In cooperation with the Bureau of Land Management

Potential Demographic and Genetic Effects of a Sterilant

Applied to Wild Horse Mares

Open-File Report 2015–1045

U.S. Department of the Interior

U.S. Geological Survey
Photo credit: Jason Ransom, USGS Fort Collins Science Center
Potential Demographic and Genetic Effects of a Sterilant

Applied to Wild Horse Mares

By James E. Roelle and Sara J. Oyler-McCance 

In cooperation with the Bureau of Land Management

Open-File Report 2015–1045

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2015 

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Suggested citation:

Roelle, J.E., and Oyler-McCance, S.J., 2015, Potential demographic and genetic effects of a sterilant applied to wild 

horse mares: U.S. Geological Survey Open-File Report 2015-1045, 153 p., http://dx.doi.org/10.3133/ofr20151045. 

ISSN 2331-1258 (online)
Contents

Abstract ...................................................................................................................................................................... 1

Introduction................................................................................................................................................................. 1

Model Parameters ...................................................................................................................................................... 2

Demographic Parameters ....................................................................................................................................... 4

Mating System..................................................................................................................................................... 4

Age of First Reproduction.................................................................................................................................... 4

Maximum Age and Maximum Age of Reproduction ............................................................................................ 4

Maximum Number of Progeny per Year.............................................................................................................. 5

Density-Dependent Reproduction ....................................................................................................................... 5

Reproductive and Mortality Rates ....................................................................................................................... 5

Sex Ratio at Birth ................................................................................................................................................ 6

Mate Monopolization ........................................................................................................................................... 6

Initial Population Size.......................................................................................................................................... 7

Initial Age Distribution.......................................................................................................................................... 7

Carrying Capacity................................................................................................................................................ 7

Genetic Parameters ................................................................................................................................................ 8

Removal and Contraception Programs ................................................................................................................... 8

Removals ............................................................................................................................................................ 8

Contraception...................................................................................................................................................... 9

Random Variation ................................................................................................................................................... 9

Environmental Variation in Breeding and Mortality.............................................................................................. 9

Concordance of Environmental Variation in Breeding and Mortality.................................................................... 9

Number and Types of Catastrophes .................................................................................................................. 10

Distribution of Litter Sizes.................................................................................................................................. 10

Simulation Control................................................................................................................................................. 10

Number of Iterations.......................................................................................................................................... 10

Number of Years per Iteration ........................................................................................................................... 10

Number of Populations...................................................................................................................................... 10

Extirpation Definition ......................................................................................................................................... 11

Interpreting Model Output......................................................................................................................................... 11

Conclusions.............................................................................................................................................................. 12

References Cited...................................................................................................................................................... 12

Appendix A. Simulation Results................................................................................................................................ 14

Tables

1. Parameter values and options used in simulations of the effects of a mare sterilant applied to 

wild horses..................................................................................................................................................... 3

2. Annual survival and reproductive rates used to achieve various annual population growth rates.................. 6 

3. Translation of the annual rates shown in table 1 into VORTEX parameter values for an annual 

population growth rate of 20 percent (λ = 1.20)............................................................................................. 6 
Abbreviations Used in This Report

≥ Greater than or equal to

< Less than

λ lambda; annual population growth rate multiplier for a herd

BLM Bureau of Land Management

K carrying capacity

N population size

U.S. United States
Potential Demographic and Genetic Effects of a Sterilant 

Applied to Wild Horse Mares

By James E. Roelle and Sara J. Oyler-McCance 

Abstract

Wild horse populations on western ranges can increase rapidly, resulting in the need for the 

Bureau of Land Management (BLM) to remove animals in order to protect the habitat that horses share 

with numerous other species. As an alternative to removals, BLM has sought to develop a long-term, 

perhaps even permanent, contraceptive to aid in reducing population growth rates. With long-term 

(perhaps even permanent) efficacy of contraception, however, comes increased concern about the 

genetic health of populations and about the potential for local extirpation. We used simulation modeling 

to examine the potential demographic and genetic consequences of applying a mare sterilant to wild 

horse populations. Using the VORTEX software package, we modeled the potential effects of a sterilant 

on 70 simulated populations having different initial sizes (7 values), growth rates (5 values), and genetic 

diversity (2 values). For each population, we varied the treatment rate of mares from 0 to 100 percent in 

increments of 10 percent. For each combination of these treatment levels, we ran 100 stochastic 

simulations, and we present the results in the form of tables and graphs showing mean population size 

after 20 years, mean number of removals after 20 years, mean probability of extirpation after 50 years, 

and mean heterozygosity after 50 years. By choosing one or two combinations of initial population size, 

population growth rate, and genetic diversity that best represent a herd of interest, a manager can assess 

the likely effects of a contraceptive program by examining the output tables and graphs representing the 

selected conditions. 

Introduction

As the primary agency responsible for management of wild horses (Equus caballus) on public 

lands in the United States (U.S.), the Bureau of Land Management (BLM) has a need for a long-lasting, 

non-lethal method to control population growth rates. Given the protection afforded by The Wild FreeRoaming Horses and Burros Act of 1971 (P.L. 92–195 as amended) and general lack of natural 

predators, wild horse populations commonly increase at rates of 15–25 percent per year (Eberhardt and 

others, 1982; Garrott and others, 1991a) and quickly exceed the carrying capacity of their ranges. In the 

past, BLM has managed excess horses through a gather, removal, and adoption program, with 

unadopted horses held in short- and long-term holding facilities until the end of their natural lives. The 

sustainability of this strategy has recently been called into question, however (U.S. Government 

Accountability Office, 2008; Garrott and Oli, 2013; National Research Council, 2013). Therefore, BLM 

has increased efforts to develop a contraceptive that will reduce population growth rates in wild horse 

herds and thus reduce the number of excess animals that must be removed and cared for. 

1
The contraceptive SpayVac has recently demonstrated the potential for long-lasting efficacy 

(at least 4 years) in wild horses (Killian and others, 2008). Maximizing the duration of contraceptive 

effectiveness is especially important in managing wild horses, which in most cases must be captured in 

order to successfully administer the drug. With extended efficacy (or perhaps even permanent sterility), 

however, comes increased concern for both the genetic health of a horse herd and the possibility of 

extirpation. Simulation modeling can be a useful tool in understanding the likely consequences of 

alternative management actions. We used the VORTEX software package (Lacy and others, 2014; Lacy 

and Pollak, 2014) to simulate the effects of treating various proportions of mares with a permanent 

sterilant. Response variables included population size, number of animals removed, average 

heterozygosity, and probability of local extirpation. (The VORTEX manual (Lacy and others, 2014) 

uses the term “extinction” rather than “extirpation.” We believe that extirpation is more appropriate in 

this case, as we are simulating local populations, not the entire species.) We chose the VORTEX 

software because it can be used to simulate both demographic and genetic effects, and because it has

been useful in simulating management of the horse population on Assateague Island (Ballou and others, 

2008). 

VORTEX is an individual-based model in which events happen or fail to happen on the basis of 

probabilities for each modeled individual. For example, if 100 females are of breeding age, each of 

which can produce at most one offspring, and fecundity is set to 80 percent, there is no guarantee that 

exactly 80 offspring will be born. Rather, for each female of breeding age, a random number chosen 

from a uniform distribution between 0 and 1 is compared to the probability of producing an offspring (in 

this example, 0.8). If the random number is less than 0.8, then the female is tagged in the model to give 

birth but otherwise does not. Thus, no two simulations are identical even when they use the same 

demographic parameters, and multiple iterations must be run in order to examine the possible range of 

outcomes. In general, we present results in the form of mean values for the multiple simulations; 

however, it is important to remember that extreme values can also be of interest. In addition, it is 

important to note that these simulations represent the results of management prescriptions applied 

consistently through time, without adaptation based on monitoring of results. In the real world, there 

would be many opportunities to adjust management strategies based on previous results. 

Model Parameters

Parameter values and VORTEX options used in our simulations are summarized in table 1 and 

described in some detail in the sections that follow. Our knowledge of the biology and demography of 

horse populations and the efficacy of SpayVac and other forms of contraception is incomplete; what is 

applicable to one herd may not be applicable to all herds. In light of that fact, in cases where specific 

parameter values were in question, we tried to select the value or option that would have the largest 

effect on one or more of the response variables. For example, we don’t know that SpayVac is a sterilant, 

but it may be. Furthermore, BLM is considering the use of other techniques (for instance, ovariectomy) 

that definitely will be permanent. So, for modeling purposes, we assume a permanent sterilant; once a 

mare is treated and the treatment works, she is infertile for life. This assumption is likely to minimize 

the number of animals tagged for removal during a simulation, while at the same time maximizing any 

decline in heterozygosity. We were similarly conservative in our choice of other parameter values and 

options, always choosing those that were likely to have the most detrimental effect on population 

demography and genetics. 

2
Table 1. Parameter values and options used in simulations of the effects of a mare sterilant applied to wild 

horses.

[Ho, observed heterozygosity; ≥, equal to or greater than; BLM, Bureau of Land Management]

Parameter or option Value selected for simulations

Mating system Long-term polygyny

Age of first reproduction Females = 3 years, males = 5 years

Maximum age (life span) 25 years

Maximum age of reproduction 20 years

Basic time cycle 1 year

Maximum litters per year 1

Maximum progeny per litter 1

Density-dependent reproduction Not used

Reproductive rates See tables 2 and 3

Mortality or survival rates See tables 2 and 3

Sex ratio at birth 50 percent males

Mate monopolization Mean of 3.0 mates per successful sire

Initial population size 100, 250, 500, 750, 1,000, 1,250, or 1,500

Initial age distribution Stable age distribution calculated from age-specific schedules in table 2 and 3

Carrying capacity Arbitrarily set at 5× the initial population size, but the contraception and removal programs prevent 

carrying capacity from having any effect

Initial heterozygosity Actual allele frequencies at 13 microsatellite loci from the Lost Creek herd in Wyoming (high diversity, 

Ho = 0.78) or the Cibola-Trigo herd in Arizona (low diversity, Ho = 0.49)

Removals When the simulated population reaches ≥150 percent of the initial population size, try to remove enough 

animals to get back to the initial population size. BLM’s age-class removal criteria are used, but are 

constrained such that no more than 90 percent of any age and sex class are removed. 

