutate(trials,mu_DOR=DOR/L_Area)
trials<-mutate(trials,mu_OE=OE/L_Area)
trials<-mutate(trials,mu_DOE=DOE/L_Area)
trials<-mutate(trials,mu_HR=HR/L_Area)
trials<-mutate(trials,mu_DHR=DHR/L_Area)
trials<-mutate(trials,mu_HE=HE/L_Area)
trials<-mutate(trials,mu_DHE=DHE/L_Area)
trials<-mutate(trials,mu_RE=RE/L_Area)
trials<-mutate(trials,mu_DRE=DRE/L_Area)
trials<-mutate(trials,mu_OHR=OHR/L_Area)
trials<-mutate(trials,mu_HR=HR/L_Area)
186

trials<-mutate(trials,mu_OHE=OHE/L_Area)
trials<-mutate(trials,mu_DOHE=DOHE/L_Area)
trials<-mutate(trials,mu_HRE=HRE/L_Area)
trials<-mutate(trials,mu_DHRE=DHRE/L_Area)
trials<-mutate(trials,mu_ALL=ALL/L_Area)
trials<-mutate(trials,mu_DALL=DALL/L_Area)
#Positive Controls
P_Controls<-mutate(P_Controls,mu_C=PC_C/L_Area)
P_Controls<-mutate(P_Controls,mu_DC=PC_DC/L_Area)
P_Controls<-mutate(P_Controls,mu_O=PC_O/L_Area)
P_Controls<-mutate(P_Controls,mu_DO=PC_DO/L_Area)
P_Controls<-mutate(P_Controls,mu_H=PC_H/L_Area)
P_Controls<-mutate(P_Controls,mu_DH=PC_DH/L_Area)
P_Controls<-mutate(P_Controls,mu_E=PC_E/L_Area)
P_Controls<-mutate(P_Controls,mu_DE=PC_DE/L_Area)
P_Controls<-mutate(P_Controls,mu_OH=PC_OH/L_Area)
P_Controls<-mutate(P_Controls,mu_DOH=PC_DOH/L_Area)
P_Controls<-mutate(P_Controls,mu_OR=PC_OR/L_Area)
P_Controls<-mutate(P_Controls,mu_DOR=PC_DOR/L_Area)
P_Controls<-mutate(P_Controls,mu_OE=PC_OE/L_Area)
P_Controls<-mutate(P_Controls,mu_DOE=PC_DOE/L_Area)
P_Controls<-mutate(P_Controls,mu_HR=PC_HR/L_Area)
P_Controls<-mutate(P_Controls,mu_DHR=PC_DHR/L_Area)
P_Controls<-mutate(P_Controls,mu_HE=PC_HE/L_Area)
P_Controls<-mutate(P_Controls,mu_DHE=PC_DHE/L_Area)
P_Controls<-mutate(P_Controls,mu_RE=PC_RE/L_Area)
P_Controls<-mutate(P_Controls,mu_DRE=PC_DRE/L_Area)
P_Controls<-mutate(P_Controls,mu_OHR=PC_OHR/L_Area)
P_Controls<-mutate(P_Controls,mu_HR=PC_HR/L_Area)
P_Controls<-mutate(P_Controls,mu_OHE=PC_OHE/L_Area)
P_Controls<-mutate(P_Controls,mu_DOHE=PC_DOHE/L_Area)
P_Controls<-mutate(P_Controls,mu_HRE=PC_HRE/L_Area)
P_Controls<-mutate(P_Controls,mu_DHRE=PC_DHRE/L_Area)
P_Controls<-mutate(P_Controls,mu_ALL=PC_ALL/L_Area)
P_Controls<-mutate(P_Controls,mu_DALL=PC_DALL/L_Area)
#egative Controls
N_Controls<-mutate(N_Controls,mu_C=NC_C/L_Area)
N_Controls<-mutate(N_Controls,mu_DC=NC_DC/L_Area)
N_Controls<-mutate(N_Controls,mu_O=NC_O/L_Area)
N_Controls<-mutate(N_Controls,mu_DO=NC_DO/L_Area)
N_Controls<-mutate(N_Controls,mu_H=NC_H/L_Area)
N_Controls<-mutate(N_Controls,mu_DH=NC_DH/L_Area)
N_Controls<-mutate(N_Controls,mu_E=NC_E/L_Area)
N_Controls<-mutate(N_Controls,mu_DE=NC_DE/L_Area)
187

N_Controls<-mutate(N_Controls,mu_OH=NC_OH/L_Area)
N_Controls<-mutate(N_Controls,mu_DOH=NC_DOH/L_Area)
N_Controls<-mutate(N_Controls,mu_OR=NC_OR/L_Area)
N_Controls<-mutate(N_Controls,mu_DOR=NC_DOR/L_Area)
N_Controls<-mutate(N_Controls,mu_OE=NC_OE/L_Area)
N_Controls<-mutate(N_Controls,mu_DOE=NC_DOE/L_Area)
N_Controls<-mutate(N_Controls,mu_HR=NC_HR/L_Area)
N_Controls<-mutate(N_Controls,mu_DHR=NC_DHR/L_Area)
N_Controls<-mutate(N_Controls,mu_HE=NC_HE/L_Area)
N_Controls<-mutate(N_Controls,mu_DHE=NC_DHE/L_Area)
N_Controls<-mutate(N_Controls,mu_RE=NC_RE/L_Area)
N_Controls<-mutate(N_Controls,mu_DRE=NC_DRE/L_Area)
N_Controls<-mutate(N_Controls,mu_OHR=NC_OHR/L_Area)
N_Controls<-mutate(N_Controls,mu_HR=NC_HR/L_Area)
N_Controls<-mutate(N_Controls,mu_OHE=NC_OHE/L_Area)
N_Controls<-mutate(N_Controls,mu_DOHE=NC_DOHE/L_Area)
N_Controls<-mutate(N_Controls,mu_HRE=NC_HRE/L_Area)
N_Controls<-mutate(N_Controls,mu_DHRE=NC_DHRE/L_Area)
N_Controls<-mutate(N_Controls,mu_ALL=NC_ALL/L_Area)
N_Controls<-mutate(N_Controls,mu_DALL=NC_DALL/L_Area)
##################################
#Write Out MND Summary Statistics#
##################################
#Trials
trials_mnd<-select(trials,test_sites,mu_C:mu_DALL)
stargazer(trials_mnd,digits = 3,type="html", out = "Trial Mean Nest Denstity Summary
Table.doc")
#Positive Controls
P_Controls_mnd<-select(P_Controls,PC_Test_Sites,mu_C:mu_DALL)
stargazer(P_Controls_mnd,digits = 3,type="html", out = "Positive Mean Nest Denstity
Summary Table.doc")
#Negative Controls
N_Controls_mnd<-select(N_Controls,NC_Test_Sites,mu_C:mu_DALL)
stargazer(N_Controls_mnd,digits = 3,type="html", out = "Negative Mean Nest Denstity
Summary Table.doc")
###################
#WRite out raw MND#
###################
#Trials
# trialsmnd1<-select(trials_mnd,test_sites:DOH)
# trialsmnd2<-select(trials_mnd,test_sites,OR:DRE)
# trialsmnd3<-select(trials_mnd,test_sites,OHR:DALL)
188

#Positive Controls
# pconmnd1<-select(P_Controls_mnd,PC_Test_Sites:PC_DOH)
# pconmnd2<-select(P_Controls_mnd,PC_Test_Sites,PC_OR:PC_DRE)
# pconmnd3<-select(P_Controls_mnd,PC_Test_Sites,PC_OHR:PC_DALL)
#Negative Controls
# nconmnd1<-select(N_Controls_mnd,NC_Test_Sites:NC_DOH)
# nconmnd2<-select(N_Controls_mnd,NC_Test_Sites,NC_OR:PC_DRE)
# nconmnd3<-select(N_Controls_mnd,NC_Test_Sites,NC_OHR:PC_DALL)
#write out trials
# stargazer(trialsmnd1,digits = 3,summary=FALSE,type="html", out = "Trials mnd Table
1.doc")
# stargazer(trialsmnd2,digits = 3,summary=FALSE,type="html", out = "Trials mnd Table
2.doc")
# stargazer(trialsmnd3,digits = 3,summary=FALSE,type="html", out = "Trials mnd Table
3.doc")
stargazer(trials_mnd,digits = 3,summary=FALSE,type="html", out = "Trials mnd
Table.doc")
#write out Positive Controls
# stargazer(pconmnd1,digits = 3,summary=FALSE,type="html", out = "Pcon mnd Table
1.doc")
# stargazer(pconmnd2,digits = 3,summary=FALSE,type="html", out = "Pcon mnd Table
2.doc")
# stargazer(pconmnd3,digits = 3,summary=FALSE,type="html", out = "pcon mnd Table
3.doc")
stargazer(P_Controls_mnd,digits = 3,summary=FALSE,type="html", out = "Pcon mnd
Table.doc")
#Write out negative controls
# stargazer(nconmnd1,digits = 3,summary=FALSE,type="html", out = "Ncon mnd Table
1.doc")
# stargazer(nconmnd2,digits = 3,summary=FALSE,type="html", out = "Ncon mnd Table
2.doc")
# stargazer(nconmnd3,digits = 3,summary=FALSE,type="html", out = "Ncon mnd Table
3.doc")
stargazer(N_Controls_mnd,digits = 3,summary=FALSE,type="html", out = "Ncon mnd
Table.doc")
#######################
#Prepare MND for Anova#
#######################
#Trials
Anchorage_mu<-as.vector(unlist(trials[1,35:61]))
Baltimore_mu<-as.vector(unlist(trials[2,35:61]))
189

Biloxi_mu<-as.vector(unlist(trials[3,35:61]))
Boston_mu<-as.vector(unlist(trials[4,35:61]))
Charleston_mu<-as.vector(unlist(trials[5,35:61]))
Houston_mu<-as.vector(unlist(trials[6,35:61]))
Jacksonville_mu<-as.vector(unlist(trials[7,35:61]))
Los_Angeles_mu<-as.vector(unlist(trials[8,35:61]))
Miami_mu<-as.vector(unlist(trials[9,35:61]))
Mobile_mu<-as.vector(unlist(trials[10,35:61]))
New_Orleans_mu<-as.vector(unlist(trials[11,35:61]))
New_York_mu<-as.vector(unlist(trials[12,35:61]))
Pensacola_mu<-as.vector(unlist(trials[13,35:61]))
Philadelphia_mu<-as.vector(unlist(trials[14,35:61]))
Port_Charlotte_mu<-as.vector(unlist(trials[15,35:61]))
Portland_ME_mu<-as.vector(unlist(trials[16,35:61]))
Portland_OR_mu<-as.vector(unlist(trials[17,35:61]))
Providence_mu<-as.vector(unlist(trials[18,35:61]))
San_Francisco_mu<-as.vector(unlist(trials[19,35:61]))
Savannnah_mu<-as.vector(unlist(trials[20,35:61]))
SaintJohn_mu<-as.vector(unlist(trials[21,35:61]))
St_Petersurg_mu<-as.vector(unlist(trials[22,35:61]))
Seattle_mu<-as.vector(unlist(trials[23,35:61]))
Vancouver_mu<-as.vector(unlist(trials[24,35:61]))
mean_by_site n_mu,Jacksonville_mu,Los_Angeles_mu,Miami_mu,Mobile_mu,New_Orleans_mu,New
_York_mu,Pensacola_mu,Philadelphia_mu,Port_Charlotte_mu,Portland_ME_mu,Portlan
d_OR_mu,Providence_mu,San_Francisco_mu,Savannnah_mu,SaintJohn_mu,St_Petersur
g_mu,Seattle_mu,Vancouver_mu)
#Positive Controls
Busan_mu<-as.vector(unlist(P_Controls[1,35:61]))
Nerac_mu<-as.vector(unlist(P_Controls[2,35:61]))
Tsushima_mu<-as.vector(unlist(P_Controls[3,35:61]))
pcon_by_site<-data.frame(Busan_mu,Nerac_mu,Tsushima_mu)
#Negative Controls
Albuquerque_mu<-as.vector(unlist(N_Controls[1,35:61]))
Barry_mu<-as.vector(unlist(N_Controls[2,35:61]))
Montreal_mu<-as.vector(unlist(N_Controls[3,35:61]))
StPaul_mu<-as.vector(unlist(N_Controls[4,35:61]))
Walhalla_mu<-as.vector(unlist(N_Controls[4,35:61]))
ncon_by_site ##########
#Z-Scores#
190

