6

Population Models and Evaluation of Models

The Bureau of Land Management (BLM) Wild Horses and Burros Management Handbook states that the WinEquus model,1 developed by Stephen Jenkins at the University of Nevada, Reno, “will be used during gather or herd management area planning to analyze and compare the effects of proposed wild horse management” and “to identify whether any of the alternatives would be likely to ‘crash’ the population based on a number of stochastic factors (varying environmental conditions)” (BLM, 2010a, p. 28). This chapter briefly reviews the purpose and utility of modeling population dynamics and the kinds of models that have been applied to free-ranging horse and burro populations. It then examines models that have been developed specifically for the BLM Wild Horse and Burro Program. After reviewing their strengths and weaknesses, the chapter concludes with an overview of alternative modeling approaches that can be useful for managing the free-ranging equid populations on the western rangelands.

UTILITY OF POPULATION MODELS

Models of population dynamics (hereafter, referred to as population models) are useful tools for understanding, explaining, and predicting the dynamics and persistence of biological populations. From a management perspective, such models can be used for assessing the status of a population, diagnosing causes of population declines or explosive growth, prescribing management targets, and evaluating the prognosis of a population’s likely responses to alternative management actions (Caswell, 2001). For example, population modeling played an important role in reversing the decline of the endangered loggerhead sea turtle population in the United States (Crouse et al., 1987; Crowder et al., 1994; Caswell, 2001). Until the 1980s, sea turtle conservation efforts had focused on the protection of nests, eggs, and hatchlings on nesting beaches. Analysis of stage-structured population models revealed that the sea turtle population growth rate was proportionately most

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1 The WinEquus is available online at http://wolfweb.unr.edu/homepage/jenkins/.



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6 Population Models and Evaluation of Models T he Bureau of Land Management (BLM) Wild Horses and Burros Management Handbook states that the WinEquus model,1 developed by Stephen Jenkins at the University of Nevada, Reno, “will be used during gather or herd management area planning to analyze and compare the effects of proposed wild horse management” and “to iden- tify whether any of the alternatives would be likely to ‘crash’ the population based on a number of stochastic factors (varying environmental conditions)” (BLM, 2010a, p. 28). This chapter briefly reviews the purpose and utility of modeling population dynamics and the kinds of models that have been applied to free-ranging horse and burro populations. It then examines models that have been developed specifically for the BLM Wild Horse and Burro Program. After reviewing their strengths and weaknesses, the chapter concludes with an overview of alternative modeling approaches that can be useful for managing the free-ranging equid populations on the western rangelands. UTILITY OF POPULATION MODELS Models of population dynamics (hereafter, referred to as population models) are use- ful tools for understanding, explaining, and predicting the dynamics and persistence of biological populations. From a management perspective, such models can be used for assess­ ng the status of a population, diagnosing causes of population declines or explosive i growth, prescribing management targets, and evaluating the prognosis of a population’s likely responses to alternative management actions (Caswell, 2001). For example, popula- tion modeling played an important role in reversing the decline of the endangered logger­ head sea turtle population in the United States (Crouse et al., 1987; Crowder et al., 1994; Caswell, 2001). Until the 1980s, sea turtle conservation efforts had focused on the protection of nests, eggs, and hatchlings on nesting beaches. Analysis of stage-structured popula- tion models revealed that the sea turtle population growth rate was proportionately most 1  The WinEquus is available online at http://wolfweb.unr.edu/homepage/jenkins/. 175