Efficacy of treatment Treatment is efficacious in 90 percent of all newly treated mares

Duration of efficacy If treatment is efficacious, female remains contracepted for life

Proportion of females treated 0 percent–100 percent, in 10 percent increments

Standard deviation due to environmental variability SEV = 0.12 for fecundity; SEV = 0.06 for mortality

Concordance Yes. Breeding and mortality are affected simultaneously.

Probability of catastrophe 10 percent annually

Impact of catastrophe Reduce reproduction to 50 percent of normal; reduce survival to 75 percent of normal

Distribution of litter sizes Not used; litter size in horses is virtually always 1

Number of iterations per simulation 100

Number of years per iteration 20 years for population size and removals; 50 years for heterozygosity and probability of extirpation

Number of populations in each simulation 1

Definition of extirpation The population is considered to be extirpated when it no longer has individuals of both sexes.

3
Demographic Parameters

Mating System

VORTEX models breeding systems as monogamous or polygamous and short-term or longterm. With monogamous breeding, a male is needed for every breeding female; males may therefore 

become a limiting factor restricting breeding. In polygamous models, only one male is needed for all 

females to have an opportunity to breed. However, another parameter (see the section Mate 

Monopolization) can specify that only a subset of males has an opportunity to breed. For example, a 

polygynous system can be created in which successful males control harems of, say, five females on 

average, while the remaining males are excluded from breeding. 

If a short-term option is chosen, then VORTEX assumes that mates are randomly reshuffled 

each year and that all available individuals have an equal probability of breeding. If a long-term option 

is chosen, then once harem relationships between stallions and mares are formed, those relationships 

remain intact across years of the simulation until a member dies or disperses to a different population. 

Demographically, it does not matter whether long-term relationships or rearrangement of harems each 

year is chosen. Genetically, there may be a small effect on the rate of loss of genetic diversity from the 

population, with greater loss of diversity expected in populations with higher harem fidelity. 

We realize that wild horses do not necessarily mate for life (mares do move between harems) 

but, of the two choices available in VORTEX, long-term polygyny comes closer to representing the 

mating system of wild horses. We therefore used long-term polygyny as the mating system in all of our 

simulations. This is a conservative assumption, in the sense that it represents the greatest opportunity for 

loss of genetic diversity. Any additional interchange that does occur in the real world will tend to 

ameliorate effects and result in higher genetic diversity than predicted by our models. 

Age of First Reproduction

VORTEX describes reproduction in terms of the age when the first offspring are born, not the 

age at onset of sexual maturity or the age at first conception. The program also assumes that breeding 

(and, for that matter, all other events) takes place at discrete intervals, usually years. Thus, age at first 

reproduction is entered as an integer value. The value used should represent something like the median 

age of first reproduction, not the earliest age ever observed, because the earliest observed age may not 

be typical of the population. We therefore used 3 years as the age of first reproduction in females and 

5 years as the age of first reproduction in males (Garrott and Taylor, 1990; Garrott and others, 1991b; 

Roelle and others, 2010). 

Maximum Age and Maximum Age of Reproduction

If the species being modeled does not reproduce throughout its entire adult life, the age when the 

species ceases to reproduce must be specified. For example, humans typically reach reproductive 

senescence before they die. If the typical life expectancy is 70 years but reproduction ceases at 50 years, 

then 50 years would be the maximum age of reproduction. VORTEX requires that the maximum age be 

the same for both sexes, but allows the maximum age of reproduction to vary by sex. Establishing the 

maximum age of reproduction is difficult because old animals are hard to age (unless they were marked 

or identified in the year of birth) and because sample sizes of old animals are typically small. Garrott 

and others (1991b) present information showing that some mares can reproduce at greater than 20 years 

4
of age, whereas Roelle and others (2010) found no evidence of reproduction by females older than 

16 years. Roelle and others (2010) also found that very few harems are held by stallions older than 

age 20. On the basis of available evidence, we used 20 years as the maximum age of reproduction and 

25 years as the maximum age.

Maximum Number of Progeny per Year

VORTEX provides a great deal of flexibility in specifying the maximum number of progeny that 

can be born to a given female in a year (or other time interval), thus allowing species that produce 

multiple clutches or litters to be modeled. However, most of this flexibility is not needed for modeling 

a horse population. Given that horses produce only a single litter per year (the average gestation period 

is 335–342 days; Card and Hillman, 1993) and that twins are virtually unknown, we used 1 for the 

maximum number of litters per year, 1 for the maximum number of progeny per litter, and a year 

(365 days) as the basic time cycle.

Density-Dependent Reproduction

VORTEX allows the reproductive rate of the population being modeled to change with changing 

population size. For example, reproduction could be low when the population is small owing to a 

difficulty in finding mates (Allee effect) or, conversely, reproduction could drop off when the 

population is large (more specifically, at high density) owing to limited resources or territories, 

intraspecific competition, crowding, or stress. 

Density-dependent reproduction, also known as compensatory reproduction, has been reported 

for wild horses (Kirkpatrick and Turner, 1991; Jenkins, 2000; Roelle and others, 2010), but quantifying 

the magnitude of the effect is difficult, and the information available is insufficient to allow 

generalization or calculation of some average function. In addition, many of our simulated populations 

differed only about 50 percent (that is, between N and 1.5 × N) because of the way we implemented the 

removal function (see section Removal and Contraception Programs). In our estimation, reproductive 

rates are not likely to change substantially owing to density in that relatively small range. We therefore 

did not use density-dependent reproduction in our simulations. 

Reproductive and Mortality Rates 

VORTEX models reproductive rate as the proportion of adult females giving birth each year (or 

other time interval), where an adult female is defined by the age of first reproduction (see previous 

discussion). Similarly, mortality rates are modeled as the proportion of animals dying in each age and 

sex class. From age 0 to the age of first reproduction, each age and sex class can have a different 

mortality rate; after the age of first reproduction, all animals are considered adults, and the mortality rate 

can vary only by sex.

While these parameters are fundamental to modeling population dynamics, values are well 

known for perhaps only a handful of wild horse populations. In our estimation, however, wild horse 

managers are more likely to have at least some idea of the annual population growth rate multiplier for a 

herd (λ, lambda), which is just a different way of expressing the growth rate itself. We therefore 

modeled a set of scenarios in which λ = 1.05, 1.10, 1.15, 1.20, or 1.25 (that is, annual growth rates of 

5 percent, 10 percent, 15 percent, 20 percent, or 25 percent in the absence of contraception). To produce 

these growth rates, we used reproductive and survival rates (table 2) derived largely from Garrott 

5
(1991a). We arrived at the values for λ = 1.25 by experimenting with parameters in the model. Table 3

provides an example of how we translated these parameters into VORTEX.

Table 2. Annual survival and reproductive rates used to simulate various annual population growth rates. 

Population

growth rate 

(percent)

Juvenile

survival rate

(percent)

Adult

survival rate

(percent)

Mares foaling

(percent)

5 80 91 50

10 80 92 65

15 80 97 65

20 80 99 80

25 90 99 92

Table 3. Translation of the annual rates shown in table 1 into VORTEX parameter values for an annual 

population growth rate of 20 percent (λ = 1.20).

[λ, annual population growth rate multiplier for a herd; <, less than; ≥, equal to or greater than]

Reproduction Female Mortality Male Mortality

Mare age

(years)

Mares foaling 

(percent)

Age

(years)

Rate

(percent)

Age

(years)

Rate

(percent)

1 0 <1 20 <1 20

2 0 1 to <2 1 1 to <2 1

≥3 80 ≥2 1 2 to <3 1

3 to <4 1

4 to <5 1

≥5 1

We believe that, in the absence of contraception, growth rates of most wild horse herds will fall 

within the range shown in table 2. Rather than having to specify reproductive and mortality rates, a 

manager will need only to choose one or perhaps two values for the annual population growth rate to 

use the output from the model. 

Sex Ratio at Birth

While foal sex ratio can differ from 50:50 in small herds in a given year (Roelle and others, 

2010), over time the ratio tends to be fairly even in most herds. For example, Garrott (1991b) found that 

for a 12-year period 65 of 74 (88 percent) herds sampled in Nevada, Oregon, and Wyoming had a foal 

sex ratio that did not differ from 50:50. We therefore used 50 percent males in the foal crop in our 

simulations.

Mate Monopolization

As noted in the previous section, we ran our simulations using a polygynous breeding system. In 

order to do so, VORTEX requires that one of the following three parameters be specified: percentage of 

males in the breeding pool, percentage of males successfully siring offspring, or mean number of mates 

per successful sire. The remaining two parameter values are calculated from the one that is supplied 

based on the assumptions that some males are excluded from the breeding pool and that breeding 

6
success among males in the pool of available breeders is described by a Poisson distribution. Only the 

first parameter (percentage of males in the breeding pool) is used by VORTEX. 

Of the three ways in which mate monopolization can be described in VORTEX, mean number 

of mates per successful sire is the one most commonly discussed in the literature on feral horses, but 

comparisons among studies are hampered by inconsistencies in defining what constitutes a potential 

mate (that is, the age classes of mares). Roelle and others (2010) defined potential mates as all mares 

2 years of age and older, and found a mean harem size of 2.2 mares (range 1.9 to 2.7) during 12 years. 

Using the same age criteria, Kaseda and Khalil (1996) found average harem sizes of 1.8 to 5.3 mares 

in many years.

Potential effects of using different values for the mean number of mates per successful sire are 

not intuitive; to a first approximation, however, one might expect that varying this parameter would 

affect genetics more than demography. We explored sensitivity of model results to mean number of 

mates per successful sire in a series of simulations with initial population size = 500, proportion of 

mares treated = 0.5, lambda = 1.05 (in the absence of contraception and removals), and initial 

heterozygosity = 0.77. We varied mean number of mates per successful sire systematically between 

1.5 and 5.0. The fairly low growth rate and fairly high proportion of mares treated consistently kept the 

simulated population after 50 years at 200–250 animals; however, final heterozygosity ranged only from 

0.74 to 0.75. Given the apparent lack of sensitivity of the model, we decided to set the value of mean 

number of mates per successful sire to 3.0 for all simulations. 