##########
#TRials
trials<-mutate(trials,z_C=((C-mean(C))/sd(C)))
trials<-mutate(trials,z_DC=((DC-mean(DC))/sd(DC)))
trials<-mutate(trials,z_O=((O-mean(O))/sd(O)))
trials<-mutate(trials,z_DO=((DO-mean(DO))/sd(DO)))
trials<-mutate(trials,z_H=((H-mean(H))/sd(H)))
trials<-mutate(trials,z_DH=((DH-mean(DH))/sd(DH)))
trials<-mutate(trials,z_E=((E-mean(E))/sd(E)))
trials<-mutate(trials,z_DE=((DE-mean(DE))/sd(DE)))
trials<-mutate(trials,z_OH=((OH-mean(OH))/sd(OH)))
trials<-mutate(trials,z_DOH=((DOH-mean(DOH))/sd(DOH)))
trials<-mutate(trials,z_OR=((OR-mean(OR))/sd(OR)))
trials<-mutate(trials,z_DOR=((DOR-mean(DOR))/sd(DOR)))
trials<-mutate(trials,z_OE=((OE-mean(OE))/sd(OE)))
trials<-mutate(trials,z_DOE=((DOE-mean(DOE))/sd(DOE)))
trials<-mutate(trials,z_HR=((HR-mean(HR))/sd(HR)))
trials<-mutate(trials,z_DHR=((DHR-mean(DHR))/sd(DHR)))
trials<-mutate(trials,z_HE=((HE-mean(HE))/sd(HE)))
trials<-mutate(trials,z_DHE=((DHE-mean(DHE))/sd(DHE)))
trials<-mutate(trials,z_RE=((RE-mean(RE))/sd(RE)))
trials<-mutate(trials,z_DRE=((DRE-mean(DRE))/sd(DRE)))
trials<-mutate(trials,z_OHR=((OHR-mean(OHR))/sd(OHR)))
trials<-mutate(trials,z_HR=((HR-mean(HR))/sd(HR)))
trials<-mutate(trials,z_OHE=((OHE-mean(OHE))/sd(OHE)))
trials<-mutate(trials,z_DOHE=((DOHE-mean(DOHE))/sd(DOHE)))
trials<-mutate(trials,z_HRE=((HRE-mean(HRE))/sd(HRE)))
trials<-mutate(trials,z_DHRE=((DHRE-mean(DHRE))/sd(DHRE)))
trials<-mutate(trials,z_ALL=((ALL-mean(ALL))/sd(ALL)))
trials<-mutate(trials,z_DALL=((DALL-mean(DALL))/sd(DALL)))
#Repeat for trials_no_alaska
trials_no_alaska<-mutate(trials_no_alaska,z_C=((C-mean(C))/sd(C)))
trials_no_alaska<-mutate(trials_no_alaska,z_DC=((DC-mean(DC))/sd(DC)))
trials_no_alaska<-mutate(trials_no_alaska,z_O=((O-mean(O))/sd(O)))
trials_no_alaska<-mutate(trials_no_alaska,z_DO=((DO-mean(DO))/sd(DO)))
trials_no_alaska<-mutate(trials_no_alaska,z_H=((H-mean(H))/sd(H)))
trials_no_alaska<-mutate(trials_no_alaska,z_DH=((DH-mean(DH))/sd(DH)))
trials_no_alaska<-mutate(trials_no_alaska,z_E=((E-mean(E))/sd(E)))
trials_no_alaska<-mutate(trials_no_alaska,z_DE=((DE-mean(DE))/sd(DE)))
trials_no_alaska<-mutate(trials_no_alaska,z_OH=((OH-mean(OH))/sd(OH)))
trials_no_alaska<-mutate(trials_no_alaska,z_DOH=((DOH-mean(DOH))/sd(DOH)))
trials_no_alaska<-mutate(trials_no_alaska,z_OR=((OR-mean(OR))/sd(OR)))
trials_no_alaska<-mutate(trials_no_alaska,z_DOR=((DOR-mean(DOR))/sd(DOR)))
trials_no_alaska<-mutate(trials_no_alaska,z_OE=((OE-mean(OE))/sd(OE)))
trials_no_alaska<-mutate(trials_no_alaska,z_DOE=((DOE-mean(DOE))/sd(DOE)))
191

trials_no_alaska<-mutate(trials_no_alaska,z_HR=((HR-mean(HR))/sd(HR)))
trials_no_alaska<-mutate(trials_no_alaska,z_DHR=((DHR-mean(DHR))/sd(DHR)))
trials_no_alaska<-mutate(trials_no_alaska,z_HE=((HE-mean(HE))/sd(HE)))
trials_no_alaska<-mutate(trials_no_alaska,z_DHE=((DHE-mean(DHE))/sd(DHE)))
trials_no_alaska<-mutate(trials_no_alaska,z_RE=((RE-mean(RE))/sd(RE)))
trials_no_alaska<-mutate(trials_no_alaska,z_DRE=((DRE-mean(DRE))/sd(DRE)))
trials_no_alaska<-mutate(trials_no_alaska,z_OHR=((OHR-mean(OHR))/sd(OHR)))
trials_no_alaska<-mutate(trials_no_alaska,z_HR=((HR-mean(HR))/sd(HR)))
trials_no_alaska<-mutate(trials_no_alaska,z_OHE=((OHE-mean(OHE))/sd(OHE)))
trials_no_alaska<-mutate(trials_no_alaska,z_DOHE=((DOHEmean(DOHE))/sd(DOHE)))
trials_no_alaska<-mutate(trials_no_alaska,z_HRE=((HRE-mean(HRE))/sd(HRE)))
trials_no_alaska<-mutate(trials_no_alaska,z_DHRE=((DHREmean(DHRE))/sd(DHRE)))
trials_no_alaska<-mutate(trials_no_alaska,z_ALL=((ALL-mean(ALL))/sd(ALL)))
trials_no_alaska<-mutate(trials_no_alaska,z_DALL=((DALLmean(DALL))/sd(DALL)))
#Positive Controls
P_Controls<-mutate(P_Controls,z_C=((PC_C-mean(PC_C))/sd(PC_C)))
P_Controls<-mutate(P_Controls,z_DC=((PC_DC-mean(PC_DC))/sd(PC_DC)))
P_Controls<-mutate(P_Controls,z_O=((PC_O-mean(PC_O))/sd(PC_O)))
P_Controls<-mutate(P_Controls,z_DO=((PC_DO-mean(PC_DO))/sd(PC_DO)))
P_Controls<-mutate(P_Controls,z_H=((PC_H-mean(PC_H))/sd(PC_H)))
P_Controls<-mutate(P_Controls,z_DH=((PC_DH-mean(PC_DH))/sd(PC_DH)))
P_Controls<-mutate(P_Controls,z_E=((PC_E-mean(PC_E))/sd(PC_E)))
P_Controls<-mutate(P_Controls,z_DE=((PC_DE-mean(PC_DE))/sd(PC_DE)))
P_Controls<-mutate(P_Controls,z_OH=((PC_OH-mean(PC_OH))/sd(PC_OH)))
P_Controls<-mutate(P_Controls,z_DOH=((PC_DOH-mean(PC_DOH))/sd(PC_DOH)))
P_Controls<-mutate(P_Controls,z_OR=((PC_OR-mean(PC_OR))/sd(PC_OR)))
P_Controls<-mutate(P_Controls,z_DOR=((PC_DOR-mean(PC_DOR))/sd(PC_DOR)))
P_Controls<-mutate(P_Controls,z_OE=((PC_OE-mean(PC_OE))/sd(PC_OE)))
P_Controls<-mutate(P_Controls,z_DOE=((PC_DOE-mean(PC_DOE))/sd(PC_DOE)))
P_Controls<-mutate(P_Controls,z_HR=((PC_HR-mean(PC_HR))/sd(PC_HR)))
P_Controls<-mutate(P_Controls,z_DHR=((PC_DHR-mean(PC_DHR))/sd(PC_DHR)))
P_Controls<-mutate(P_Controls,z_HE=((PC_HE-mean(PC_HE))/sd(PC_HE)))
P_Controls<-mutate(P_Controls,z_DHE=((PC_DHE-mean(PC_DHE))/sd(PC_DHE)))
P_Controls<-mutate(P_Controls,z_RE=((PC_RE-mean(PC_RE))/sd(PC_RE)))
P_Controls<-mutate(P_Controls,z_DRE=((PC_DRE-mean(PC_DRE))/sd(PC_DRE)))
P_Controls<-mutate(P_Controls,z_OHR=((PC_OHR-mean(PC_OHR))/sd(PC_OHR)))
P_Controls<-mutate(P_Controls,z_DOHR=((PC_DOHRmean(PC_DOHR))/sd(PC_DOHR)))
P_Controls<-mutate(P_Controls,z_OHE=((PC_OHE-mean(PC_OHE))/sd(PC_OHE)))
P_Controls<-mutate(P_Controls,z_DOHE=((PC_DOHEmean(PC_DOHE))/sd(PC_DOHE)))
P_Controls<-mutate(P_Controls,z_HRE=((PC_HRE-mean(PC_HRE))/sd(PC_HRE)))
192

P_Controls<-mutate(P_Controls,z_DHRE=((PC_DHREmean(PC_DHRE))/sd(PC_DHRE)))
P_Controls<-mutate(P_Controls,z_ALL=((PC_ALL-mean(PC_ALL))/sd(PC_ALL)))
P_Controls<-mutate(P_Controls,z_DALL=((PC_DALLmean(PC_DALL))/sd(PC_DALL)))
#Negative Controls
N_Controls<-mutate(N_Controls,z_C=((NC_C-mean(NC_C))/sd(NC_C)))
N_Controls<-mutate(N_Controls,z_DC=((NC_DC-mean(NC_DC))/sd(NC_DC)))
N_Controls<-mutate(N_Controls,z_O=((NC_O-mean(NC_O))/sd(NC_O)))
N_Controls<-mutate(N_Controls,z_DO=((NC_DO-mean(NC_DO))/sd(NC_DO)))
N_Controls<-mutate(N_Controls,z_H=((NC_H-mean(NC_H))/sd(NC_H)))
N_Controls<-mutate(N_Controls,z_DH=((NC_DH-mean(NC_DH))/sd(NC_DH)))
N_Controls<-mutate(N_Controls,z_E=((NC_E-mean(NC_E))/sd(NC_E)))
N_Controls<-mutate(N_Controls,z_DE=((NC_DE-mean(NC_DE))/sd(NC_DE)))
N_Controls<-mutate(N_Controls,z_OH=((NC_OH-mean(NC_OH))/sd(NC_OH)))
N_Controls<-mutate(N_Controls,z_DOH=((NC_DOHmean(NC_DOH))/sd(NC_DOH)))
N_Controls<-mutate(N_Controls,z_OR=((NC_OR-mean(NC_OR))/sd(NC_OR)))
N_Controls<-mutate(N_Controls,z_DOR=((NC_DOR-mean(NC_DOR))/sd(NC_DOR)))
N_Controls<-mutate(N_Controls,z_OE=((NC_OE-mean(NC_OE))/sd(NC_OE)))
N_Controls<-mutate(N_Controls,z_DOE=((NC_DOE-mean(NC_DOE))/sd(NC_DOE)))
N_Controls<-mutate(N_Controls,z_HR=((NC_HR-mean(NC_HR))/sd(NC_HR)))
N_Controls<-mutate(N_Controls,z_DHR=((NC_DHR-mean(NC_DHR))/sd(NC_DHR)))
N_Controls<-mutate(N_Controls,z_HE=((NC_HE-mean(NC_HE))/sd(NC_HE)))
N_Controls<-mutate(N_Controls,z_DHE=((NC_DHE-mean(NC_DHE))/sd(NC_DHE)))
N_Controls<-mutate(N_Controls,z_RE=((NC_RE-mean(NC_RE))/sd(NC_RE)))
N_Controls<-mutate(N_Controls,z_DRE=((NC_DRE-mean(NC_DRE))/sd(NC_DRE)))
N_Controls<-mutate(N_Controls,z_OHR=((NC_OHR-mean(NC_OHR))/sd(NC_OHR)))
N_Controls<-mutate(N_Controls,z_DOHR=((NC_DOHRmean(NC_DOHR))/sd(NC_DOHR)))
N_Controls<-mutate(N_Controls,z_OHE=((NC_OHE-mean(NC_OHE))/sd(NC_OHE)))
N_Controls<-mutate(N_Controls,z_DOHE=((NC_DOHEmean(NC_DOHE))/sd(NC_DOHE)))
N_Controls<-mutate(N_Controls,z_HRE=((NC_HRE-mean(NC_HRE))/sd(NC_HRE)))
N_Controls<-mutate(N_Controls,z_DHRE=((NC_DHREmean(NC_DHRE))/sd(NC_DHRE)))
N_Controls<-mutate(N_Controls,z_ALL=((NC_ALL-mean(NC_ALL))/sd(NC_ALL)))
N_Controls<-mutate(N_Controls,z_DALL=((NC_DALLmean(NC_DALL))/sd(NC_DALL)))