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176 USING SCIENCE TO IMPROVE THE BLM WILD HORSE AND BURRO PROGRAM sensitive to changes in survival and that reducing mortality of subadult and adult turtles at sea would be a more efficient way of increasing population growth rate than protecting nests and hatchlings on nesting beaches. Informed in part by those findings, regulations were imposed to require turtle excluder devices (TEDs) in shrimp trawls in the sea turtle range. Although controversial initially, the use of TEDs was later endorsed by a National Research Council committee (NRC, 1990) and is thought to have had a substantial favorable effect on loggerhead sea turtle populations (Caswell, 2001). Models of population dynamics can also help to predict populations’ responses to environmental changes, such as global climate change. Global climate change is predicted to influence arctic sea ice adversely, and this could affect the population dynamics and per- sistence of species that depend on sea ice environments. For example, polar bears depend on arctic sea ice for feeding and breeding. By integrating field data, climate-change models, and population models, Hunter et al. (2010) predicted that the polar bear population in the southern Beaufort Sea would experience a drastic decline because of a reduction in sea ice extent by the end of the 21st century. Population models are also useful tools in the management of overabundant species. For example, the American bullfrog is an introduced species on Vancouver Island and is ad- versely affecting biodiversity on parts of the island. A modeling study by ­ ovindarajulu et G al. (2005) reported that the management strategy of targeting removal of tadpoles may not be effective because partial removal of tadpoles could lead to higher tadpole survival owing ­ to reduced density-dependent effects. Their results revealed that culling metamorphs in fall would be most effective in controlling bullfrog populations. A theoretical study by Zipkin et al. (2009) suggested that control of overabundant species by harvest (or removal) could backfire because populations of species characterized by early maturity and high fecundity may experience rapid growth after harvest or removal as a result of density-dependent overcompensation. Other examples of the application of population models include as- sessing the influences of culling and fertility control on the population dynamics of an overabundant elk population (Bradford and Hobbs, 2008) and controlling the fertility of the koala on koala-forest dynamics (Todd et al., 2008), evaluating the efficacy of ­ uthanasia e versus trap-neuter-return for management of free-roaming cats (Andersen et al., 2004) and the efficacy of fertility control in a white-tailed deer population (Merrill et al., 2003), discerning mechanisms underlying a recent rapid population growth in yellow-bellied marmots (Ozgul et al., 2010), predicting effects of El Niño on the dynamics and persistence of the Galapagos penguin population (Vargas et al., 2007), assessing harvest impact on the persistence of dugongs (Heinsohn et al., 2004), and projecting the impact of anticipated cli- mate change on the dynamics and persistence of emperor penguin populations (­Jenouvrier et al., 2009). POPULATION MODELS APPLIED TO HORSES AND BURROS Population models have been applied to free-ranging horse populations to address a variety of ecological and management questions. The modeling frameworks used have ranged from simple, unstructured models to complex spatially explicit, individual-based simulation models. In the United States, Garrott and Taylor (1990) were among the first to report estimates of age-specific survival, reproductive rates, and population growth rates in a free-ranging horse population. Since then, several population-modeling studies have been conducted, including those by Garrott et al. (1991, 1992), Garrott and Siniff (1992), C ­ oughenour (1999, 2000, 2002), Gross (2000), Ballou et al. (2008), and Bartholow (2007). Outside the United States, population dynamics in free-ranging or semi–free-ranging horse

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POPULATION MODELS AND EVALUATION OF MODELS 177 populations have been studied and modeled in Australia (Walter, 2002; Dawson, 2005; Dawson and Hone, 2012), Argentina (Scorolli and Lopez Cazorla, 2010), New Zealand (Linklater et al., 2004), and France (Grange et al., 2009). Relatively few studies have exam- ined demography and population dynamics of free-ranging asses or free-ranging burros either inside or outside the United States (Freeland and Choquenot, 1990; Choquenot, 1991; Saltz and Rubenstein, 1995; Saltz et al., 2006). From a management perspective, free-ranging horse population-modeling efforts have focused on management strategies to reduce population size and growth rate (Garrott and Siniff, 1992; Garrott et al., 1992; Gross 2000). The primary foci have been to determine the number (or proportion), sex, and age of animals to be removed or made infertile to achieve a target population size or growth rate and to determine the frequency of removal or fertility-control treatments necessary to achieve management objectives. Motivated by a controversy regarding the sex of animals to be targeted for fertility control, Garrott and Siniff (1992) conducted a simulation study to determine the population effects of male-directed fertility control in free-ranging horses. They concluded that male- oriented contraception would result in only modest reductions in population growth rate and potentially would disrupt seasonal foaling patterns. In one of the first and most com- prehensive modeling efforts, Garrott et al. (1992) used an age-structured population model and evaluated population effects and costs associated with five management alternatives: selective removal, nonselective removal, and three different fertility-control treatments. Their results revealed pros and cons of each management alternative but suggested that a female-directed fertility-control program can reduce the number of horses that need to be removed to keep the horse numbers within an acceptable range and can reduce associated costs of management activities. Gross (2000) developed an individual-based model to simulate free-ranging horse population dynamics and genetic diversity and to evaluate the efficacy of alternative man- agement strategies. The model operated on a yearly time step,2 followed each animal from birth to death, and was parameterized with (that is, based on) demographic data from the Pryor Mountain herd. Sex, age, reproductive status, and genetic constitution of each animal were explicitly considered, and such processes as breeding, recruitment, contraception, and removal were simulated. Genetic diversity was modeled by simulating Mendelian in- heritance at 10 independent loci. Management strategies implemented included removals, ­ contraceptive treatments, or both. Management strategies were “simulated by applying rules based on current population size, post-treatment population objective, sex and age of animals to be treated, the minimum number of horses in each sex/age class that were to be unaffected by the treatment, and for removals, the length of time since a previous removal” (Gross, 2000, p. 321). Model output included the number of animals by sex and age classes, the age and sex of animals removed, the age of animals given contraceptive treatment, and measures of genetic diversity for each year of simulation. Gross concluded that management strategies based on removal and fertility control were most effective in achieving management goals but advocated strategies that rely less on removal and more on fertility control; he also highlighted the importance of management actions to delay age at first reproduction and increase generation length to reduce population growth. The model was somewhat unique in that it tracked individual animals throughout their lives and simulated breeding and genetic diversity. 2  simulation models, the model user projects population size (or some other variable of interest) from one time In “step” to the next, for example, from year 1 to year 2 and then from year 2 to year 3 and so on. The length of the time step (e.g., day, month, or year) is specified by the model user.