Initial Population Size

Horse herds managed by BLM vary considerably in size, and the size of the herd is potentially 

very important relative to demographic and genetic results of contraception. We approached this 

problem by simulating herds with initial populations of 100, 250, 500, 750, 1,000, 1,250, and 1,500 

animals. These initial populations should encompass the appropriate management level (AML; 

population goal) for many herds. We recommend a more detailed, site-specific analysis before a 

sterilant is applied to any herd with fewer than 100 animals. In addition, we implicitly assume that a 

herd is at its appropriate size before the results of these simulations can be used to evaluate a fertility 

control program. For example, the results of the simulations having an initial population and appropriate 

management level of 500 animals cannot be used if the population in fact contains, say, 1,000 animals. 

Initial Age Distribution

VORTEX allows two options for specifying the initial age distribution used in a simulation. A 

specific age distribution (the number of individuals in each sex and age class) can be entered, or 

VORTEX can calculate the stable age distribution (proportion of animals) that would result from the 

age-specific schedules of reproduction and mortality described previously. We used the latter option, 

and the proportions were applied to the initial population size to determine the number of animals

initially in each sex and age class.

Carrying Capacity

Carrying capacity (K) describes a theoretical upper limit to the size of a population. In 

VORTEX, if the actual population, N, exceeds K at the end of a particular year, then additional 

mortality is applied equally across all age and sex classes to reduce the population such that N = K. 

While carrying capacity is an important theoretical construct, values for K are difficult to estimate. We 

7
somewhat arbitrarily set the value for K at 5 times the initial population size. With the contraception and 

removal programs specified as described in subsequent sections, simulated populations never reach 

carrying capacity.

Genetic Parameters

VORTEX allows inbreeding depression to be incorporated into the population model as a 

reduction in first-year survival among inbred individuals. Although some diploid species that have been 

studied show depressed fitness when inbred (O’Brien and Evermann, 1988; Quattro and Vrijenhoek, 

1989), the rate at which inbreeding affects survival and reproduction is not well understood for most 

species. Therefore, we elected not to use this function in the wild horse model. A better approach for 

investigating the potential genetic consequences of contraception and gathers (round-ups) is to track the 

degree of genetic diversity, which can be loosely linked to fitness and an ability to adapt to 

environmental change. 

VORTEX tracks changes in genetic diversity using heterozygosity (the frequency of two 

different alleles at a given gene) as a metric. Heterozygosity ranges from 0 (all individuals are 

homozygous and the same at all genes) to 1 (all individuals are heterozygous with different alleles at all 

genes). It is generally believed that higher levels of heterozygosity are associated with more genetic 

variation and lower probability of inbreeding depression. 

VORTEX can track heterozygosity in two ways. Because VORTEX includes a detailed 

simulation of genetic change in the populations, one way to measure changes in heterozygosity is to 

start with maximum heterozygosity (1) by assigning each founder individual two unique alleles at a 

number of loci (genes). Each offspring is randomly assigned one of the two alleles from each parent at 

each locus. This method tracks relative loss of heterozygosity through time. Perhaps a more realistic 

way to examine loss of heterozygosity is to mimic real populations by starting with individuals that 

have a known level of heterozygosity. VORTEX allows this option by allowing real allele frequencies 

to be used as a starting point for model simulations. Thus, if we know the level of heterozygosity for a 

population, we can enter real allele frequencies such that the starting point of the simulations will have 

exactly that level of heterozygosity. We used the latter of these two approaches and ran the simulations 

for two different initial levels of heterozygosity (high and low) as reported for two real-world herds 

(Gus Cothran, Texas A&M University, unpublished reports prepared for BLM). Actual allele 

frequencies at 13 microsatellite loci were taken from the Lost Creek herd in Wyoming (high genetic 

diversity, Ho = 0.78; report prepared in 2010) and the Cibola-Trigo herd in Arizona (low genetic 

diversity, Ho = 0.49; report prepared in 2008). Absent site-specific information, we typically expect 

larger herds to have higher genetic diversity.

Removal and Contraception Programs

Removals

Given the limitations of available contraceptive methods, and facing population sizes that greatly 

exceed the desired number of animals in many herd management areas, BLM currently views 

contraception as a means of reducing the number of animals that must be removed, and perhaps 

increasing the interval between gathers, rather than as a replacement for gathers. We therefore simulated 

a gather-and-removal program that is as similar as possible to the program that BLM uses in the field. 

We modeled a gather-and-removal event in any year in which the simulated population was 150 percent

or more of the initial population, and we attempted to remove sufficient animals to return the population 

8
to its initial size. We removed animals from age classes according to BLM’s removal criteria, which 

specify the following order: ages 4 and under, followed by ages 11–19, followed by ages 5–10. We 

constrained the number of animals removed, however, such that no more than 90 percent of any group 

was taken (because it would rarely be possible or desirable to remove every animal from a given age 

class). Our response variable is the total number of animals removed in 20 years averaged for 100 

iterations.

Contraception

We implemented a simulated contraception program using capabilities in VORTEX called 

“population state” variables and “individual state” variables. Briefly, we used these variables to define 

the proportion of previously untreated females that are treated in each application and the probability 

that the treatment works if it is given (efficacy). In most cases, animals in BLM herds need to be 

gathered in order to apply a fertility control agent; we therefore treated mares following every gather 

and removal. Killian and others (2008) found that 17 percent of mares treated with SpayVac were 

pregnant in years 2 through 4 of their study, which implies efficacy of 83 percent. The most aggressive 

assumption would be that the treatment is 100 percent efficacious. However, it is probably also fair to 

assume that some mares will not respond to an immunocontraceptive such as SpayVac. We therefore 

assumed efficacy of 90 percent for all simulations. We also assumed that once a mare is successfully 

contracepted, she remains contracepted for life without further treatment (we assumed permanent 

sterility). We varied the proportion of mares treated from 0 to 100 percent in increments of 10 percent to 

illustrate the range of possible contraceptive effects. For example, when the proportion of mares treated 

is set at 20 percent, each mare not successfully treated in the past has a 20 percent chance of being 

caught and treated, and there is a 90 percent chance that the treatment will be effective. Note that high 

treatment rates (90–100 percent, for example) would likely be very difficult to achieve in the real world 

because some animals are difficult or impossible to gather.

Random Variation

Environmental Variation in Breeding and Mortality

In addition to the variability inherent in an individual-based model, VORTEX allows 

specification of variability (standard deviation) in the proportion of females breeding and in the 

proportion of both sexes dying due to factors external to the population (such as weather, predation, 

parasite loads). Estimates of variability in these parameters are generally not available for wild horse 

herds, but sufficient information was available to calculate standard deviations in fecundity and 

mortality for the Pryor Mountain herd (Roelle and others, 2010). 

The standard deviation due to environmental variability, sev, for either fecundity or mortality, 

can be expressed as sev = �stot

2 − sds

2 , where stot

2 is the total variance in the parameter for all years and 

sds

2 is the sampling (binomial) variance for all individual rates. From the Pryor Mountain data set 

(Roelle and others, 2010), we calculated sev = 0.12 for fecundity and sev = 0.06 for mortality. We 

combined ages and sexes for both of these calculations and used the resulting values in all simulations. 

Concordance of Environmental Variation in Breeding and Mortality

Factors such as those already described (weather, predation, parasite loads) can affect 

reproduction and survival independently or simultaneously. Simultaneously means that good years for 

9
reproduction are also good years for survival. We know of no information that can be brought to bear on 

this subject in regard to wild horse demography, but it seems logical that demographic effects would be 

most pronounced if these parameters vary simultaneously. We therefore opted for concordance in 

environmental variation. 

Number and Types of Catastrophes

The VORTEX software allows specification of catastrophes (floods, forest fires, epidemic 

diseases) through particular effects on reproduction and survival. Perhaps the most common such event 

on western ranges is drought, and although droughts occur fairly frequently, we know of no specific 

information relating drought to reproduction and survival in wild horses. Nevertheless, we felt that it 

was important to include some form of catastrophe in our simulations. We therefore specified that 

drought would have a 10 percent probability in any year and that it would reduce reproduction to 

50 percent of the normal level and survival to 75 percent of the normal level. 

Distribution of Litter Sizes

VORTEX allows for one additional form of random variation if females can produce litters of 

different sizes. Because wild horses almost never produce more than one offspring, we did not use this 

parameter.

Simulation Control

Number of Iterations

As noted in the previous section, VORTEX uses a random number generator to simulate random 

events in an organism’s life cycle. Therefore, no two runs or iterations of the model are identical even 

with a single set of input data. To obtain a more complete picture of demographic behavior, multiple 

iterations are required. We explored changes in the standard deviation of both mean population size and 

heterozygosity after 50 years while varying the number of iterations from 25 to 1,000. Because of the 

complexity of the removal and contraception functions, no consistent pattern emerged in the standard 

deviations of these parameters. More particularly, increasing the number of iterations to more than 100 

did not consistently lead to lower variance about the mean. We therefore chose 100 iterations for all of 

our simulations. 

Number of Years per Iteration

Initial simulations with some basic data indicated that significant changes in heterozygosity are 

rare in less than 50 years. On the other hand, significant demographic changes can occur in as little as 

20 years. We therefore evaluated mean population size and removals at the end of 20 years of 

simulation, but we used 50 years to evaluate heterozygosity and probability of extirpation. 

Number of Populations

VORTEX can be used to model a single, isolated population or a complex metapopulation 

composed of as many as 50 populations with interchange of animals between them. Although it is clear 

that some animals move between certain populations of wild horses, we know of no information on 

10
rates of such movement. We therefore modeled only a single population without introduction of animals 

from outside, which is the worst case from the perspective of genetic diversity. 