####################
#Write Z scores out#
####################
193

#Split trials into 3
trialz1<-select(trials,test_sites,z_C:z_DOH)
trialz2<-select(trials,test_sites,z_OR:z_DRE)
trialz3<-select(trials,test_sites,z_OHR:z_DALL)
#split trials nno alaska into 3
trialnaz1<-select(trials_no_alaska,test_sites,z_C:z_DOH)
trialnaz2<-select(trials_no_alaska,test_sites,z_OR:z_DRE)
trialnaz3<-select(trials_no_alaska,test_sites,z_OHR:z_DALL)
#Split positive controls into 3
pconz1<-select(P_Controls,PC_Test_Sites,z_C:z_DOH)
pconz2<-select(P_Controls,PC_Test_Sites,z_OR:z_DRE)
pconz3<-select(P_Controls,PC_Test_Sites,z_OHR:z_DALL)
#split negative controls into 3
nconz1<-select(N_Controls,NC_Test_Sites,z_C:z_DOH)
nconz2<-select(N_Controls,NC_Test_Sites,z_OR:z_DRE)
nconz3<-select(N_Controls,NC_Test_Sites,z_OHR:z_DALL)
#Write trials out
stargazer(trialz1,digits = 3,summary=FALSE,type="html", out = "Trials Z Table 1.doc")
stargazer(trialz2,digits = 3,summary=FALSE,type="html", out = "Trials Z Table 2.doc")
stargazer(trialz3,digits = 3,summary=FALSE,type="html", out = "Trials Z Table 3.doc")
#write no alaska out
stargazer(trialnaz1,digits = 3,summary=FALSE,type="html", out = "Trials No alaska Z
Table 1.doc")
stargazer(trialnaz2,digits = 3,summary=FALSE,type="html", out = "Trials NO Alaska Z
Table 2.doc")
stargazer(trialnaz3,digits = 3,summary=FALSE,type="html", out = "Trials No Alaska Z
Table 3.doc")
#Pos out
stargazer(pconz1,digits = 3,summary=FALSE,type="html", out = "Positive Control Z
Table 1.doc")
stargazer(pconz2,digits = 3,summary=FALSE,type="html", out = "Positive Control Z
Table 2.doc")
stargazer(pconz3,digits = 3,summary=FALSE,type="html", out = "Positive Control Z
Table 3.doc")

194

#Neg Out
stargazer(nconz1,digits = 3,summary=FALSE,type="html", out = "Negative Control Z
Table 1.doc")
stargazer(nconz2,digits = 3,summary=FALSE,type="html", out = "Negative Control Z
Table 2.doc")
stargazer(nconz3,digits = 3,summary=FALSE,type="html", out = "Negative Control Z
Table 3.doc")
########
#ANOVAS#
########
#Trials-Nest projections
site_anova eles+Miami+Mobile+New_Orleans+New_York+Pensacola+Philadelphia+Port_Charlotte
+Portland_ME+Portland_OR+Providence+San_Francisco+Savannnah+SaintJohn+St_Pet
ersurg+Seattle+Vancouver,data=trials_by_site)

#TRials -nest density
mean_anova mu+Jacksonville_mu+Los_Angeles_mu+Miami_mu+Mobile_mu+New_Orleans_mu+Ne
w_York_mu+Pensacola_mu+Philadelphia_mu+Port_Charlotte_mu+Portland_ME_mu+P
ortland_OR_mu+Providence_mu+San_Francisco_mu+Savannnah_mu+SaintJohn_mu+St
_Petersurg_mu+Seattle_mu+Vancouver_mu)
#summarize
summary(site_anova)
summary(mean_anova)
summary(pos_anova)
summary(mean_pos_anova)
summary(neg_anova)
summary(mean_neg_anova)

#########################
#Other Statistical Tests#
#########################
195

#correlation tests
#Try PCA
pca<-prcomp(trials[,2:35])
summary(pca)
biplot(pca)
plot(pca,type='l')#elbow plot
########
#Graphs#
########
#graph HPD by H
hlin<-lm(H~hpop,data=trials)
summary(hlin)
trials$h_pred<-predict(hlin)
ggplot(trials,aes(hpop,H))+geom_point()+geom_path(aes(hpop,h_pred))+theme_classic()
#graph HPD by L_area
alin<-lm(hpop~L_Area,data=trials)
summary(alin)
trials$a_pred<-predict(alin)
ggplot(trials,aes(L_Area,hpop))+geom_point()+geom_path(aes(hpop,h_pred))+theme_cl
assic()+xlab("Land Area (Square Map Units)")+ylab("Human Population Density Per
Square Map Unit")+ggtitle("Regression of Human Population Density\n by Land Area")

#GGPLOT above-look at hpop
trials$PC1<-(pca$x[,1])
trials$PC2<-(pca$x[,2])
ggplot(trials,aes(PC1,PC2,color=hpop))+geom_point()+
stat_ellipse()+theme_classic()
#look at p_occur
ggplot(trials,aes(PC1,PC2,color=p_occur))+geom_point()+
stat_ellipse()+theme_classic()
#look at Land Area
ggplot(trials,aes(PC1,PC2,color=L_Area))+geom_point()+
stat_ellipse()+theme_classic()
#Look at Elevation
ggplot(trials,aes(PC1,PC2,color=Elev))+geom_point()+
196

stat_ellipse()+theme_classic()
#Look at river presece
ggplot(trials,aes(PC1,PC2,color=riv_pres))+geom_point()+
stat_ellipse()+theme_classic()
#O
ggplot(trials,aes(PC1,PC2,color=O))+geom_point()+
stat_ellipse()+theme_classic()
#DO
ggplot(trials,aes(PC1,PC2,color=DO))+geom_point()+
stat_ellipse()+theme_classic()
#How to Boxplot with GGPLot
#Try without
#TRials
melt_trials<-melt(trials_only)
boxplot(data=melt_trials,value~variable)
ggplot(melt_trials)+geom_boxplot(aes(x=variable,y=value))+theme_classic()+xlab("Tria
l Model Statement")+ylab("Projection (Nests)")+ggtitle("Nest Projections after 10
Years",subtitle="Boxplot per Model Statement")
#Poscons
P_only<-select(P_Controls,PC_Test_Sites:PC_DALL)
melt_P<-melt(P_only)
ggplot(melt_P)+geom_boxplot(aes(x=variable,y=value))+theme_classic()+xlab("Trial
Model Statement")+ylab("Projection (Nests)")+ggtitle("Nest Projections after 10 Years\n
Positive Controls",subtitle="Boxplot per Model Statement")
#Neg_Cons
N_only<-select(N_Controls,NC_Test_Sites:NC_DALL)
melt_N<-melt(N_only)
ggplot(melt_N)+geom_boxplot(aes(x=variable,y=value))+theme_classic()+xlab("Trial
Model Statement")+ylab("Projection (Nests)")+ggtitle("Nest Projections after 10 Years\n
Negative Controls",subtitle="Boxplot per Model Statement")
##############
#Impact Phase#
##############
#IMPACT PHAsE DAtaframe
State
197

ME","MI","MN","MS","MO","MT","NE","NJ","NY","NC","ND","OH","OR","PA","SC
","SD","TN","TX","UT","VT","VA","WA","WV","WI","WY")
Product 58,9435,4530,1882,1836,24012,5266,2861,9608,1957,63636,3416,5897,2502,1665,2776
2,1343,16711,1724,1314,1003,7796,924,8221,3287)
Suitable<-c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,1,0,1,1,1,1,1,1,1,0,1)
honey_by_state<-data.frame(State,Product,Suitable)
honey_by_state<-mutate(honey_by_state,impact=product*suitable*0.05)
sum(honey_by_state$impact)
stargazer(honey_by_state,digits = 3,summary=FALSE,type="html", out = "Honey
table.doc")
#######################################################
#
Fin
########################################################
#Read in Data
thesis_means <- read_excel(“thesis_means.xlsx”)
View(thesis_means)
thes <-thesis_means #rename for my convenience
#For some bizarre reason, Rstudio thinks
#my numbers are strings and I can’t convert
#them to numerics. Must add manually :-[
#Graph Data in GGPLot
#SEM
ggplot(thes,aes(trial_num,mean2,color=char))+geom_point()+geom_errorbar(aes(ymin=
mean2-sd, ymax=mean2+sd))+theme_classic()+xlab(“Trial Number”)+ylab(“Projection
(nests)”)+ggtitle(“Mean Nest Projection per Trial”,subtitle = “With Standard Error”)
###Statistical tests
##T-test of dontinuous/ descrete trials
#filter dfs by character
thes_con <- filter(thes,char==”contin”)
thes_des <- filter(thes,char==”discrete”)
#run t-test
t.test(thes_con$mean2,thes_des$mean2)
#boxplot of means
boxplot(thes_con$mean2,thes_des$mean2)
#Vectors of OO,DOO,OO w/ Control, DOO w/ control

198

con_spread 4,306.67826269490524,240.0589550085555,251.6867671389566,172.97333262133998,
264.37481038074105,183.82403385229242,245.9127573076799,235.29588615787273,1
77.86955686325135,309.19070431258274,255.05855715033513,180.0798023205787,31
1.96453600535045,295.0904953434762,164.21253307746161,218.73098495499403,242
.39631115955086,167.33252336332365,5.454347919454735,178.7574604505544)
dis_spread 431.69932655938777,340.5484108730364,300.5638580045394,252.74088335089925,35
2.9639052201521,258.0899334367345,347.65534688022643,346.4655111126585,260.9
7389396873314,431.916485144801,338.44077487278304,1.0,439.82182718578474,408.
9963809402848,244.97832716943594,307.97034829069423,296.8565879484672,247.11
31013994907,0.13865526681529508,1.0)
con_spread2 4,306.67826269490524,240.0589550085555,251.6867671389566,172.97333262133998,
264.37481038074105,183.82403385229242,245.9127573076799,235.29588615787273,1
77.86955686325135,309.19070431258274,255.05855715033513,180.0798023205787,31
1.96453600535045,295.0904953434762,164.21253307746161,218.73098495499403,242
.39631115955086,167.33252336332365,5.454347919454735,178.7574604505544,.0000
00262,20.199,385.929,439.680,.0000000000000000005079)
dis_spread2 431.69932655938777,340.5484108730364,300.5638580045394,252.74088335089925,35
2.9639052201521,258.0899334367345,347.65534688022643,346.4655111126585,260.9
7389396873314,431.916485144801,338.44077487278304,1.0,439.82182718578474,408.
9963809402848,244.97832716943594,307.97034829069423,296.8565879484672,247.11
31013994907,0.13865526681529508,1.0,.0000002626994069466892,20.1992589820072
65,385.9297073145402,.0000000000000000005079264514609942,439.68015996791206
)
#t.test of OO*DOO
t.test(con_spread,dis_spread)
#t.test for OO*DOO with controls
t.test(con_spread2,dis_spread2)
#Boxplots
boxplot(con_spread,dis_spread)
boxplot(con_spread2,dis_spread2)