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178 USING SCIENCE TO IMPROVE THE BLM WILD HORSE AND BURRO PROGRAM Coughenour (1999, 2000) used a spatially explicit ecosystem model to simulate the eco- system dynamics in the Pryor Mountains, of which free-ranging horses were a component. Coughenour’s model (SAVANNA; Coughenour, 1993) operated on weekly time steps and was driven by monthly weather data. The model simulated net primary productivity, litter decomposition and nitrogen cycling, animal forage intake and energy balance, and popu- lation dynamics of free-ranging horses and sympatric bighorn sheep. Horse populations were represented as age-sex classes, and birth and death rates were allowed to be affected by horse nutritional status, which in turn was affected by forage availability. The model was run to simulate a variety of management alternatives, including density-dependent self- regulation, that is, food-limited carrying capacity (see Chapter 3). Coughenour concluded that without culling horses have the capacity to increase to higher densities and can persist at quasiequilibrium with available forage, although vegetation cover would be reduced in many areas and horses would generally be in poorer condition and exhibit higher mortal- ity (see Chapter 3). The model was unique in that it was process-oriented and explicitly linked free-ranging horse population dynamics with climate, vegetation, and ecosystem processes. More recently, Bartholow (2007) used WinEquus (reviewed below) to simulate costs and demographic effects of removal and contraception in four horse populations managed by BLM: Challis, Little Book Cliffs, McCullough Peaks, and Pryor Mountains. Alternative scenarios simulated included status quo of selective removal, adoption, and sanctuary; changing the frequency and efficiency of roundups; and status quo plus a variety of contra- ceptive applications. Bartholow (2007) concluded that prudent use of contraceptives could lead to reductions in costs of management activities of up to 30 percent. Ballou et al. (2008) used the program VORTEX3 (Miller and Lacy, 2005) to simulate population-dynamic and genetic effects of alternative management scenarios for horses on Assateague Island (managed by the National Park Service). Specifically, they examined the rate of population decline, the time to reach the management target, and the level of inbreeding under the existing contraceptive strategy and under an adaptive contraceptive strategy. They concluded that the continued use of the current fertility-control strategy would further reduce the population growth rate, cause a major shift in age structure in favor of older animals, and lead to a low percentage of females that have reproductive opportunities. VORTEX was not developed specifically for horses, but it has many features that could be useful for modeling free-ranging horse population dynamics. It is an individual-based simulation model that allows users to evaluate potential effects of deterministic forces (e.g., density dependence) and stochastic forces (e.g., demographic and environmental stochasticity and catastrophes) on the dynamics and persistence of age-structured wildlife populations (Lacy, 2000; Miller and Lacy, 2005). The program allows users to create and ana- lyze alternative management scenarios easily. The program has been in existence for many years, is fully and adequately documented, offers an easy-to-use graphical user interface, and has been one of the most popular population-viability analysis software packages (see Miller and Lacy [2005] for a bibliography of publications that use VORTEX). Age-structured or stage-structured matrix population models (Caswell, 2001) have often been used to explore questions relevant to free-ranging horse management. For ex- ample, Hobbs et al. (2000) used a female-only, density-dependent, stage-structured matrix ­ model for theoretical exploration of questions pertaining to the effects of culling and fertility control on ungulate population dynamics. Only recruitment was assumed to be 3  VORTEX is available online at http://www.vortex9.org/vortex.html.