Extirpation Definition

VORTEX offers several methods for defining extirpation of a population. We used the definition 

that says a population is extirpated when it no longer contains individuals of both sexes. 

Interpreting Model Output

Appendix A contains output from 70 sets of simulations representing two levels of genetic 

diversity (low or high), seven initial population sizes (100, 250, 500, 750, 1,000, 1,250, or 1,500 

animals), and five population growth multipliers (1.05, 1.10, 1.15, 1.20, or 1.25). Each set of 

simulations is represented by a figure, and each figure contains five graphs and a table of supporting 

data. The order of the figures varies first by annual growth rate, then by population size, and then by 

genetic diversity. Thus, figure 1 has low genetic diversity, an initial population size of 100, and a 

growth multiplier of 1.05, and is followed by figure 2 with low genetic diversity, an initial population 

size of 100, and a growth multiplier of 1.10, and so on. In each figure, the first four (black and white) 

graphs and the table represent the same set of simulations, and the graphs and table have identical 

values. Due to a nuance in the way VORTEX operates, however, the final (color) graph represents a 

different set of simulations having the same parameter values but differing slightly due to random 

variation as already discussed. Thus, the value for average population size at 20 years on the color graph 

will not in general be identical to that in the table, but the two values will usually be very similar.

The black and white graphs present mean values (that is, averaged for 100 iterations) of four 

response variables on the vertical axes: mean population size after 20 years, mean number of removals 

after 20 years, mean probability of extirpation after 50 years, and mean heterozygosity in the herd after 

50 years. In all cases, the horizontal axis is the percentage of previously untreated mares that are treated 

following each gather, varying from 0 percent to 100 percent. The colored graph represents the mean 

trajectory of the population size for a subset of the treatment levels (0 percent, 20 percent, 40 percent, 

and so on) depicted as lines of different color. It is very important to understand that there is some 

information that cannot be conveyed by mean values. For example, there are many cases where the table 

and black and white graphs show that animals were removed, but the colored graph lines never plot 

higher than 1.5 × the initial population. The appropriate interpretation is that on average the population 

stayed below the threshold (1.5 × the initial population), but in some individual iterations the population 

grew sufficiently to trigger a removal.

As an example application of model results, suppose a manager wants to know what proportion 

of mares can be treated with a sterilant in a herd having low genetic diversity, an initial population size 

of about 750, and a population growth multiplier of 1.15. This set of conditions is represented by figure

18 in appendix A. The first thing to notice about figure 18 is that no treatment level has any real effect 

on either mean probability of extirpation after 50 years or mean heterozygosity after 50 years. The graph 

of mean population size after 20 years, however, shows that treatment levels greater than 50 percent of 

the mares result in populations somewhat less than 750. We also see that if 50 percent of the mares are 

treated, the mean number of removals after 20 years is around 900, or about 500 fewer than in the 

scenario where no mares are treated. The number of removals can be further reduced by treating a 

higher proportion of mares, but only if average population levels below 750 are acceptable. The average 

trajectory of the population size through time can be examined by looking at the last (color) graph in the 

11
figure 18, which also shows that treatment rates more than about 50 percent will result in populations 

that are commonly below the starting point of 750 animals. 

Finally, uncertainties about level of genetic diversity, population size, or growth rate can be 

addressed by examining figures representing nearby values in the parameter space. Thus, in the example 

in the preceding paragraph, a manager might also wish to look at the figures representing 500 and 1,000 

animals in the population and growth multipliers of 1.10 and 1.20 to gain some understanding of how 

sensitive model results are to these assumptions.

Conclusions

We believe that simulation results presented herein represent a useful starting point for 

evaluating a management program involving a contraceptive technique that is permanent (or nearly so). 

In particular, the results show that only in the most extreme circumstances (such as low initial genetic 

diversity, low population growth rate, high proportion of mares treated, no change in management for 

50 years) would there likely be any noticeable effect on genetic diversity or a significant probability of 

extirpation of a herd. Monitoring and adaptive management would reduce the probability of 

unacceptable results even further. For example, a simple exchange program in which an animal or two 

were moved between herds periodically would help to maintain genetic diversity, and the contraceptive 

program could always be modified or discontinued in the event that the reduction of population was 

greater than anticipated. In short, we see nothing in our results that should steer wild horse managers 

away from permanent contraceptive techniques, as long as results are monitored and adjustments are 

made if necessary.

References Cited

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Kaseda, Y., and Khalil, A.M., 1996, Harem size and reproductive success of stallions in Misaki feral 

horses: Applied Animal Behaviour Science, v. 47, p. 163–173. 

Killian, Gary, Thain, D., Diehl, N.K., Rhyan, J., and Miller, L., 2008, Four-year contraception rates of 

mares treated with single-injection porcine zona pellucida and GnRH vaccines and intrauterine 

devices: Wildlife Research, v. 35, p. 531–539. 

Kirkpatrick, J.F., and Turner, J.W., Jr., 1991, Compensatory reproduction in feral horses: Journal of 

Wildlife Management, v. 55, p. 649–652. 

Lacy, R.C., Miller, P.S., and Traylor-Holzer, K., 2014, VORTEX—A stochastic simulation of the 

extinction process, Version 10.0.0.4 User’s Manual: Apple Valley, Minn., IUCN SSC Conservation 

Breeding Specialist Group and Chicago Zoological Society, 175 p. 

Lacy, R.C., and Pollak, J.P., 2014, Vortex—A stochastic simulation of the extinction process, Version 

10.0: Brookfield, Ill., Chicago Zoological Society. (software) 

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way forward: Washington, D.C., National Acadamies Press, 383 p. 

O’Brien, S.J., and Evermann, J.F., 1988, Interactive influence of infectious disease on genetic diversity 

of natural populations: Trends in Ecology and Evolution, v 3, p. 254–259. 

Quattro, J.M., and Vrijenhoek, R.C., 1989, Fitness differences among remnant populations of the 

endangered Sonoran topminnow: Science, v. 245, p. 976–978. 

Roelle, J.E., Singer, F.J., Zeigenfuss, L.C., Ransom, J.I., Coates-Markle, L., and Schoenecker, K.A., 

2010, Demography of the Pryor Mountain wild horses, 1993–2007: U.S. Geological Survey Scientific 

Investigations Report 2010–5125, 31 p. 

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unadoptable wild horses: Washington, D.C., GAO-09-77, 81 p. 

ISSN 2331-1258 (online)

http://dx.doi.org/10.3133/ofr20151045. 

13
Figure 1. Initial population size = 100, lambda = 1.05, genetic diversity = low.

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14

Appendix A. Simulation Results
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 93.71 82.73 83.68 82.28 76.81 77.32 68.49 71.19 60.66 61.53 51.22

Mean number of removals after 20 years 45.83 39.52 36.34 34.74 33.65 41.69 34.88 33.26 35.4 32.7 36.94

Mean probability of extirpation after 50 years 0.02 0.04 0.02 0.02 0 0.04 0.04 0.07 0.1 0.17 0.37

Mean heterozygosity after 50 years 0.46 0.44 0.45 0.45 0.44 0.45 0.44 0.44 0.44 0.43 0.43

Figure 1. Initial population size = 100, lambda = 1.05, genetic diversity = low.—Continued

15
Figure 2. Initial population size = 100, lambda = 1.10, genetic diversity = low.

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Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 105.96 104.13 99.93 91.74 89 83.71 83.91 80.41 74.37 58.79 43.07

Mean number of removals after 20 years 124.34 109.22 87.59 94.47 73.54 71.53 69.56 68.28 62.33 58.98 57.08

Mean probability of extirpation after 50 years 0 0 0 0.01 0 0 0 0.01 0.05 0.09 0.21

Mean heterozygosity after 50 years 0.46 0.46 0.46 0.45 0.46 0.45 0.45 0.43 0.45 0.43 0.41

Figure 2. Initial population size = 100, lambda = 1.10, genetic diversity = low.—Continued

17
Figure 3. Initial population size = 100, lambda = 1.15, genetic diversity = low.

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Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 116.67 107.04 106.93 103.8 101.36 99.18 94.47 90.36 88.82 82.5 63.9

Mean number of removals after 20 years 196.1 175.66 147.22 150.85 131.53 123.08 106.05 99.21 90.8 82.28 71.23

Mean probability of extirpation after 50 years 0 0 0 0 0.02 0 0 0 0 0.08 0.08

Mean heterozygosity after 50 years 0.47 0.47 0.46 0.47 0.46 0.46 0.46 0.45 0.45 0.45 0.43

Figure 3. Initial population size = 100, lambda = 1.15, genetic diversity = low.—Continued

19
Figure 4. Initial population size = 100, lambda = 1.20, genetic diversity = low.

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Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 117.66 115.72 111.98 102.21 105.14 102.37 98.63 98.73 95.01 90.61 87.04

Mean number of removals after 20 years 289.73 250.34 233.51 202.32 180.67 166.39 150.74 138.75 124.57 112.71 88.13

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0.01 0.01 0.1

Mean heterozygosity after 50 years 0.47 0.47 0.47 0.46 0.46 0.46 0.46 0.46 0.45 0.44 0.43

Figure 4. Initial population size = 100, lambda = 1.20, genetic diversity = low.—Continued

21
Figure 5. Initial population size = 100, lambda = 1.25, genetic diversity = low.

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Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 120.71 117.59 117.22 113.11 110.75 107.17 102.75 96.64 100.1 89.18 82.72

Mean number of removals after 20 years 367.4 325.91 285.86 245.19 225.62 197.56 182.24 162.3 144.4 126.13 111.72

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0.03 0.04 0.17

Mean heterozygosity after 50 years 0.47 0.47 0.46 0.46 0.47 0.45 0.46 0.45 0.45 0.44 0.43

Figure 5. Initial population size = 100, lambda = 1.25, genetic diversity = low.—Continued

23
Figure 6. Initial population size = 250, lambda = 1.05, genetic diversity = low.

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Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 209.16 220.46 211.25 201.33 194.71 184.37 182.2 163.33 153.91 147.12 151.88