B.2 Python Script for Data Processing and Statistical Analysis

199

# Import Modules #
import funx as f
import mfunx as m
import ufunx as u

## Matrices ##

test_data_density=[[“Anchorage AK”,[287, 301]],[“Baltimore MD”, [506,
1033]],[“Biloxi MS”, [595, 911]], [“Boston MA”,[476, 1089]],[“Charleston SC”, [572,
1000]],[“Houston TX”,[602, 846]],[“Jacksonville FL”, [596, 983]],[“Los Angeles CA”,
[559, 617]],[“Miami FL”, [642, 997]],[“Mobile AL”, [593, 918]],[“New Orleans
LA”,[600, 899]],[“New York NY”, [492, 1059]],[“Pensacola FL”, [595,
927]],[“Philadelphia PA”,[500, 1048]], [“Port Charlotte-Ft. Meyers FL”,[632,
981]],[“Portland ME”, [463, 1097]],[“Portland OR”, [444, 573]], [“Providence RI”,[481,
1085]], [“San Fransisco CA”,[522, 575]],[“Savannah GA”,[578, 989]],[“Saint John
NB”,[447, 1139]],[“St. Petersburg-Tampa FL”,[620, 975]],[“Seattle WA”, [422,
576]],[“Vancouver BC”,[407,568]]]
test_data_zscore=[[“Anchorage AK”,[287, 301]],[“Baltimore MD”, [506, 1033]],[“Biloxi
MS”, [595, 911]], [“Boston MA”,[476, 1089]],[“Charleston SC”, [572, 1000]],[“Houston
TX”,[602, 846]],[“Jacksonville FL”, [596, 983]],[“Los Angeles CA”, [559,
617]],[“Miami FL”, [642, 997]],[“Mobile AL”, [593, 918]],[“New Orleans LA”,[600,
899]],[“New York NY”, [492, 1059]],[“Pensacola FL”, [595, 927]],[“Philadelphia
PA”,[500, 1048]], [“Port Charlotte-Ft. Meyers FL”,[632, 981]],[“Portland ME”, [463,
1097]],[“Portland OR”, [444, 573]], [“Providence RI”,[481, 1085]], [“San Fransisco
CA”,[522, 575]],[“Savannah GA”,[578, 989]],[“Saint John NB”,[447, 1139]],[“St.
Petersburg-Tampa FL”,[620, 975]],[“Seattle WA”, [422, 576]],[“Vancouver
BC”,[407,568]]]

control_data_density=[[“Albuquerque NM”,[549, 734]],[“Barry County MI”,[475,
946]],[“Montreal QC”,[448,1068]],[“St Paul MN”,[450,869]],[“Walhalla
SC”,[555,966]]]

200

control_data_zscore=[[“Albuquerque NM”,[549, 734]],[“Barry County MI”,[475,
946]],[“Montreal QC”,[448,1068]],[“St Paul MN”,[450,869]],[“Walhalla
SC”,[555,966]]]
control_data_raw_z=[[“Albuquerque NM”,[549, 734]],[“Barry County MI”,[475,
946]],[“Montreal QC”,[448,1068]],[“St Paul MN”,[450,869]],[“Walhalla
SC”,[555,966]]]

test_means=[]
control_means=[]

test_sd=[]
control_sd=[]

test_range=[]
control_range=[]

## Trials ##
my_data=[[“Discrete_Statistics_Data_Control.asc”,”Discrete_Contr_Statistics_Data_Con
trol.asc”],
[“Discrete_Statistics_Data_Occur_Final.asc”,”Discrete_Contr_Statistics_Data_Occur_Fi
nal.asc”],
[“Discrete_Statistics_Data_Pop_Final.asc”,”Discrete_Contr_Statistics_Data_Pop_Final.a
sc”],
[“Discrete_Statistics_Data_River.asc”,”Discrete_Contr_Statistics_Data_River.asc”],
[“Discrete_Statistics_Data_Elev.asc”,”Discrete_Contr_Statistics_Data_Elev.asc”],
[“Discrete_Statistics_Data_Occur_Pop.asc”,”Discrete_Contr_Statistics_Data_Occur_Pop
.asc”],
201

[“Discrete_Statistics_Data_Occur_River.asc”,”Discrete_Contr_Statistics_Data_Occur_Ri
ver.asc”],
[“Discrete_Statistics_Data_Occur_Elev.asc”,”Discrete_Contr_Statistics_Data_Occur_Ele
v.asc”],
[“Discrete_Statistics_Data_Pop_River.asc”,”Discrete_Contr_Statistics_Data_Pop_River.
asc”],
[“Discrete_Statistics_Data_Pop_Elev.asc”,”Discrete_Contr_Statistics_Data_Pop_Elev.as
c”],
[“Discrete_Statistics_Data_River_Elev.asc”,”Discrete_Contr_Statistics_Data_River_Elev
.asc”],
[“Discrete_Statistics_Data_Occur_Pop_River.asc”,”Discrete_Contr_Statistics_Data_Occ
ur_Pop_River.asc”],
[“Discrete_Statistics_Data_Occur_Pop_Elev.asc”,”Discrete_Contr_Statistics_Data_Occu
r_Pop_Elev.asc”],
[“Discrete_Statistics_Data_Pop_River_Elev.asc”,”Discrete_Contr_Statistics_Data_Pop_
River_Elev.asc”],
[“Discrete_Statistics_Data_Occur_Pop_River_Elev.asc”,”Discrete_Contr_Statistics_Data
_Occur_Pop_River_Elev.asc”]]

## Loop ##
for tr in my_data:
dat_file=open(tr[0],”r”)
dat_lin=dat_file.readlines()
dat_file.close()

202

contr_file=open(tr[1],”r”)
contr_lin=contr_file.readlines()
contr_file.close()

##############
#Process Data#
##############
#Pull Data to Matrix
dat_mat=[]#open data matrix
contr_mat=[] #control data matrix
for I in range(0,72,3): #this is to start over: o,3,etc. compute new total
dat_cell=[]#open data row
dat_cell.append(dat_lin[i])#append title to row
dat_cell.append(dat_lin[i+1])#append population to row
dat_cell.append(dat_lin[i+2])#append nest density at origin to row
dat_mat.append(dat_cell)#append row to matrix

for I in range(0,15,3):#change middle # to total #
contr_cell=[]
contr_cell.append(contr_lin[i])#append title to row
contr_cell.append(contr_lin[i+1])#append population to row
contr_cell.append(contr_lin[i+2])#append nest density at origin to row
contr_mat.append(contr_cell)#append row to matrix

#convert number strings to floats
#test data
for I in dat_mat:
i[1]=float(i[1])#strings to floats without additional steps
203

i[2]=float(i[2])

#control data
for I in contr_mat:
i[1]=float(i[1])
i[2]=float(i[2])
#Process coordinates
for I in dat_mat:
tit=i[0]#title string
tit_cut=u.NumbersFromString(tit,”_”)#numbers and “_”
tit_list=u.RobustSplit(tit_cut,”_”)#split at “_”
tit_x=tit_list[0]
x_num=int(tit_x)
tit_y=tit_list[1]
y_num=int(tit_y)
tit_coord=[x_num,y_num]
i.append(tit_coord)
#print(dat_mat[0])

##

tit_coord=[int(tit_list[0][0]),int(tit_list[1][0])]#pull 204onca

##

print(tit_coord)

##

#print(“ “)

##

i[0]=tit_coord#change 1st element to coord

##
for I in contr_mat:
tit=i[0]
tit_cut=u.NumbersFromString(tit,”_”)
tit_list=u.RobustSplit(tit_cut,”_”)
204

tit_x=tit_list[0]
x_num=int(tit_x)
tit_y=tit_list[1]
y_num=int(tit_y)
tit_coord=[x_num,y_num]
i.append(tit_coord)
##

tit_coord=[int(tit_list[0][0]),int(tit_list[1][0])]

##

print(tit_coord)

##

i[0]=tit_coord

###########################
## Compute Summary Stats ##
###########################
#pull population data to one list
#test data
p_list=[]
for I in dat_mat:
p_list.append(i[1])
#control list
cp_list=[]
for I in contr_mat:
cp_list.append(i[1])

#Compute Summary Statistics
pop_mean=f.Mu(p_list)
contr_mean=f.Mu(cp_list)
pop_sd=f.SD(pop_mean,p_list)
contr_sd=f.SD(contr_mean,cp_list)
205

#Range
pop_range=f.MaxMinRange(p_list)
contr_range=f.MaxMinRange(cp_list)
test_range.append(pop_range)
control_range.append(contr_range)

#compute z Score
try:
pop_z=f.Z_Score(p_list)
except:
pop_z=”NA”

try:
contr_z=f.Z_Score(cp_list)
contr_raw_z=f.raw_z(cp_list,pop_mean,pop_sd)
except:
contr_z=”NA”
contr_raw_z=”NA”

##########################
## Write Stats to Lists ##
##########################
test_means.append(pop_mean)
control_means.append(contr_mean)
test_sd.append(pop_sd)
control_sd.append(contr_sd)

206

#write population vals to matrix
for j in dat_mat:
for k in test_data_density:
if j[3]==k[1]:
k.append(j[1])

#write control vals to matrix
for j in contr_mat:
for k in control_data_density:
if j[3]==k[1]:
k.append(j[1])
#write population z scores to matrix
if pop_z!=”NA”:
lmax=len(dat_mat)
for I in range(lmax):
dat_mat[i].append(pop_z[i])
for j in dat_mat:
for k in test_data_zscore:
if j[3]==k[1]:
k.append(j[2])
if pop_z==”NA”:
for I in test_data_zscore:
i.append(“NA”)

#write control z_score to list
if contr_z!=”NA”:
l2max=len(contr_mat)
for I in range(l2max):
207

contr_mat[i].append(contr_raw_z[i])
contr_mat[i].append(contr_z[i])
for j in contr_mat:
for k in control_data_zscore:
if j[3]==k[1]:
k.append(j[2])
for h in control_data_raw_z:
if j[3]==h[1]:
h.append(j[2])
if contr_z==”NA”:
for I in control_data_zscore:
i.append(“NA”)
for I in control_data_raw_z:
i.append(“NA”)

## Write Data to Out ##

outfil=open(“Summary_Stats_Discrete_Data.asc”,”w”)
outfil.write(“Summary Statistics: Discrete Data \n”)
outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“Test Simulations – Population Values \n”)
outfil.write(“\n”)
for I in test_data_density:
lin_str=””
for k in i:
lin_str=lin_str+str(k)+” “
208

lin_str=lin_str+”\n”
outfil.write(lin_str)
outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“Test Simulation – Population Z Scores \n”)
outfil.write(“\n”)
for I in test_data_zscore:
lin_str=””
for k in i:
lin_str=lin_str+str(k)+” “
lin_str=lin_str+”\n”
outfil.write(lin_str)
outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“Test Simulation – Trial Means”)
outfil.write(“\n”)
mean_str=””
for I in test_means:
mean_str=mean_str+str(i)+” “
mean_str=mean_str+”\n”
outfil.write(mean_str)
outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“Test Simulations – Trial Standard Deviations”)
outfil.write(“\n”)
209

sd_str=””
for I in test_sd:
sd_str=sd_str+str(i)+” “
sd_str=sd_str+”\n”
outfil.write(sd_str)
outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“\n”)

outfil.write(“Test Simulation – Trial Range”)
outfil.write(“\n”)
tr_str=””
for I in test_range:
tr_str=tr_str+str(i)+” “
tr_str=tr_str+”\n”
outfil.write(tr_str)
outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“Control Simulations – Population Values \n”)
outfil.write(“\n”)
for I in control_data_density:
lin_str=””
for k in i:
lin_str=lin_str+str(k)+” “
lin_str=lin_str+”\n”
outfil.write(lin_str)
outfil.write(“\n”)
210

outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“Control Simulations – Population Z Scores \n”)
outfil.write(“\n”)
for I in control_data_zscore:
lin_str=””
for k in i:
lin_str=lin_str+str(k)+” “
lin_str=lin_str+”\n”
outfil.write(lin_str)
outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“Control Simulations – Z Scores Relative to Test Distribution \n”)
outfil.write(“\n”)
for I in control_data_raw_z:
lin_str=””
for k in i:
lin_str=lin_str+str(k)+” “
lin_str=lin_str+”\n”
outfil.write(lin_str)
outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“Control Simulations – Trial Means \n”)
outfil.write(“\n”)
cmean_str=””
for I in control_means:
211

cmean_str=cmean_str+str(i)+” “
cmean_str=cmean_str+”\n”
outfil.write(cmean_str)
outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“Control Simulations – Trial Standard Deviations \n”)
outfil.write(“\n”)
csd_str=””
for I in control_sd:
csd_str=csd_str+str(i)+” “
csd_str=csd_str+”\n”
outfil.write(csd_str)
outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“Control Simulation – Range \n”)
outfil.write(“\n”)
cr_str=””
for I in control_range:
cr_str=cr_str+str(i)+” “
cr_str=cr_str+”\n”
outfil.write(cr_str)
outfil.write(“\n”)
outfil.write(“\n”)
outfil.write(“\n”)

outfil.close()
212

APPENDIX C
RAW OUTPUT
C.1 Output 1: Population Projections (N10) for Each Trial in the Test Group. All
Projections are in nests. Table Produced in Stargazer (Hlavac 2018).
Trial
C
DC
O
DO
H
DH
R
DR
E

Anchorage Baltimore
AK
MD
Biloxi MS
11.179
0.173784
5.454
0.138655

9.755

7.649

Boston
MA
11.469

0.205841 0.220778 0.248942
273.275

196.919

244.18

387.7931 276.9595 344.2016

Charleston Houston
SC
TX
7.221

11.887

0.231726 0.247375
172.97

306.67

252.7409 431.6993

-4.137

14.627

-9.25

32.642

-5.488

45.56

1.19E-14

2.53E-05

3.34E-13

2.93E-05

1.65E-12

6.44E-06

24.115

28.776

18.784

42.979

17.881

48.751

2.897572 3.641763 3.034524

5.064218

7.69022

172.973

306.678

1.897087
197.641

273.275

196.919

244.18

DE

143.4174

OH

-7.054

14.627

-9.253

32.642

-5.488

45.56

8.32E-32

2.53E-05

3.34E-13

2.93E-05

1.65E-12

6.44E-06

-1.684

11.57

7.649

21.199

7.685

22.583

DOH
OR
DOR
OE
DOE
HR
DHR
HE
DHE
RE

0.004421
17.31
0.155001

387.7931 276.9595 344.2016

0.44378 0.561033 0.466011
153.327

110.652

137.626

154.8852 145.1704

169.635

252.7409 431.6993

0.78521 1.187544
97.473

172.23

144.1516 181.9393

22.599

28.776

18.784

42.979

17.881

48.751

1.17E-17

6.98E-08

4.05E-16

7.13E-08

1.66E-15

9.27E-09

-4.137

14.627

-9.253

32.642

-5.488

45.56

1.19E-14

2.53E-05

3.34E-13

2.93E-05

1.65E-12

6.44E-06

22.599

28.776

18.784

42.979

17.881

48.751

DRE

0.536682

2.897572 3.641763 3.034524

5.064218

7.69022

OHR

-6.91039

-11.1207

-7.75207

-8.68559

-9.77011

-4.60399

213

Trial

Anchorage Baltimore
AK
MD

Biloxi MS

Boston Charleston
MA
SC

DOHR

8.12E-35

6.98E-08

4.05E-16

OHE

-6.60267

3.547302

-9.45136 16.86926

-6.45654 21.85924

DOHE

2.09E-21

1.06E-08

6.15E-17

1.08E-08

2.52E-16

1.41E-09

HRE

-6.43265

-8.99565

-9.71923

-1.41667

-7.57574

-4.83308

DHRE

1.17E-17

6.98E-08

4.05E-16

7.13E-08

1.66E-15

9.27E-09

ALL

-6.91039

-11.1207

-9.77011

-4.60399

-7.75207

-8.68559

DALL

2.09E-21

1.06E-08

6.15E-17

1.08E-08

2.52E-16

1.41E-09

Miami FL

Mobile
AL

Trial
C
DC
O
DO
H
DH
R
DR
E
DE
OH
DOH
OR
DOR
OE

Los
Jacksonville Angeles
FL
CA
5.596

New York
NY

0.254671 0.250916 0.297334 0.261155 0.227386

0.224607

224.563

235.295

352.9639 300.5639 258.0899 347.6553 336.9733

346.4655

-13.66

183.824

10.918

New
Orleans
LA

9.27E-09

10.943

251.686

6.92

1.66E-15

10.944

264.37

5.363

7.13E-08

Houston
TX

245.912

99.88

42.727

-10.05

-4.105

85.861

1.70E-10 0.025087

8.53E-05

4.39E-12

2.50E-12

0.085882

17.357

51.277

92.18

24.083

9.713704 1.641003 1.936918 3.878029

11.7447

3.427349

224.563

235.295

352.9639 88.19749 258.0899 347.6553 336.9733

346.4655

80.481

264.374

-13.66

20.037

209.253

183.824

245.912

99.88

42.727

-10.05

-4.105

85.861

1.70E-10 0.024391

8.53E-05

4.39E-12

2.50E-12

0.085882

6.92

26.522

52.285

10.943

1.519089 0.169004 0.297334

0.59653

1.84934

0.526275

138.501

126.919

132.76

42.234

147.286

5.363

116.734

103.326

214

Trial

Jacksonville
FL

DOE

173.7094

HR

Los
Angeles
CA

New
Orleans
LA

New York
NY

16.9351 166.3445 175.5776 158.6246

158.8154

Miami FL

Mobile
AL

80.481

14.707

17.357

51.277

92.18

24.083

1.01E-11

2.46E-05

8.36E-08

4.57E-15

4.14E-13

9.21E-05

-13.66

99.869

42.727

-10.05

-4.105

85.861

1.70E-10 0.023642

8.53E-05

4.39E-12

2.50E-12

0.085882

17.357

51.277

92.18

24.083

DRE

9.713704 0.122799 1.936918 3.878029

11.7447

3.427349

OHR

-16.4539

-6.60625

-4.37538

-10.6001

-5.95496

-0.446

DOHR

1.01E-11

2.39E-05

8.36E-08

4.57E-15

4.14E-13

9.21E-05

OHE

-15.4974 53.96497

22.6569

-10.2623

-5.88075

48.43523

DOHE

1.53E-12

3.52E-06

1.27E-08

6.94E-16

6.28E-14

1.40E-05

HRE

-15.1797 0.267192

-1.26159

-10.5422

-4.2115

5.12773

DHRE

1.01E-11

2.32E-05

8.36E-08

4.57E-15

4.14E-13

9.21E-05

ALL

-16.4539

-6.60979

-4.37538

-10.6001

-5.95496

-0.446

DALL

1.53E-12

3.52E-06

1.27E-08

6.94E-16

6.28E-14

1.40E-05

DHR
HE
DHE
RE

Trial
C

80.481

14.707

Port
Pensacola Philadelphia Charlotte Portland Portland
FL
PA
FL
ME
OR
9.394

12.074

4.814

DC

0.243754

0.236423

0.25963

O

177.869

309.19

255.058

DO
H
DH
R

260.9739

431.9165 338.4408

12.538

Providence
RI

12.845

10.818

1 0.216503

0.30199

180.079

311.964

295.09

1 439.8218

408.9964

-5.255

32.625

-16.916

-2.317

21.505

1.81

2.06E-11

1.07E-05

1.72E-07

1

3.29E-09

2.05E-05

19.218

57.463

19.738

22.176

85.55

27.553
215

Trial
DR
E

Port
Pensacola Philadelphia Charlotte Portland
FL
PA
FL
ME
2.9929
177.869

2.721083 1.697571
309.19

255.058

1 2.673465
180.079

2.905003

311.192

295.09

1 225.5075

408.9964

DE

260.9739

OH

-5.255

32.625

-16.916

-2.317

21.505

1.81

2.06E-11

1.07E-05

1.72E-07

1

3.29E-09

2.05E-05

9.394

27.993

4.814

12.538

45.994

10.818

0.460736

0.416398

0.25963

1 0.408907

0.445128

100.665

173.624

141.966

DOH
OR
DOR
OE
DOE
HR

150.4554

431.9165 338.4408

Portland Providence
OR
RI

176.3095 173.2533

102.696

174.983

165.587

1 48.51785

204.2721

19.218

57.463

19.738

22.176

85.462

27.553

2.09E-14

2.91E-08

1.68E-10

1

5.85E-11

5.63E-08

-5.255

32.625

-16.916

-2.317

21.505

1.81

2.06E-11

1.07E-05

1.72E-07

1

3.29E-09

2.05E-05

RE

19.218

57.463

19.738

22.176

85.462

27.553

DRE

2.9929

1 0.676225

2.905003

OHR

-5.89621

-5.6428

-18.4536

2.54148

-2.2335

-13.58

DOHR

2.09E-14

2.91E-08

1.68E-10

1

5.85E-11

5.63E-08

2.40032 7.695108

-4.73652

DHR
HE
DHE

2.721083 1.697571

OHE

-5.50211

14.45903

-17.5556

DOHE

3.17E-15

4.41E-09

2.55E-11

HRE
DHRE

1

8.88E-12

8.54E-09

2.51784 5.563813

-12.5185

-5.8337

0.257453

-18.3252

2.09E-14

2.91E-08

1.68E-10

1

5.85E-11

5.63E-08

-2.2335

-13.58

8.88E-12

8.54E-09

ALL

-5.89621

-5.6428

-18.4536

2.54148

DALL

3.17E-15

4.41E-09

2.55E-11

1

216

Trial
C

San
Francisco Savannah Saint
CA
GA
John NB

St.
Petersburg Seattle
FL
WA

10.972

5.918

8.36

DC

0.214382

0.238596

1

O

164.212

240.058

178.757

244.9783

340.5484

1

26.827

-13.494

-3.734

1.818

16.415

21.795

2.15E-05

1.61E-12

1

8.49E-07

1.22E-05

1.74E-05

19.789

59.584

43.142

21.251

23.257

39.438

2.068973

4.253359

1

1.673355 1.897695

2.704244

164.212

240.058

178.757

DE

245.2357

340.5484

1

OH

26.827

-13.494

-3.734

1.818

16.415

21.795

2.15E-05

1.61E-12

1

8.49E-07

1.22E-05

1.74E-05

10.972

29.985

22.941

7.452

11.2

19.511

0.317655

0.654716

1

0.25616

0.29065

0.416373

93.438

134.173

100.84

135.239

123.439

72.276

126.9236

164.4033

1

163.3759 21.92372

16.16719

19.789

59.584

43.142

21.251

23.257

34.457

2.12E-08

2.69E-15

1

8.29E-10

1.23E-08

3.77E-07

26.827

-13.494

-3.734

1.818

16.415

21.795

2.15E-05

1.61E-12

1

8.49E-07

1.22E-05

1.74E-05

19.789

59.584

43.142

21.251

23.257

34.457

1.906817

4.253359

1

1.673355 0.233293

0.508665

-12.3778

-5.10318

-2.40642

8.29E-10

1.23E-08

3.77E-07

-4.57158 7.208964

9.387321

DO
H
DH
R
DR
E

DOH
OR
DOR
OE
DOE
HR
DHR
HE
DHE
RE
DRE
OHR

0.000849

-15.697

6.96362

DOHR

2.12E-08

2.69E-15

1

OHE

15.02639

-14.4626

-5.1781

7.452

Vancouver
BC

11.2

4.717

0.25616 0.184544

0.182227

242.396

218.73

167.332

296.8566 307.9703

247.1131

242.396

218.73

129.298

296.8566 113.0637

74.47554

217

Trial

San
Francisco Savannah
CA
GA

DOHE

3.22E-09

St.
Saint Petersburg
John NB
FL

Seattle Vancouver
WA
BC

4.09E-16

1

1.26E-10

1.86E-09

5.73E-08

1.7034

-15.5089

6.75021

-11.4349

-3.63927

2.833053

DHRE

2.12E-08

2.69E-15

1

8.29E-10

1.23E-08

3.77E-07

ALL

0.000849

-15.697

6.96362

-12.3778

-5.10318

-2.40642

DALL

3.22E-09

4.09E-16

1

1.26E-10

1.86E-09

5.73E-08

HRE

218

C.2 Output 2: Population Projections (N10) for Each Trial in the Positive Control Group.
All Projections are in nests. Table Produced in Stargazer (Hlavac 2018).
Trial