Mean number of removals after 20 years 96.65 107.54 105.05 89.47 87.49 75.07 79.56 89.29 111.56 74 85.79

Mean probability of extirpation after 50 years 0 0 0 0.01 0 0 0.01 0.01 0.01 0.03 0.11

Mean heterozygosity after 50 years 0.47 0.47 0.47 0.47 0.46 0.47 0.47 0.47 0.46 0.46 0.45

Figure 6. Initial population size = 250, lambda = 1.05, genetic diversity = low.—Continued

25
Figure 7. Initial population size = 250, lambda = 1.10, genetic diversity = low.

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Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 260.38 264.77 262.05 239.17 236 224.01 219.74 196.91 171.78 142.36 117.4

Mean number of removals after 20 years 278.3 259.21 237.83 223.07 202.93 192.93 179.33 153.23 145.94 137.16 137.79

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0.02 0.04

Mean heterozygosity after 50 years 0.48 0.48 0.48 0.48 0.48 0.47 0.47 0.47 0.47 0.46 0.46

Figure 7. Initial population size = 250, lambda = 1.10, genetic diversity = low.—Continued

27
Figure 8. Initial population size = 250, lambda = 1.15, genetic diversity = low.

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Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 281.13 275.97 262.64 268.65 259.12 258.31 244.81 226.37 211.37 220.14 169.63

Mean number of removals after 20 years 458.22 448.92 387.51 351.03 328.21 304.61 282.41 247.07 239.97 207.47 173.26

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0.02

Mean heterozygosity after 50 years 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.47 0.46

Figure 8. Initial population size = 250, lambda = 1.15, genetic diversity = low.—Continued

29
Figure 9. Initial population size = 250, lambda = 1.20, genetic diversity = low.

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Mean population size after 20 years 303.72 277.47 274.27 271.98 275.36 262.1 260.81 256.62 226.89 207.59 223.76

Mean number of removals after 20 years 722.53 634.9 570.99 490.14 455.85 412 373.4 340.01 311.73 282.63 232.31

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0.02

Mean heterozygosity after 50 years 0.48 0.48 0.48 0.48 0.48 0.47 0.47 0.47 0.47 0.47 0.46

Figure 9. Initial population size = 250, lambda = 1.20, genetic diversity = low.—Continued

31
Figure 10. Initial population size = 250, lambda = 1.25, genetic diversity = low.

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Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 308.52 304.15 285.11 278.16 284.69 283.85 262.37 245.28 246.89 216.51 226.76

Mean number of removals after 20 years 944.59 783.74 711.97 616.4 558.71 501.11 459.28 409.28 370.9 316.51 288.81

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0.01

Mean heterozygosity after 50 years 0.48 0.48 0.48 0.48 0.48 0.47 0.47 0.48 0.47 0.47 0.47

Figure 10. Initial population size = 250, lambda = 1.25, genetic diversity = low.—Continued

33
Figure 11. Initial population size = 500, lambda = 1.05, genetic diversity = low.

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Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 425.35 444.78 401.43 354.61 387.64 355.61 352.23 319.32 310.27 304.15 276.61

Mean number of removals after 20 years 255.36 190.95 241.46 196.02 208.87 147.97 176.38 156.08 177.73 169.95 181.87

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0.01 0 0.01 0.02

Mean heterozygosity after 50 years 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.47 0.46

Figure 11. Initial population size = 500, lambda = 1.05, genetic diversity = low.—Continued

35
Figure 12. Initial population size = 500, lambda = 1.10, genetic diversity = low.

0

100

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

0

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Percentage of mares treated

Mean number of removals after 20 years

0

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

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0.30

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0.70

0.80

0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

36
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 532.14 517.32 494.85 494.04 476.94 463.89 417.36 433.64 355.55 286.94 232.49

Mean number of removals after 20 years 610.21 520.05 465.8 436.08 406.01 384.76 332.11 307.18 318.48 289.02 279.16

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.47

Figure 12. Initial population size = 500, lambda = 1.10, genetic diversity = low.—Continued

37
Figure 13. Initial population size = 500, lambda = 1.15, genetic diversity = low.

0

100

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

0

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Percentage of mares treated

Mean number of removals after 20 years

0

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

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0.70

0.80

0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

38
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 565.34 543.12 549.14 551.57 495.37 516.42 473.26 453.73 453.48 416.08 385.94

Mean number of removals after 20 years 1002.92 863.83 755.3 764.15 660.85 598.87 539.63 512.76 475.42 384.89 328.2

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.48 0.49 0.48 0.48 0.48 0.48 0.48 0.49 0.48 0.48 0.48

Figure 13. Initial population size = 500, lambda = 1.15, genetic diversity = low.—Continued

39
Figure 14. Initial population size = 500, lambda = 1.20, genetic diversity = low.

0

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

0

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Percentage of mares treated

Mean number of removals after 20 years

0

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

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0.30

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0.50

0.60

0.70

0.80

0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

40
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 606.16 564.12 546.4 555.28 531.1 513.41 515.42 502.94 486.58 450.15 452.21

Mean number of removals after 20 years 1451.75 1258.73 1122.91 997.36 900.23 820.29 752.55 671.84 624.39 559.54 432.37

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0.01

Mean heterozygosity after 50 years 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48

Figure 14. Initial population size = 500, lambda = 1.20, genetic diversity = low.—Continued

41
Figure 15. Initial population size = 500, lambda = 1.25, genetic diversity = low.

0

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

0

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Percentage of mares treated

Mean number of removals after 20 years

0

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

42
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 615.29 628.52 599.27 559.22 543.09 550.12 520.04 495.03 507.73 456.42 437.97

Mean number of removals after 20 years 1868.95 1612.35 1406.33 1227.35 1083.85 1009.6 928.44 822.54 721.17 626.66 583.8

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.48 0.49 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.47

Figure 15. Initial population size = 500, lambda = 1.25, genetic diversity = low.—Continued

43
Figure 16. Initial population size = 750, lambda = 1.05, genetic diversity = low.

0

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

0

0.1

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

0.10

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0.30

0.40

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0.60

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0.80

0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

44
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 650.88 631.43 581.13 590.12 602.15 557.46 570.81 506.51 491.17 411.2 401.89

Mean number of removals after 20 years 361.95 328.24 272.67 288.49 279.12 276.66 243.67 261.64 241.29 302.35 297.91

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0.03

Mean heterozygosity after 50 years 0.48 0.48 0.48 0.48 0.49 0.48 0.48 0.48 0.48 0.48 0.48

Figure 16. Initial population size = 750, lambda = 1.05, genetic diversity = low.—Continued

45
Figure 17. Initial population size = 750, lambda = 1.10, genetic diversity = low.

0

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

0

0.1

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

0.10

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0.30

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0.60

0.70

0.80

0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

46
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 795.56 823.24 762.24 718.7 721.89 717.77 597.06 573.89 561.16 460.9 363.9

Mean number of removals after 20 years 908.52 760.43 736.27 703.39 611.56 562.49 523.38 486.72 462.27 420.49 450.7

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.48 0.49 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.47

Figure 17. Initial population size = 750, lambda = 1.10, genetic diversity = low.—Continued

47
Figure 18. Initial population size = 750, lambda = 1.15, genetic diversity = low.

0

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

0

0.1

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

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0.30

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0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

48
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 853.53 831.08 794.36 763.4 813.88 747.49 698.91 707.4 683.74 650.95 535.33

Mean number of removals after 20 years 1458.62 1341.8 1260.79 1054.92 979.41 928.62 825.18 733.54 738.13 602.52 512.15

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.49 0.48 0.48 0.48 0.49 0.48 0.48 0.49 0.48 0.48 0.48

Figure 18. Initial population size = 750, lambda = 1.15, genetic diversity = low.—Continued

 

49
Figure 19. Initial population size = 750, lambda = 1.20, genetic diversity = low.

0

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

0

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Percentage of mares treated

Mean probability of extirpation after 50 years 

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0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

50
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 872.42 860.25 830.74 792.41 807.75 763.95 749.48 733.6 683.58 657.07 670.54

Mean number of removals after 20 years 2112.42 1885.73 1646.6 1507.2 1345.72 1244.22 1162.02 999.18 944.68 809.02 709.93

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.49 0.48 0.49 0.49 0.48 0.48 0.48 0.49 0.48 0.48 0.48

Figure 19. Initial population size = 750, lambda = 1.20, genetic diversity = low.—Continued

51
Figure 20. Initial population size = 750, lambda = 1.25, genetic diversity = low.

0

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

0

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Percentage of mares treated

Mean probability of extirpation after 50 years 

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0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

52
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 962.21 882.4 866.81 832.94 790.31 832.37 794.81 730.52 778.33 701.12 625.35

Mean number of removals after 20 years 2796.8 2371.7 2191.6 1846.0 1667.5 1492.6 1328.4 1264.1 1078.9 951.3 870.4

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.49 0.49 0.49 0.49 0.49 0.49 0.48 0.48 0.48 0.48 0.48

Figure 20. Initial population size = 750, lambda = 1.25, genetic diversity = low.—Continued

53
Figure 21. Initial population size = 1000, lambda = 1.05, genetic diversity = low.

0

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Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

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Percentage of mares treated

Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

54
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 889.31 819.79 873.34 808.05 727.98 770.69 737.69 675.8 681.41 613.88 525.62

Mean number of removals after 20 years 462.82 404.15 400.39 327.35 297.35 318.94 349.73 348.62 252.02 354.25 356.61

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0.01 0 

Mean heterozygosity after 50 years 0.48 0.48 0.48 0.48 0.48 0.49 0.48 0.48 0.48 0.48 0.48

Figure 21. Initial population size = 1000, lambda = 1.05, genetic diversity = low.—Continued

55
Figure 22. Initial population size = 1000, lambda = 1.10, genetic diversity = low.

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Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

0

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Percentage of mares treated

Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

56
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1063.82 1064.02 1019.82 959.43 930.43 875.89 872.81 839.08 764.81 549.04 483.72