Montreal
QC

Walhalla
SC

Busan SK

Nerac FR

C

12.84304

12.84592

6.250625

12.84304

-1.35245

DC

0.21489

0.21489

0.263515

0.215509

0.711775

O

265.9033

311.9645

139.6254

311.9617

27.357

DO

385.9297

439.6802

177.3503

440.829

33.68451

H

-9.42872

-14.6894

37.73063

-14.6597

-4.25268

0

0

0.004721

0

0

37.254

104.951

47.6554

75.14869

0.46196

DR

4.205925

9.296599

5.778534

2.84269

3.732911

E

311.9617

306.896

146.6133

311.9617

27.357

DE

435.027

330.2139

215.9556

440.829

33.68451

OH

-9.58442

-14.6894

37.72569

-14.6597

-4.25268

0

0

0.003807

0

0

OR

14.39748

54.58461

26.07553

39.27415

-1.35245

DOR

0.568127

1.437427

0.429474

0.4349

0.711775

OE

158.6687

172.6959

80.37907

175.389

14.84971

DOE

132.1923

87.87648

91.73193

166.0678

26.60819

HR

-10.6915

-14.7422

14.46248

-14.7538

-4.25341

0

0

4.32E-05

0

0

-9.42872

-14.6894

37.73063

-14.6597

-4.25268

0

0

0.004721

0

0

RE

37.25407

104.3679

47.6554

75.14869

0.46196

DRE

4.051729

5.574616

5.778534

2.84269

3.732911

OHR

-12.6085

-14.7673

6.665106

-14.7757

-4.25352

0

0

3.68E-05

0

0

-11.9524

-14.7266

20.71365

-14.7115

-4.25295

DH
R

DOH

DHR
HE
DHE

DOHR
OHE

Tsushima City JP

219

Trial
DOHE
HRE
DHRE
ALL
DALL

Montreal
QC

Walhalla
SC

Busan SK

Nerac FR

Tsushima City JP

0

0

0.000639

0

0

-10.6915

-14.7422

14.46248

-14.7538

-4.25341

0

0

4.32E-05

0

0

-12.6085

-14.7673

6.665106

-14.7757

-4.25352

0

0

6.02E-06

0

0

220

C.3 Output 3: Population Projections (N10) for Each Trial in the Negative Control Group.
All Projections are in nests. Table Produced in Stargazer (cite).
Trial

Albuquerque NM

Barry County MI

12.84592

12.84592

12.84592

DC

0.21489

0.21489

0.21489

O

-9.40036

33.88079

-14.7457

DO

2.63E-07

20.19926

5.08E-19

H

1.549252

-13.1205

10.84489

0

0

1.53E-08

83.241

30.389

97.167

DR

2.622653

1.971025

5.824315

E

-14.8459

311.9645

311.9645

DE

0

439.6802

439.6802

OH

-14.8328

-14.3126

-14.8243

0

0

7.82E-29

OR

-3.66749

-1.22957

-2.99888

DOR

0.000719

0.030638

0.00095

OE

-14.8459

66.04125

13.45103

0

22.47677

0.230588

-10.2408

-14.4772

5.452217

0

0

6.15E-10

-14.8459

-13.1205

10.84489

0

0

1.53E-08

-14.8459

30.38966

97.16766

DRE

0

1.971025

5.824315

OHR

-14.1627

-14.6694

-12.4926

0

0

4.16E-30

-14.8459

-14.198

-11.8551

0

0

1.00E-13

C

DH
R

DOH

DOE
HR
DHR
HE
DHE
RE

DOHR
OHE
DOHE

St Paul MN

221

Trial

Albuquerque NM

Barry County MI

St Paul MN

HRE

-14.8459

-14.4772

5.452217

0

0

6.15E-10

-14.8459

-14.6694

-12.4926

0

0

1.00E-13

DHRE
ALL
DALL

222

C.4 Output 4: Mean Nest Density for Each Trial in the Test Group. All Projections are in
nests. Table Produced in Stargazer (Hlavac 2018).
Trial

Anchorage Baltimore
AK
MD
Biloxi MS

Boston
MA

C

0.155264

0.110852 0.119516 0.145177

DC

0.002414

0.002339

O

Charleston Houston
SC
TX
0.12239 0.121296

0.00345 0.003151

0.003928 0.002524

0.07575

3.105398 3.076859 3.090886

2.931695 3.129286

DO

0.001926

4.406739 4.327493 4.356982

4.283744 4.405095

H

-0.05746

0.166216

-0.14453

0.41319

-0.09302 0.464898

DH

1.66E-16

2.87E-07

5.22E-15

3.71E-07

2.80E-14

R

0.334931

0.327

DR

6.57E-08

0.2935 0.544038

0.303068 0.497459

0.026348

0.032927 0.056903 0.038412

0.085834 0.078472

E

2.745014

3.105398 3.076859 3.090886

2.931746 3.129367

DE

1.991909

4.406739 4.327493 4.356982

4.283744 4.405095

OH

-0.09797

0.166216

-0.14458

0.41319

-0.09302 0.464898

DOH

1.16E-33

2.87E-07

5.22E-15

3.71E-07

2.80E-14

OR

-0.02339

0.131477 0.119516 0.268342

0.130254 0.230439

DOR

6.14E-05

0.005043 0.008766 0.005899

0.013309 0.012118

OE

0.240417

1.742352 1.728938 1.742101

1.652085 1.757449

DOE

0.002153

1.76006 2.268287 2.147278

2.443248 1.856524

HR

0.313875

0.327

DHR

1.62E-19

7.94E-10

6.33E-18

9.02E-10

2.82E-17

HE

-0.05746

0.166216

-0.14458

0.41319

-0.09302 0.464898

DHE

1.66E-16

2.87E-07

5.22E-15

3.71E-07

2.80E-14

RE

0.313875

0.327

DRE

0.2935 0.544038

6.57E-08

0.303068 0.497459
9.46E-11

6.57E-08

0.2935 0.544038

0.303068 0.497459

0.007454

0.032927 0.056903 0.038412

0.085834 0.078472

OHR

-0.09598

-0.12637

-0.13139

OHE

-0.0917

0.04031

-0.14768 0.213535

-0.10943 0.223053

2.91E-23

1.20E-10

9.61E-19

4.28E-18

DOHE

-0.15266

-0.05828

1.37E-10

-0.08863

1.44E-11

223

Trial

Anchorage Baltimore
AK
MD

Biloxi MS

Boston Charleston
MA
SC

Houston
TX

HRE

-0.08934

-0.10222

-0.15186

-0.01793

-0.1284

-0.04932

DHRE

1.62E-19

7.94E-10

6.33E-18

9.02E-10

2.82E-17

9.46E-11

ALL

-0.09598

-0.12637

-0.15266

-0.05828

-0.13139

-0.08863

DALL

2.91E-23

1.20E-10

9.61E-19

1.37E-10

4.28E-18

1.44E-11

Trial

Los
Jacksonville Angeles
FL
CA

Miami FL

Mobile
AL

New
Orleans
LA

New
York NY

C

0.069086 0.068756 0.113443 0.136475

DC

0.003144 0.003217 0.004874 0.003264 0.002953 0.002843

O

3.263827 3.226744 3.013508

DO

4.357579 3.853383 4.230983 4.345692 4.376277 4.385639

H

-0.16864 1.280513 0.700443

-0.12563

-0.05331 1.086848

DH

2.10E-12 0.000322

5.49E-14

3.24E-14 0.001087

R

0.993593 0.256885 0.284541 0.640963 1.197143 0.304848

DR

0.119922 0.021039 0.031753 0.048475 0.152529 0.043384

E

3.263877 2.682731 3.013508

DE

4.357579 1.130737 4.230983 4.345692 4.376277 4.385639

OH

-0.16864 1.280513 0.700443

-0.12563

-0.05331 1.086848

DOH

2.10E-12 0.000313

5.49E-14

3.24E-14 0.001087

OR

0.521407 0.068756 0.113443 0.331525 0.679026 0.138519

DOR

0.018754 0.002167 0.004874 0.007457 0.024017 0.006662

OE

1.818346

DOE

2.144561 0.217117 2.726958

HR

0.993593 0.188551 0.284541 0.640963 1.197143 0.304848

DHR

1.25E-13

1.37E-09

5.72E-17

5.37E-15

HE

-0.16864 1.280372 0.700443

-0.12563

-0.05331 1.086848

1.40E-06

1.40E-06

0.14213 0.138519

3.0739 2.916403 2.978418

3.0739 2.916403 2.978418

1.49659 1.693869 1.731263 1.648299 1.680506

3.15E-07

2.19472 2.060059 2.010322

1.17E-06

224

Los
Angeles
CA

Miami FL

Mobile
AL

DHE

2.10E-12 0.000303

1.40E-06

5.49E-14

RE

0.993593 0.188551 0.284541 0.640963 1.197143 0.304848

DRE

0.119922 0.001574 0.031753 0.048475 0.152529 0.043384

OHR

-0.20313

-0.07173

-0.1325

OHE

-0.19133 0.691859 0.371425

-0.12828

-0.07637 0.613104

DOHE

1.89E-14

Trial

HRE

Jacksonville
FL

-0.0847

New
Orleans
LA

New
York NY

3.24E-14 0.001087

-0.07734

-0.00565

4.51E-08

2.08E-10

8.68E-18

8.16E-16

1.77E-07

-0.1874 0.003426

-0.02068

-0.13178

-0.05469 0.064908

DHRE

1.25E-13

2.97E-07

1.37E-09

5.72E-17

5.37E-15

1.17E-06

ALL

-0.20313

-0.08474

-0.07173

-0.1325

-0.07734

-0.00565

DALL

1.89E-14

4.51E-08

2.08E-10

8.68E-18

8.16E-16

1.77E-07

Port
Pensacola Philadelphia Charlotte Portland
FL
PA
FL
ME

Portland
OR

Providence
RI

Trial
C

0.154

DC

0.003996

O

2.915885

DO

0.123204 0.061718 0.192892

0.12845

0.115085

0.002412 0.003329 0.015385 0.002165

0.003213

3.155 3.269974 2.770446

3.11964

3.139255

4.278261

4.407311 4.338984 0.015385 4.398218

4.351025

H

-0.08615

0.332908

-0.21687

-0.03565

0.21505

0.019255

DH

3.38E-13

1.09E-07

2.21E-09 0.015385

3.29E-11

2.18E-07

R

0.315049

0.586357 0.253051 0.341169

0.8555

0.293117

DR

0.049064

0.027766 0.021764 0.015385 0.026735

0.030904

E

2.915885

DE

3.155 3.269974 2.770446

3.11192

3.139255

4.278261

4.407311 4.338984 0.015385 2.255075

4.351025

OH

-0.08615

0.332908

-0.21687

-0.03565

0.21505

0.019255

DOH

3.38E-13

1.09E-07

2.21E-09 0.015385

3.29E-11

2.18E-07

225

Trial
OR

Port
Pensacola Philadelphia Charlotte
FL
PA
FL
0.154

Portland
ME

0.285643 0.061718 0.192892

Portland Providence
OR
RI
0.45994

0.115085

DOR

0.007553

0.004249 0.003329 0.015385 0.004089

0.004735

OE

1.650246

1.771673 1.820077 1.579938

1.74983

1.761564

DOE

2.466483

1.799077 2.221196 0.015385 0.485179

2.173108

HR

0.315049

0.586357 0.253051 0.341169

0.85462

0.293117

DHR

3.43E-16

2.96E-10

2.16E-12 0.015385

5.85E-13

5.98E-10

HE

-0.08615

0.332908

-0.21687

-0.03565

0.21505

0.019255

DHE

3.38E-13

1.09E-07

2.21E-09 0.015385

3.29E-11

2.18E-07

RE

0.315049

0.586357 0.253051 0.341169

0.85462

0.293117

DRE

0.049064

0.027766 0.021764 0.015385 0.006762

0.030904

OHR

-0.09666

-0.05758

-0.23658

-0.02233

-0.14447

OHE

-0.0902

0.147541

-0.22507

-0.03693 0.076951

-0.05039

DOHE

5.20E-17

4.50E-11

3.27E-13 0.015385

HRE

-0.09563

0.002627

-0.23494

DHRE

3.43E-16

2.96E-10

2.16E-12 0.015385

5.85E-13

5.98E-10

ALL

-0.09666

-0.05758

-0.23658

-0.0391

-0.02233

-0.14447

DALL

5.20E-17

4.50E-11

3.27E-13 0.015385

8.88E-14

9.08E-11

Trial

San
Francisco Savannah Saint
CA
GA
John NB

C

0.192491

0.075872 0.139333

DC

0.003761

O

-0.0391

8.88E-14

9.08E-11

-0.03874 0.055638

-0.13318

St.
Petersburg Seattle
FL
WA
0.16

0.082754

0.003059 0.016667

0.003712 0.002636

0.003197

2.880912

3.077667 2.979283

3.512986 3.124714

2.935649

DO

4.297865

4.366005 0.016667

4.302269 4.399576

4.335318

H

0.470649

0.026348

0.382368

-0.173

-0.06223

0.108

Vancouver
BC

0.2345

226

Trial

San
Francisco Savannah
CA
GA

DH

3.77E-07

2.07E-14 0.016667

1.23E-08

1.74E-07

3.06E-07

R

0.347175

0.763897 0.719033

0.307986 0.332243

0.691895

DR

0.036298

0.05453 0.016667

0.024252

0.02711

0.047443

E

2.880912

3.077667 2.979283

3.512986 3.124714

2.268386

DE

4.30238

4.366005 0.016667

4.302269 1.615196

1.306588

OH

0.470649

-0.06223

0.026348

0.2345

0.382368

DOH

3.77E-07

2.07E-14 0.016667

1.23E-08

1.74E-07

3.06E-07

OR

0.192491

0.384423

0.108

0.16

0.342298

DOR

0.005573

0.008394 0.016667

0.003712 0.004152

0.007305

OE

1.639263

1.720167 1.680667

1.959986 1.763414

1.268

DOE

2.22673

2.107735 0.016667

2.367766 0.313196

0.283635

HR

0.347175

0.763897 0.719033

0.307986 0.332243

0.604509

DHR

3.72E-10

3.45E-17 0.016667

1.20E-11

1.75E-10

6.62E-09

HE

0.470649

-0.06223

0.026348

0.2345

0.382368

DHE

3.77E-07

2.07E-14 0.016667

1.23E-08

1.74E-07

3.06E-07

RE

0.347175

0.763897 0.719033

0.307986 0.332243

0.604509

DRE

0.033453

0.05453 0.016667

0.024252 0.003333

0.008924

OHR

1.49E-05

-0.20124

-0.11606

-0.17939

-0.0729

-0.04222

OHE

0.263621

-0.18542

-0.0863

-0.06625 0.102985

0.16469

DOHE

5.65E-11

5.24E-18 0.016667

1.82E-12

2.66E-11

1.00E-09

HRE

0.029884

-0.19883

-0.1125

-0.16572

-0.05199

0.049703

DHRE

3.72E-10

3.45E-17 0.016667

1.20E-11

1.75E-10

6.62E-09

ALL

1.49E-05

-0.20124

-0.11606

-0.17939

-0.0729

-0.04222

DALL

5.65E-11

5.24E-18 0.016667

1.82E-12

2.66E-11

1.00E-09

-0.173

-0.173

St.
Saint Petersburg
John NB
FL

0.38235

Seattle Vancouver
WA
BC

227

C.5 Output 5: Mean Nest Density for Each Trial in the Positive Control Group. All
Projections are in nests. Table Produced in Stargazer (Hlavac 2018).
Busan SK

Nerac FR

Tsushima
City JP

0.12843 0.128459 0.122561

0.12843

-0.16906

DC

0.002149 0.002149 0.005167 0.002155

0.088972

O

2.659033 3.119645 2.737753 3.119617

3.419625

DO

3.859297 4.396802 3.477457

4.40829

4.210564

H

-0.09429

-0.1466

-0.53158

0

0

0.93442 0.751487

0.057745

DR

0.042059 0.092966 0.113305 0.028427

0.466614

E

3.119617

3.419625

Trial
C

DH
R

DE

Montreal Walhalla
QC
SC

-0.14689 0.739816

0

0

0.37254

1.04951

9.26E-05

3.06896 2.874771 3.119617
4.40829

4.210564

-0.1466

-0.53158

0

0

OR

0.143975 0.545846 0.511285 0.392741

-0.16906

DOR

0.005681 0.014374 0.008421 0.004349

0.088972

OE

1.586687 1.726959

1.75389

1.856214

DOE

1.321923 0.878765 1.798665 1.660678

3.326024

HR

-0.10692

-0.14754

-0.53168

8.47E-07

0

0

-0.14689 0.739816

-0.1466

-0.53158

0

0

OH
DOH

DHR
HE
DHE

4.35027 3.302139 4.234423
-0.09584
0

0
-0.09429
0

-0.14689 0.739719
0

7.47E-05

1.57606

-0.14742 0.283578
0

0

9.26E-05

RE

0.372541 1.043679

0.93442 0.751487

0.057745

DRE

0.040517 0.055746 0.113305 0.028427

0.466614

OHR

-0.12609

-0.14767 0.130688

-0.14776

-0.53169

OHE

-0.11952

-0.14727

0.40615

-0.14712

-0.53162

0

0

1.25E-05

0

0

DOHE

228

Trial

Montreal
QC

Walhalla
SC

HRE

-0.10692

-0.14742 0.283578

DHRE
ALL
DALL

0
-0.12609
0

Busan SK

Tsushima
Nerac FR
City JP
-0.14754

-0.53168

8.47E-07

0

0

-0.14767 0.130688

-0.14776

-0.53169

0

0

0

0

1.18E-07

229

C.6 Output 6: Mean Nest Density for Each Trial in the Negative Control Group. All
Projections are in nests. Table Produced in Stargazer (Hlavac 2018).

Trials

Barry
Albuquerque County
NM
MI

St Paul
MN

C

0.128459 0.128459 0.128459

DC

0.002149 0.002149 0.002149

O

-0.094 0.338808

-0.14746

DO

2.63E-09 0.201993

5.08E-21

H

0.015493

DH
R

-0.1312 0.108449

0

0

1.53E-10

0.83241

0.30389

0.97167

DR

0.026227

E

-0.14846 3.119645 3.119645

DE
OH

0.01971 0.058243

0 4.396802 4.396802
-0.14833

-0.14313

-0.14824

0

0

7.82E-31

OR

-0.03667

-0.0123

-0.02999

DOR

7.19E-06 0.000306

9.50E-06

OE

-0.14846 0.660413

0.13451

DOH

DOE
HR
DHR
HE
DHE
RE

0 0.224768 0.002306
-0.10241
0
-0.14846
0

-0.14477 0.054522
0

6.15E-12

-0.1312 0.108449
0

1.53E-10

-0.14846 0.303897 0.971677

DRE

0

0.01971 0.058243

OHR

-0.14163

-0.14669

-0.12493

OHE

-0.14846

-0.14198

-0.11855

230

Trials

Albuquerque
NM

Barry
County
MI

St Paul
MN

DOHE

0

0

1.00E-15

HRE
DHRE
ALL
DALL

-0.14846

-0.14477 0.054522

0

0

6.15E-12

-0.14846

-0.14669

-0.12493

0

0

1.00E-15

231

C.7 Output 7: Z-Score for Each Trial in the Test Group. Table Produced in Stargazer
(Hlavac 2018).
Trials