Mean number of removals after 20 years 1118.7 991.5 988.6 908.4 728.6 785.9 642.2 621.2 577.2 585.4 577.7

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.49 0.49 0.49 0.48 0.48 0.48 0.48 0.49 0.48 0.48 0.48

Figure 22. Initial population size = 1000, lambda = 1.10, genetic diversity = low.—Continued

57
Figure 23. Initial population size = 1000, lambda = 1.15, genetic diversity = low.

0

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Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

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Percentage of mares treated

Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

58
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1106.82 1117.06 1065.72 1020.7 1093.2 1008.49 970.31 948.69 895.72 845.6 752.22

Mean number of removals after 20 years 1979.8 1841.8 1512.9 1445.2 1296.8 1201.1 1143.0 1020.5 883.9 764.1 669.3

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.49 0.49 0.48 0.49 0.48 0.48 0.49 0.48 0.49 0.48 0.48

Figure 23. Initial population size = 1000, lambda = 1.15, genetic diversity = low.—Continued

59
Figure 24. Initial population size = 1000, lambda = 1.20, genetic diversity = low.

0

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Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

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Percentage of mares treated

Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

60
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1201.08 1184.02 1176.54 1085.77 1090.8 1024.31 1030.98 1029.85 970.74 885.67 910.27

Mean number of removals after 20 years 2890.6 2543.6 2191.6 2009.4 1861.7 1689.8 1515.9 1357.8 1215.4 1107.5 961.8

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.48 0.48 0.48 0.48

Figure 24. Initial population size = 1000, lambda = 1.20, genetic diversity = low.—Continued

61
Figure 25. Initial population size = 1000, lambda = 1.25, genetic diversity = low.

0

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Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

0

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Percentage of mares treated

Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

62
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1202.9 1207.36 1205.51 1111.97 1097.25 1076.74 1016.51 975.02 1092.2 911.9 896.56

Mean number of removals after 20 years 3713.4 3151.0 2838.8 2498.7 2250.0 1960.2 1756.7 1654.6 1417.1 1247.7 1131.8

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.49 0.49 0.49 0.49 0.49 0.48 0.49 0.49 0.48 0.48 0.48

Figure 25. Initial population size = 1000, lambda = 1.25, genetic diversity = low.—Continued

63
Figure 26. Initial population size = 1250, lambda = 1.05, genetic diversity = low.

0

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Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

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Percentage of mares treated

Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

64
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1181.85 1024.21 1000.58 1032.15 948.63 904.73 923.82 859.2 824.58 782.46 666.31

Mean number of removals after 20 years 574.25 523.43 544.18 483.72 493.96 463.54 459.15 412.01 352.83 491.73 425.11

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0.01

Mean heterozygosity after 50 years 0.49 0.48 0.49 0.49 0.48 0.48 0.48 0.49 0.49 0.48 0.48

Figure 26. Initial population size = 1250, lambda = 1.05, genetic diversity = low.—Continued

65
Figure 27. Initial population size = 1250, lambda = 1.10, genetic diversity = low.

0

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Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

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Percentage of mares treated

Mean probability of extirpation after 50 years 

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1.00

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Percentage of mares treated

Mean heterozygosity after 50 years

66
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1398.94 1275.26 1198.43 1215.27 1214.22 1094.1 1138.43 1019.54 893.99 821.65 649.09

Mean number of removals after 20 years 1458.6 1191.7 1140.2 1004.3 1038.6 948.0 915.8 720.1 788.2 708.3 672.1

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.49 0.48 0.49 0.49 0.49 0.49 0.49 0.49 0.48 0.49 0.48

Figure 27. Initial population size = 1250, lambda = 1.10, genetic diversity = low.—Continued

67
Figure 28. Initial population size = 1250, lambda = 1.15, genetic diversity = low.

0

200

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

0

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0 20 40 60 80 100

Percentage of mares treated

Mean number of removals after 20 years

0

0.1

0.2

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0.6

0.7

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0 20 40 60 80 100

Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

68
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1413.8 1407.5 1390.5 1311.6 1313.5 1204.9 1207.4 1213.3 1084.0 1120.9 874.2

Mean number of removals after 20 years 2465.8 2243.6 2057.3 1822.6 1733.3 1522.9 1385.8 1252.5 1198.7 990.3 829.2

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.48 0.49 0.48

Figure 28. Initial population size = 1250, lambda = 1.15, genetic diversity = low.—Continued

69
Figure 29. Initial population size = 1250, lambda = 1.20, genetic diversity = low.

0

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

0

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0 20 40 60 80 100

Percentage of mares treated

Mean number of removals after 20 years

0

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

70
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1447.5 1481.5 1392.3 1386.1 1362.7 1312.3 1309.2 1287.2 1182.8 1077.5 1116.7

Mean number of removals after 20 years 3615.2 3121.2 2802.8 2538.6 2179.6 2071.5 1859.4 1671.5 1576.1 1398.1 1103.3

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.48 0.49 0.48 0.48

Figure 29. Initial population size = 1250, lambda = 1.20, genetic diversity = low.—Continued

71
Figure 30. Initial population size = 1250, lambda = 1.25, genetic diversity = low.

0.0

200.0

400.0

600.0

800.0

1000.0

1200.0

1400.0

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Percentage of mares treated

Mean population size after 20 years

0

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Percentage of mares treated

Mean number of removals after 20 years

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

72
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1536.3 1557.9 1445.1 1433.6 1394.1 1407.8 1243.9 1279.1 1248.4 1154.4 1039.9

Mean number of removals after 20 years 4509.1 3960.3 3453.9 3146.1 2711.4 2577.9 2226.4 2122.1 1782.3 1559.0 1409.3

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.49 0.49 0.49 0.48 0.49 0.48 0.49 0.49 0.48 0.49 0.48

Figure 30. Initial population size = 1250, lambda = 1.25, genetic diversity = low.—Continued

73
Figure 31. Initial population size = 1500, lambda = 1.05, genetic diversity = low.

0

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

0

0.1

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

0.10

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0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

74
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1279.4 1173.9 1220.8 1167.1 1224.9 1117.3 1098.7 987.4 1053.9 873.3 830.5

Mean number of removals after 20 years 547.92 557.55 504.35 573.75 514.62 487.4 459.94 558.95 591.28 496.54 524.2

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.49 0.49 0.49 0.49 0.49 0.48 0.49 0.49 0.48 0.48 0.48

Figure 31. Initial population size = 1500, lambda = 1.05, genetic diversity = low.—Continued

75
Figure 32. Initial population size = 1500, lambda = 1.10, genetic diversity = low.

0

200

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1400

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

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0 20 40 60 80 100

Percentage of mares treated

Mean number of removals after 20 years

0

0.1

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

76
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1622.8 1461.2 1457.5 1477.4 1435.9 1380.1 1232.4 1255.8 1054.9 846.0 697.3

Mean number of removals after 20 years 1735.0 1628.0 1308.3 1327.2 1348.6 995.9 1072.9 903.0 868.5 872.8 843.8

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.49 0.49 0.49 0.49 0.48 0.49 0.48 0.48 0.49 0.48 0.48

Figure 32. Initial population size = 1500, lambda = 1.10, genetic diversity = low.—Continued

77
Figure 33. Initial population size = 1500, lambda = 1.15, genetic diversity = low.

0

200

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1400

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

0

0.1

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0 20 40 60 80 100

Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

78
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1714.8 1666.7 1643.6 1542.5 1542.7 1489.8 1436.2 1399.0 1368.2 1382.5 1033.5

Mean number of removals after 20 years 2777.7 2501.4 2591.7 2200.3 1822.5 1910.5 1669.9 1596.4 1444.0 1172.7 1004.9

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.48 0.48 0.48

Figure 33. Initial population size = 1500, lambda = 1.15, genetic diversity = low.—Continued

79
Figure 34. Initial population size = 1500, lambda = 1.20, genetic diversity = low.

0

200

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

0

0.1

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

80
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1821.8 1719.5 1697.0 1572.3 1667.0 1563.1 1523.7 1505.0 1433.3 1294.1 1376.3

Mean number of removals after 20 years 4241.3 3605.67 3348.38 3026.93 2716.34 2518.97 2225.75 2043.6 1886.32 1648.08 1381.6

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.48 0.48

Figure 34. Initial population size = 1500, lambda = 1.20, genetic diversity = low.—Continued

81
Figure 35. Initial population size = 1500, lambda = 1.25, genetic diversity = low.

0

200

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

0

0.1

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

0.10

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0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

82
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1821.3 1775.6 1704.2 1702.5 1645.8 1645.7 1631.5 1516.9 1566.6 1342.5 1343.4

Mean number of removals after 20 years 5662.1 4837.4 4282.2 3732.1 3380.2 2949.7 2731.2 2438.5 2164.2 1852.6 1756.3

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0.01 0 0 

Mean heterozygosity after 50 years 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.48 0.49 0.48

Figure 35. Initial population size = 1500, lambda = 1.25, genetic diversity = low.—Continued

83
Figure 36. Initial population size = 100, lambda = 1.05, genetic diversity = high.

0

20

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

0

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Percentage of mares treated

Mean number of removals after 20 years

0

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

0.10

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0.30

0.40

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0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

84
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 85.65 80.04 83.81 82.32 77.46 76.91 64.82 63.57 68.7 61.78 56.86

Mean number of removals after 20 years 52.51 37.59 38.83 38.02 36.03 34.27 39.99 38.8 27.57 34.2 34.23

Mean probability of extirpation after 50 years 0.03 0.03 0.04 0 0.02 0.02 0.11 0.07 0.07 0.21 0.3

Mean heterozygosity after 50 years 0.72 0.72 0.72 0.72 0.72 0.72 0.71 0.69 0.70 0.70 0.67

Figure 36. Initial population size = 100, lambda = 1.05, genetic diversity = high.—Continued

85
Figure 37. Initial population size = 100, lambda = 1.10, genetic diversity = high.

0

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

0

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Percentage of mares treated

Mean number of removals after 20 years

0

0.1

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

0.10

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0.30

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0.50

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0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