Anchorage Baltimore
AK
MD
Biloxi MS

Boston
MA

Charleston Houston
SC
TX

C

0.745217

0.207339

-0.58815 0.854757

-0.74981 1.012645

DC

-0.57464

-0.42766

-0.35917

-0.30897

O

-3.29739

0.766813

-0.39189 0.325295

-0.75532 1.273585

DO

-2.29726

0.776875

-0.10204 0.431191

-0.2941 1.125055

H

-0.62693

-0.06185

-0.84691 0.562102

-0.71676 0.692736

DH

-0.30874

-0.30868

-0.30874

-0.30866

-0.30874

-0.30873

R

-0.59712

-0.62746

-0.75561 0.202829

-0.71901

0.02464

DR

-0.60441

-0.40624 0.315974

-0.23004

-0.23722

-0.24102

1.187482 0.965699

-1.1032

0.403196 0.283907 0.342538

-0.32267 0.503389

DE

-0.93367

0.641715 0.590016 0.609255

0.561475 0.640642

OH

-0.72284

-0.0574

DOH

-0.30865

OR

-1.54078

E

DOR

-1.3873

-0.84023 0.564673

-0.71036 0.694915

-0.30859

-0.30865

-0.30857

-0.30865

-0.30864

-0.60343

-0.67583

0.22497

-0.61083

-0.00445

-0.527 0.115982

-0.37919

0.900455

0.6948

OE

-4.31456

0.324221 0.282789 0.323446

0.045427 0.370848

DOE

-1.67988

0.172748

0.70836 0.580831

0.892748

HR

-0.64643

-0.59644

-0.72402 0.230105

-0.68758 0.052719

DHR

-0.29492

-0.29492

-0.29492

-0.29492

HE

-0.62693

-0.06183

-0.84704 0.562143

-0.71677 0.692782

DHE

-0.30856

-0.30849

-0.30856

-0.30856

RE

-0.64643

-0.59644

-0.72402 0.230105

DRE

-0.91616

OHR

0.152741

-0.68951

-0.41933 0.614122

-0.01563

-0.20238

OHE

-0.62338

-0.07847

-0.85442 0.636541

-0.69656

0.67583

DOHE

-0.29517

-0.29517

-0.29517

-0.29517

-0.29517

-0.226 0.423587

-0.29492

-0.30847

-0.0774

-0.29517

0.27441

-0.29492

-0.30854

-0.68758 0.052719
1.207452 1.007973

232

Trials

Anchorage Baltimore
AK
MD

Biloxi MS

Boston Charleston
MA
SC

Houston
TX

HRE

-0.18988

-0.34226

-0.92949 0.654886

-0.65196 0.283609

DHRE

-0.29492

-0.29492

-0.29492

-0.29492

ALL

0.088163

-0.39374

DALL

-0.29491

-0.29491

Trial

Los
Jacksonville Angeles
FL
CA

-0.29492

-0.8105 0.685881
-0.29491

-0.29491

Miami FL

Mobile
AL

-0.29492

-0.47331 0.204683
-0.29491

New
Orleans
LA

-0.29491

New
York NY

C

-1.36361

-1.45162

-0.86351 0.646631 0.656452 0.656074

DC

-0.20377

-0.22099

-0.00816

O

0.631679 0.439199

-0.59061 0.351578 0.027605 0.190464

DO

0.500677

-0.25168 0.458579

H

-0.90782 2.753281 1.287809

-0.79914

-0.61645 2.264012

DH

-0.30874

-0.23752

-0.30843

-0.30874

-0.30874

-0.06802

R

1.922619

-0.89569

-0.78989 0.573618 2.701309

-0.7122

DR

2.214315

-0.76436

-0.44161 0.062122 3.196515

-0.09124

E

1.065636

-1.36355 0.019099 0.271536

-0.3868

-0.12758

DE

0.609644

-1.49548 0.527055 0.601889 0.621842

0.62795

OH

-0.90084 2.749281 1.288204

-0.79249

-0.61035 2.261479

DOH

-0.30865

-0.23941

-0.30834

-0.30865

-0.30865

-0.06794

OR

1.756697

-0.98306

-0.71259 0.607398 2.710713

-0.56081

DOR

1.840879

-1.02372

-0.55612

-0.24745

OE

0.55893

0.08514

-0.43483 0.174478

DOE

0.577967

HR

1.942147

-1.1237

DHR

-0.29492

-0.29485

-0.17404

-0.32887

-0.34161

0.37387 0.449144

-0.11017 2.749817

0.28997 0.033733 0.133208

-1.45333 1.191745 0.630829 0.488912 0.436495
-0.75814 0.599223 2.717329
-0.29492

-0.29492

-0.29492

-0.6808
-0.29466

233

Trial

Jacksonville
FL

Los
Angeles
CA

New
Orleans
LA

Miami FL

Mobile
AL

New
York NY

2.75305 1.287878

-0.79915

-0.61646 2.264119

-0.30856

-0.30856

-0.06785

-0.75814 0.599223 2.717329

-0.6808

HE

-0.90784

DHE

-0.30856

-0.24144

RE

1.942147

-1.1237

DRE

2.131024

-1.07546

OHR

-1.75638 0.213582 0.659855

-0.58537

0.34387 1.445903

OHE

-1.03459

-0.77435

-0.5601 2.285828

DOHE

-0.29517

HRE

-1.34993 0.907549 0.622362

-0.69189 0.219992 1.634878

DHRE

-0.29492

-0.29492

ALL
DALL

-0.30825

-0.25781 0.195263 3.014449 0.057324

2.6109 1.288256
-0.29515

-0.29485

-0.29517

-0.29492

-1.6108 0.266321 0.472646
-0.29491

-0.2949

-0.29491

-0.29517

-0.29517

-0.29492

-0.29512

-0.29466

-0.49092 0.383706 1.520368
-0.29491

-0.29491

Trials

Port
Pensacola Philadelphia Charlotte Portland
FL
PA
FL
ME

Portland
OR

C

0.070981

1.08328

DC

-0.25382

-0.28744

O

-0.68098

DO

-0.29487

Providence
RI

-1.65899 1.258543 1.374505

0.608859

-0.18103

-0.37877

0.013189

1.311826 0.490369

-0.64744 1.353921

1.097857

-0.22881

1.126777 0.385507

-2.29043 1.189467

0.945019

H

-0.69941

0.359281

-1.02967

-0.57182 0.061527

-0.43312

DH

-0.30874

-0.30872

-0.30874 3.097865

R

-0.67318

0.364723

-0.91035

DR

0.079852

-0.5617

E

3.21359

-0.30874

-0.30869

-0.57325

1.39434

-0.75708

-0.74251

-0.93467

-0.59277

-0.46717

-0.38896

0.610533 1.091125

-0.9969

0.43046

0.544721

DE

0.557898

0.642088 0.597513

-2.22311

-0.76198

0.605368

OH

-0.69305

-0.56585

0.0656

-0.42757

0.36246

-1.02232

234

Trials

Port
Pensacola Philadelphia Charlotte
FL
PA
FL

Portland
ME

Portland Providence
OR
RI

DOH

-0.30865

-0.30863

-0.30865 3.097884

OR

-0.46711

0.329688

-1.02566

DOR

-0.09351

-0.66412

-0.82306 1.258968

OE

0.039747

0.414781 0.564277

DOE

0.917234

0.213868 0.658731

HR

-0.64195

0.39127

DHR

-0.29492

-0.29492

-0.29492 3.102408

HE

-0.69942

0.359314

-1.02969

DHE

-0.30856

-0.30853

RE

-0.64195

0.39127

DRE

0.21121

-0.36583

OHR

0.355622

0.406315

OHE

-0.61717

0.36414

DOHE

-0.29517

-0.29517

-0.29517 3.246793

-0.29517

-0.29517

HRE

-0.26432

0.898103

-1.91227 0.408782 1.525217

-0.70843

DHRE

-0.29492

-0.29492

-0.29492 3.102408

-0.29492

-0.29492

ALL

0.077357

0.69696

-2.14114 0.989956

1.25576

-0.68065

DALL

-0.29491

-0.29491

-0.29491 3.102409

-0.29491

-0.29491

-0.87806

-0.30865

-0.3086

-0.2317 1.384654

-0.70264

-0.69173

-0.58011

-0.1774 0.347317

0.383557

-1.66593

-1.17083

0.608052

-0.54248 1.412897

-0.72548

-0.29492

-0.29492

-0.57183

0.06155

-0.43312

-0.30856 3.097904

-0.30856

-0.30851

-0.87806

-0.54248 1.412897

-0.72548

-0.52845

-0.70129

-0.9349

-0.2808

-2.1564 1.026715 1.088325

-1.18147

-1.17388

Trial

San
Francisco Savannah Saint
CA
GA
John NB

C

0.667028

-1.24199

-0.31959

DC

-0.3885

-0.27747

O

-0.88823

DO
H

-0.39729 0.072768

St.
Petersburg Seattle
FL
WA

-0.45285

Vancouver
BC

-0.66256 0.753149

-1.69563

3.21359

-0.19695

-0.52531

-0.53593

0.262743

-0.6675

0.298222

-0.06091

-0.84088

-0.35566

0.402221

-2.29043

0.055741 0.143874

-0.33873

0.707265

-0.91883

-0.63899

-0.4152 0.110665

0.484236
235

Trial

San
Francisco Savannah
CA
GA

DH

-0.30866

-0.30874 3.381749

-0.30874

-0.3087

-0.30867

R

-0.55028

1.04391 0.872281

-0.7002

-0.6074

0.768461

DR

St.
Saint Petersburg
John NB
FL

Seattle
WA

Vancouver
BC

-0.3047

0.244513

-0.89605

-0.66757

-0.58147

0.031021

E

-0.53515

0.287281

-0.12396

2.106909 0.483939

-3.0955

DE

0.573634

0.615141

-2.22227

0.573561

-1.17943

-1.38076

OH

0.709401

-0.91182

-0.63282

-0.4097

0.11459

0.48704

DOH

-0.30857

-0.30865 3.381762

-0.30865

-0.30861

-0.30858

OR

-0.23413

0.927574 0.915026

-0.74553

-0.43079

0.672605

DOR

-0.43548

0.051678 1.480373

-0.75677

-0.68084

-0.13639

OE

0.005827

0.2557 0.133703

0.99639 0.389272

-1.14083

DOE

0.664563

0.539157

-1.66458

0.813199

-1.35207

-1.38323

HR

-0.51961

1.067397 0.896541

-0.66886

-0.57648

0.460397

DHR

-0.29492

-0.29492 3.385519

-0.29492

-0.29492

-0.29492

HE

0.707312

-0.91885

-0.4152 0.110689

0.484274

DHE

-0.30847

-0.30856 3.381776

-0.30855

-0.30852

-0.30849

RE

-0.51961

1.067397 0.896541

-0.66886

-0.57648

0.460397

DRE

-0.21175

0.359312

-0.46105

-1.02782

-0.87633

OHR

1.535293

-1.60497 0.142093

-0.94098 0.514262

1.053733

OHE

0.843279

-0.51834 0.180228

0.434924

DOHE

-0.29517

-0.29517 3.246793

-0.29517

-0.29517

-0.29517

HRE

1.220551

-1.48514

-1.09346 0.251995

1.455001

DHRE

-0.29492

-0.29492 3.385519

-0.29492

-0.29492

-0.29492

ALL

1.610115

-1.58083

-1.23431 0.454014

0.940517

DALL

-0.29491

-0.29491 3.385518

-0.29491

-0.29491

-1.0102

-0.639

-0.66655

-0.60108

-0.46388

-0.23025

-0.29491

236

C.8 Output 8: Z-Score for Each Trial in the Positive Control Group. Table Produced in
Stargazer (Hlavac 2018).

Trial

Montreal
QC

Walhalla
SC

C

0.660241

0.660698

-0.38681

0.660241

-1.59437

DC

-0.50168

-0.50168

-0.27834

-0.49884

1.78054

O

0.437309

0.806627

-0.57519

0.806604

-1.47535

DO

0.496714

0.791939

-0.64891

0.798249

-1.43799

H

-0.12479

-0.23724

1.658172

-0.2366

-1.05954

DH

-0.44721

-0.44721

1.788854

-0.44721

-0.44721

R

-0.63339

1.011982

0.732256

0.28764

-1.39849

DR

-0.58853

-0.30752

-0.19525

-0.66379

1.755086

E

-0.00462

-0.26404

-1.25852

-0.00462

1.531788

DE

0.548722

-1.75982

0.293567

0.676515

0.241015

OH

-0.12741

-0.23653

1.65864

-0.23589

-1.05882

DOH

-0.44721

-0.44721

1.788854

-0.44721

-0.44721

OR

-0.47198

0.873384

0.757682

0.36083

-1.51992

DOR

-0.51421

-0.27489

-0.43878

-0.55089

1.778769

OE

-0.95535

0.22769

-1.04498

0.454822

1.317812

DOE

-0.51361

-0.9925

0.001572

-0.14754

1.652082

HR

0.079926

-0.06035

1.432226

-0.06075

-1.39105

DHR

-0.44721

-0.44721

1.788854

-0.44721

-0.44721

HE

-0.12479

-0.23724

1.658172

-0.2366

-1.05954

DHE

-0.44721

-0.44721

1.788854

-0.44721

-0.44721

RE

-0.63281

1.00423

0.737726

0.291516

-1.40066

DRE

-0.54287

-0.46053

-0.14932

-0.60824

1.760954

Busan SK

Nerac FR

Tsushima City JP

237

Trial

Montreal
QC

Walhalla
SC

Busan SK

Nerac FR

Tsushima City JP

OHR

-0.504

-0.73746

1.580296

-0.73836

0.399528

OHE

-0.03485

-0.11783

1.537647

-0.11738

-1.26758

DOHE

-0.44721

-0.44721

1.788854

-0.44721

-0.44721

HRE

0.079926

-0.06035

1.432226

-0.06075

-1.39105

DHRE

-0.44721

-0.44721

1.788854

-0.44721

-0.44721

ALL

0.162345

0.071121

1.247401

0.070767

-1.55163

DALL

-0.44721

-0.44721

1.788854

-0.44721

-0.44721

238

C.9 Output 9: Z-Score for Each Trial in the Negative Control Group.. Table Produced in
Stargazer (Hlavac 2018).

Trial

Barry
Albuquerque County
NM
MI

St Paul
MN

C

NA

NA

NA

DC

NA

NA

NA

O

-0.47421 1.148886

-0.67467

DO

-0.57735 1.154701

-0.57735

H

0.148259

-1.06585 0.917593

DH

-0.57735

-0.57735 1.154701

R

0.368312

-1.13192

DR

-0.41213

-0.72807 1.140202

0.76361

E

-1.1547

0.57735

0.57735

DE

-1.1547

0.57735

0.57735

OH

-0.59162 1.154582

-0.56296

DOH

-0.57735

OR

-0.82203 1.113296

-0.29126

DOR

-0.58404 1.154675

-0.57064

OE

-0.88666 1.083937

-0.19728

DOE

-0.58626 1.154654

-0.5684

HR

-0.36373

-0.76723 1.130957

DHR

-0.57735

-0.57735 1.154701

HE

-0.63638

-0.51623 1.152615

DHE

-0.57735

-0.57735 1.154701

RE

-0.93018

-0.12743 1.057607

DRE

-0.87714

-0.21179 1.088932

OHR

-0.34045

-0.78532 1.125773

OHE

-0.77087

-0.35909 1.129961

-0.57735 1.154701

239

Trial

Albuquerque
NM

Barry
County
MI

St Paul
MN

DOHE

-0.57735

-0.57735 1.154701

HRE

-0.59315

-0.5614 1.154555

DHRE

-0.57735

-0.57735 1.154701

ALL

-0.64338

-0.5087 1.152079

DALL

-0.57735

-0.57735 1.154701

240