86
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 107.97 99.44 96.12 98.03 95.64 85.17 85.71 78.45 70.71 53.94 55.76

Mean number of removals after 20 years 115.94 106.96 96.94 80.92 78.45 71.85 70.62 66.8 62.01 56.75 52.5

Mean probability of extirpation after 50 years 0 0 0.01 0 0 0 0.02 0.01 0.01 0.06 0.31

Mean heterozygosity after 50 years 0.74 0.74 0.73 0.73 0.73 0.72 0.72 0.71 0.71 0.68 0.67

Figure 37. Initial population size = 100, lambda = 1.10, genetic diversity = high.—Continued

87
Figure 38. Initial population size = 100, lambda = 1.15, genetic diversity = high.

0

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

0

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Percentage of mares treated

Mean number of removals after 20 years

0

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

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0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

88
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 118.53 113.82 106.1 105.09 102.72 102.37 92.64 87.6 88.79 79.15 63.95

Mean number of removals after 20 years 208.4 181.74 158.65 145.93 135.73 121.88 112.21 103.11 93.06 77.44 68.55

Mean probability of extirpation after 50 years 0 0 0 0 0.01 0 0 0.02 0.02 0.03 0.1

Mean heterozygosity after 50 years 0.75 0.75 0.75 0.74 0.74 0.74 0.74 0.73 0.72 0.72 0.68

Figure 38. Initial population size = 100, lambda = 1.15, genetic diversity = high.—Continued

89
Figure 39. Initial population size = 100, lambda = 1.20, genetic diversity = high.

0

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

0

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Percentage of mares treated

Mean number of removals after 20 years

0

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

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0.90

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0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

90
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 115.87 113.82 120.06 113.47 105.64 102.99 98.66 101.46 90.77 86.41 85.86

Mean number of removals after 20 years 287.24 255.15 222.93 205.42 179.11 170.34 151.32 134.9 123.26 112.03 97.01

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0.01 0 0.06 0.04 0.13

Mean heterozygosity after 50 years 0.75 0.75 0.75 0.75 0.74 0.74 0.74 0.72 0.72 0.71 0.70

Figure 39. Initial population size = 100, lambda = 1.20, genetic diversity = high.—Continued

91
Figure 40. Initial population size = 100, lambda = 1.25, genetic diversity = high.

0

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Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

0

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

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0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

92
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 121.02 115.17 113.84 114.66 110.88 109.29 107.18 97.48 95.07 91.82 81.06

Mean number of removals after 20 years 373.76 320.53 274.59 255.43 225.87 207.24 181.97 164.56 146.74 127.02 110.7

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0.01 0.01 0.04 0.21

Mean heterozygosity after 50 years 0.75 0.75 0.75 0.75 0.74 0.74 0.74 0.73 0.71 0.70 0.69

Figure 40. Initial population size = 100, lambda = 1.25, genetic diversity = high.—Continued

93
Figure 41. Initial population size = 250, lambda = 1.05, genetic diversity = high.

0

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Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

0

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

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Percentage of mares treated

Mean heterozygosity after 50 years

94
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 229.82 208.28 209.81 193.14 194.37 191.52 191.17 153.65 157.95 139.22 126.74

Mean number of removals after 20 years 130.33 109.21 106.87 95.15 93.21 95.93 96.1 91.98 79.41 93.08 89.13

Mean probability of extirpation after 50 years 0 0 0 0.01 0 0 0.01 0.01 0.01 0.06 0.12

Mean heterozygosity after 50 years 0.76 0.76 0.76 0.75 0.76 0.76 0.76 0.75 0.75 0.74 0.72

Figure 41. Initial population size = 250, lambda = 1.05, genetic diversity = high.—Continued

95
Figure 42. Initial population size = 250, lambda = 1.10, genetic diversity = high.

0

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Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

0

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

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0.90

1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

96
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 253.29 248.13 251.86 257.66 244.53 226.55 212.8 194.92 181.23 140.26 121.89

Mean number of removals after 20 years 294.42 244.72 240.7 229.15 190.87 195.41 180.34 161.04 149.36 148.76 141.8

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0.04

Mean heterozygosity after 50 years 0.77 0.77 0.77 0.77 0.76 0.76 0.76 0.76 0.75 0.75 0.72

Figure 42. Initial population size = 250, lambda = 1.10, genetic diversity = high.—Continued

97
Figure 43. Initial population size = 250, lambda = 1.15, genetic diversity = high.

0

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0 20 40 60 80 100

Percentage of mares treated

Mean population size after 20 years

0

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Percentage of mares treated

Mean number of removals after 20 years

0

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

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1.00

0 20 40 60 80 100

Percentage of mares treated

Mean heterozygosity after 50 years

98
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 278.95 274.39 264.77 267.48 247.95 249.86 254.3 249.36 232.19 203.01 169.11

Mean number of removals after 20 years 478.13 410.55 411.23 373.12 350.21 295.77 278.33 262.32 220.73 207.34 168.69

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0.02 0.01

Mean heterozygosity after 50 years 0.77 0.77 0.77 0.77 0.77 0.77 0.77 0.76 0.76 0.75 0.74

Figure 43. Initial population size = 250, lambda = 1.15, genetic diversity = high.—Continued

99
Figure 44. Initial population size = 250, lambda = 1.20, genetic diversity = high.

0

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Percentage of mares treated

Mean population size after 20 years

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Percentage of mares treated

Mean number of removals after 20 years

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Percentage of mares treated

Mean probability of extirpation after 50 years 

0.00

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Percentage of mares treated

Mean heterozygosity after 50 years

100
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 290.06 311.21 272.6 272.05 264.99 269.08 267.14 258.33 229.2 220.46 218.12

Mean number of removals after 20 years 711.9 618.06 550.39 491.13 458.39 405.16 385.49 331.92 307.21 279.49 227.5

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0.04

Mean heterozygosity after 50 years 0.77 0.77 0.77 0.77 0.77 0.77 0.77 0.76 0.76 0.75 0.73

Figure 44. Initial population size = 250, lambda = 1.20, genetic diversity = high.—Continued

101
Figure 45. Initial population size = 250, lambda = 1.25, genetic diversity = high.

0

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Mean probability of extirpation after 50 years 

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Mean heterozygosity after 50 years

102
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 316.89 298.09 297.94 282.24 266.75 277.65 254.56 236.14 242.76 234.27 217.59

Mean number of removals after 20 years 937.55 786.93 697.69 617.57 562.54 490.47 450.66 409.16 363.89 320.86 276.24

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0.02

Mean heterozygosity after 50 years 0.77 0.77 0.77 0.77 0.77 0.77 0.76 0.76 0.76 0.75 0.75

Figure 45. Initial population size = 250, lambda = 1.25, genetic diversity = high.—Continued

103
Figure 46. Initial population size = 500, lambda = 1.05, genetic diversity = high.

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Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

104
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 450.57 412.67 421.58 421.47 407.01 385.44 336.29 354.49 278.69 287.98 292.7

Mean number of removals after 20 years 165.39 203.66 214.47 212.76 209.18 155.55 170.07 154.49 186.23 178.59 180.8

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0.03 0.03

Mean heterozygosity after 50 years 0.77 0.77 0.77 0.77 0.77 0.77 0.77 0.77 0.76 0.76 0.75

Figure 46. Initial population size = 500, lambda = 1.05, genetic diversity = high.—Continued

105
Figure 47. Initial population size = 500, lambda = 1.10, genetic diversity = high.

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Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

106
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 530.61 530.85 517.52 493.18 467.76 453.59 454.75 415.17 356.16 318.2 252.43

Mean number of removals after 20 years 591.77 536.39 469.19 428.35 413.44 371.39 319.96 329.77 315.36 302.16 286.23

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.77 0.77 0.77 0.77 0.77 0.77 0.75

Figure 47. Initial population size = 500, lambda = 1.10, genetic diversity = high.—Continued

107
Figure 48. Initial population size = 500, lambda = 1.15, genetic diversity = high.

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Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

108
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 562.32 542.84 518.23 536.63 513.12 478.55 484.51 462.25 467.67 431.71 325.38

Mean number of removals after 20 years 985.18 870.87 799.25 721.09 665.02 606.24 577.73 482.76 475.37 406.87 352.26

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.77 0.77 0.77 0.77 0.76

Figure 48. Initial population size = 500, lambda = 1.15, genetic diversity = high.—Continued

109
Figure 49. Initial population size = 500, lambda = 1.20, genetic diversity = high.

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Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

110
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 591.83 584.93 542.73 534.42 532.9 516.29 504.75 510.67 469.76 444.23 479.71

Mean number of removals after 20 years 1435.1 1271.0 1072.6 1003.7 908.9 826.8 741.6 663.7 606.5 567.2 445.4

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.77 0.77 0.76

Figure 49. Initial population size = 500, lambda = 1.20, genetic diversity = high.—Continued

111
Figure 50. Initial population size = 500, lambda = 1.25, genetic diversity = high.

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Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

112
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 594.45 589.9 594.5 555.72 543.85 529.95 531.28 510.02 523.65 449.97 449.55

Mean number of removals after 20 years 1874.5 1624.6 1402.6 1249.2 1116.2 1021.7 907.0 809.4 707.9 631.4 559.9

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0.01

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.77 0.78 0.78 0.77 0.77 0.76

Figure 50. Initial population size = 500, lambda = 1.25, genetic diversity = high.—Continued

113
Figure 51. Initial population size = 750, lambda = 1.05, genetic diversity = high.

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Mean heterozygosity after 50 years

114
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 662.85 602.11 594.21 609.04 573.37 563.41 531.5 490.61 478.09 432.79 467.39

Mean number of removals after 20 years 357.45 343.82 320.45 290.07 234.09 234 273.83 253.99 263.92 289.45 228.35

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0.01 0 0.01 0 

Mean heterozygosity after 50 years 0.78 0.78 0.77 0.78 0.78 0.78 0.77 0.77 0.77 0.77 0.76

Figure 51. Initial population size = 750, lambda = 1.05, genetic diversity = high.—Continued

115
Figure 52. Initial population size = 750, lambda = 1.10, genetic diversity = high.

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Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

116
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 800.78 749.94 784.34 714.78 701.29 705.25 633.52 658.99 513.24 468.63 351.92

Mean number of removals after 20 years 838.9 753.64 742.14 625.1 605.75 599.52 493.98 486.5 466.16 451.41 427.27

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.77 0.76

Figure 52. Initial population size = 750, lambda = 1.10, genetic diversity = high.—Continued

117
Figure 53. Initial population size = 750, lambda = 1.15, genetic diversity = high.

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Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

118
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 863.26 828.87 793.09 812.32 758.17 742.73 683.78 670.07 677.22 660.32 478.72

Mean number of removals after 20 years 1444.8 1304.1 1189.2 1132.7 929.9 920.5 834.1 788.1 679.1 599.5 501.4

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.77

Figure 53. Initial population size = 750, lambda = 1.15, genetic diversity = high.—Continued

119
Figure 54. Initial population size = 750, lambda = 1.20, genetic diversity = high.

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Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

120
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 862.48 830.01 830.72 878.81 816.6 782.19 791.89 743.94 704.05 649.05 680.91

Mean number of removals after 20 years 2146.1 1909.2 1659.2 1506.0 1394.6 1181.1 1109.7 1021.6 923.1 847.1 675.6

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.77

Figure 54. Initial population size = 750, lambda = 1.20, genetic diversity = high.—Continued

121
Figure 55. Initial population size = 750, lambda = 1.25, genetic diversity = high.

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Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

122
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 943.03 890.54 880.47 872.85 830.01 804.21 779.9 751.3 773.8 666.84 631.64

Mean number of removals after 20 years 2741.1 2352.9 2128.9 1845.6 1703.7 1518.4 1309.1 1234.3 1086.5 937.0 868.1

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.77 0.77

Figure 55. Initial population size = 750, lambda = 1.25, genetic diversity = high.—Continued

123
Figure 56. Initial population size = 1000, lambda = 1.05, genetic diversity = high.

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Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

124
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 854.42 886.33 782.46 808.7 774.68 767.58 711.38 694.91 623.41 608.7 604

Mean number of removals after 20 years 408.46 393.28 416.19 321.57 362.43 331.22 346.92 353.96 346.09 328.18 344.26

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0.01 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.77 0.76

Figure 56. Initial population size = 1000, lambda = 1.05, genetic diversity = high.—Continued

125
Figure 57. Initial population size = 1000, lambda = 1.10, genetic diversity = high.

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Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

126
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1098.09 1061.14 972.15 967.57 933.76 901.35 828.11 810.67 669.9 638.13 489.1

Mean number of removals after 20 years 1196.9 1091.1 1048.1 899.6 804.5 755.5 702.3 621.7 597.8 560.3 541.2

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.77

Figure 57. Initial population size = 1000, lambda = 1.10, genetic diversity = high.—Continued

127
Figure 58. Initial population size = 1000, lambda = 1.15, genetic diversity = high.

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Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

128
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1124.15 1128.74 1069.1 1069.36 1056.52 964.86 940 922.21 893.25 845.4 665.68

Mean number of removals after 20 years 1907.4 1878.5 1517.7 1492.3 1343.0 1182.7 1130.2 1058.3 934.0 808.2 669.0

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78

Figure 58. Initial population size = 1000, lambda = 1.15, genetic diversity = high.—Continued

129
Figure 59. Initial population size = 1000, lambda = 1.20, genetic diversity = high.

0

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Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

130
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1219.7 1169.6 1129.0 1143.8 1073.6 1041.0 1075.2 1009.6 938.2 920.0 886.5

Mean number of removals after 20 years 2877.8 2551.9 2307.0 2013.1 1851.7 1597.8 1478.2 1362.8 1196.4 1149.4 963.0

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78

Figure 59. Initial population size = 1000, lambda = 1.20, genetic diversity = high.—Continued

131
Figure 60. Initial population size = 1000, lambda = 1.25, genetic diversity = high.

0

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Percentage of mares treated

Mean heterozygosity after 50 years

132
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1225.4 1169.7 1140.7 1117.1 1077.6 1076.7 1098.6 1071.1 1041.7 894.4 882.7

Mean number of removals after 20 years 3749.6 3175.7 2844.7 2489.0 2147.9 1978.4 1831.9 1649.2 1432.6 1223.8 1159.1

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78

Figure 60. Initial population size = 1000, lambda = 1.25, genetic diversity = high.—Continued

133
Figure 61. Initial population size = 1250, lambda = 1.05, genetic diversity = high.

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Mean heterozygosity after 50 years

134
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1066.7 1139.5 1095.1 1041.0 989.2 938.4 896.1 874.0 841.0 747.5 683.3

Mean number of removals after 20 years 575.5 629.3 519.5 406.3 442.6 524.2 422.0 420.3 393.0 422.2 428.9

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.77 0.77

Figure 61. Initial population size = 1250, lambda = 1.05, genetic diversity = high.—Continued

135
Figure 62. Initial population size = 1250, lambda = 1.10, genetic diversity = high.

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Mean heterozygosity after 50 years

136
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1388.7 1304.7 1254.2 1242.3 1126.8 1225.7 1041.3 1101.1 885.0 820.1 551.3

Mean number of removals after 20 years 1442.2 1296.3 1129.6 995.3 1024.7 845.1 834.5 866.0 738.2 721.3 735.6

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.77

Figure 62. Initial population size = 1250, lambda = 1.10, genetic diversity = high.—Continued

137
Figure 63. Initial population size = 1250, lambda = 1.15, genetic diversity = high.

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Mean heterozygosity after 50 years

138
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1468.9 1338.2 1354.4 1321.2 1271.8 1263.7 1147.8 1151.5 1135.1 1112.2 866.6

Mean number of removals after 20 years 2353.0 2166.1 2044.2 1797.3 1667.0 1529.1 1445.7 1267.1 1179.7 991.6 840.9

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78

Figure 63. Initial population size = 1250, lambda = 1.15, genetic diversity = high.—Continued

139
Figure 64. Initial population size = 1250, lambda = 1.20, genetic diversity = low.

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Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

140
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1449.1 1375.0 1398.9 1397.6 1381.6 1301.0 1306.8 1274.2 1152.3 1086.1 1090.1

Mean number of removals after 20 years 3536.0 3218.8 2791.6 2439.7 2302.0 2047.4 1874.1 1697.0 1517.3 1426.7 1110.3

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78

Figure 64. Initial population size = 1250, lambda = 1.20, genetic diversity = low.—Continued

141
Figure 65. Initial population size = 1250, lambda = 1.25, genetic diversity = low.

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Mean probability of extirpation after 50 years 

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Percentage of mares treated

Mean heterozygosity after 50 years

142
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1512.7 1430.9 1428.7 1474.7 1412.0 1480.7 1257.7 1274.9 1284.0 1193.1 1087.6

Mean number of removals after 20 years 4658.4 3937.6 3415.0 3030.1 2732.3 2491.5 2261.5 2041.8 1751.8 1629.4 1422.0

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78

Figure 65. Initial population size = 1250, lambda = 1.25, genetic diversity = low.—Continued

143
Figure 66. Initial population size = 1500, lambda = 1.05, genetic diversity = high.

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Mean heterozygosity after 50 years

144
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1401.3 1213.9 1283.2 1249.7 1035.4 1142.4 1056.3 925.6 1005.1 862.6 845.7

Mean number of removals after 20 years 764.8 589.6 604.0 530.4 578.3 527.0 547.6 539.9 516.7 534.7 497.8

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0.01

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.77

Figure 66. Initial population size = 1500, lambda = 1.05, genetic diversity = high.—Continued

145
Figure 67. Initial population size = 1500, lambda = 1.10, genetic diversity = high.

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Mean heterozygosity after 50 years

146
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1534.7 1515.0 1441.5 1468.4 1487.3 1411.4 1367.4 1280.2 1158.3 996.3 604.3

Mean number of removals after 20 years 1669.4 1636.8 1316.9 1346.6 1118.7 1139.7 979.0 911.8 846.6 799.3 886.0

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.77

Figure 67. Initial population size = 1500, lambda = 1.10, genetic diversity = high.—Continued

147
Figure 68. Initial population size = 1500, lambda = 1.15, genetic diversity = high.

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Mean heterozygosity after 50 years

148
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1712.0 1627.6 1576.6 1629.3 1553.6 1500.3 1535.1 1396.9 1306.5 1281.2 1053.2

Mean number of removals after 20 years 2896.0 2590.5 2349.9 2187.2 1938.7 1780.1 1713.2 1538.8 1441.8 1180.9 1038.4

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78

Figure 68. Initial population size = 1500, lambda = 1.15, genetic diversity = high.—Continued

149
Figure 69. Initial population size = 1500, lambda = 1.20, genetic diversity = high.

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Mean heterozygosity after 50 years

150
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1761.4 1771.4 1712.8 1660.2 1595.1 1518.3 1551.7 1551.3 1378.4 1331.5 1397.5

Mean number of removals after 20 years 4280.8 3712.2 3260.2 3005.3 2689.8 2516.5 2281.8 2007.8 1802.1 1735.3 1423.0

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78

Figure 69. Initial population size = 1500, lambda = 1.20, genetic diversity = high.—Continued

151
Figure 70. Initial population size = 1500, lambda = 1.25, genetic diversity = high.

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Mean heterozygosity after 50 years

152
Percentage of mares treated 0 10 20 30 40 50 60 70 80 90 100

Mean population size after 20 years 1902.9 1845.4 1761.8 1664.4 1620.0 1726.7 1585.1 1496.6 1543.0 1414.6 1267.5

Mean number of removals after 20 years 5436.7 4770.0 4094.4 3748.1 3344.8 2876.4 2706.6 2411.4 2203.6 1906.3 1821.2

Mean probability of extirpation after 50 years 0 0 0 0 0 0 0 0 0 0 0 

Mean heterozygosity after 50 years 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78

Figure 70. Initial population size = 1500, lambda = 1.25, genetic diversity = high.—Continued

153