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POPULATION MODELS AND EVALUATION OF MODELS 179 density-dependent. The effect of fertility control was modeled by partitioning females of reproductive age into fertile and infertile categories, and removal was modeled by includ- ing a removal term that was a function of per capita removal rate. Zhang (2000) also used a density-dependent matrix model for theoretical analysis of the efficacy of fertility control and culling for wildlife population control. Similar population-modeling frameworks have been used to evaluate the effect of fertility control on overabundant white-tailed deer popu- lations in the United States (Merrill et al., 2003) and to simulate koala-forest ­ ynamics in d Australia (Todd et al., 2008). Although generally flexible, powerful, and amenable to theo- retical explorations (Caswell, 2001), matrix models do not permit explicit consideration of such factors as allelic diversity, mating system, individual variation, and behavioral inter­ actions, which can affect free-ranging horse population dynamics. POPULATION-MODELING FRAMEWORK USED BY THE BUREAU OF LAND MANAGEMENT The committee was asked to evaluate the strengths and limitations of the population model used by BLM and the types of decisions that could be appropriately supported by the model. As mentioned previously, when the report was prepared, BLM used the popula- tion simulation model WinEquus. WinEquus uses an individual-based approach—that is, each animal is tracked individ- ually as opposed to the use of aggregated age-sex or stage classes—to simulate population dynamics and management of free-ranging horses in the framework of age-structured and sex-structured population models. Given appropriate data, it can incorporate the effects of environmental and demographic stochasticities, density dependence, and management actions and can simulate population dynamics for up to 20 years (Jenkins, 2011). The basic data requirements include initial age and sex distributions, sex-specific and age-specific survival probabilities, age-specific foaling rates, and parameter values needed to implement density dependence, environmental stochasticity, and, if desired, manage- ment options (removal, contraception of females, or both). By default, WinEquus assumes a detection (or sighting) probability of 90 percent for typical BLM inventory surveys and increases the number of horses counted in each age-sex class accordingly. The assumption of 90-percent detection probability originated in a paper published by Garrott et al. (1991) that draws from a small sample of western herds with adequate data and likely represents an optimistic estimate of the typical proportion of horses detected in routine surveys (see Chapter 2). However, the user can disable that option in such a way that initial age and sex distributions are treated as exact and no adjustments for detection probability are made. Environmental stochasticity is incorporated by sampling survival and foaling rates from the logistic distribution with user-specified parameter values. However, there are no specific linkages among parameters of logistic distribution, climatic variability (e.g., vari- ability in rainfall and winter severity), and vital rates (e.g., birth and death rates). Survival of both foals and adults is assumed to be perfectly correlated by default; however, the user can specify any correlation from –1 to +1 between survival and foaling rates if desired. Because the program uses an individual-based simulation approach, the effect of demo- graphic stochasticity (random variation among individuals in survival and foaling rates) is automatically incorporated. By default, density dependence is not considered; however, the user may choose for foal-survival probability to be density-dependent, in which case WinEquus adjusts foal-survival probability as a nonlinear function of population density in such a way that the finite population growth rate is 1.0 (births equal deaths) when popula- tion density reaches the carrying capacity (Jenkins, 2011). Management scenarios offered by

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180 USING SCIENCE TO IMPROVE THE BLM WILD HORSE AND BURRO PROGRAM the program include no management, removal only, female fertility control only, and both removal and female fertility control. The user can specify various parameter values relevant to the selected management ­alternatives, including a gather schedule, target population size, population size above which removal is implemented, percentage of animals of different sex and age classes to be removed, effectiveness of fertility control over time, and percentage of mares of different ages to be treated with fertility-control agents. The program output includes time series and summa- ries of population size, information regarding the age and sex composition of the simulated population trajectories, and information on annual population growth rates. The output also includes summary information on results of management such as number of gathers, number of horses removed, and number of mares treated with fertility-control agents; this informa- tion can be used to assess the economic costs of management alternatives although the cur- rent version of the program does not offer options for calculating economic costs. The committee evaluated WinEquus and concluded that it does what the author claims that it can do. It offers an easy-to-use user interface, provides default parameter values (age-specific foaling rates, age-specific and sex-specific survival rates, and sex and age composition), and allows users to choose management options to be simulated. A user manual was not available for the current version (Version 1.40) of the program, but the help files offer useful guidance. Results can be saved as text files for further analyses or viewed on a computer monitor. Under the assumptions of the model and given appropri- ate data, WinEquus can adequately simulate horse population dynamics under alternative management actions (no treatment, removal, female fertility control, and both removal and female fertility control). The committee found one peer-reviewed journal article that used WinEquus for modeling free-ranging horse population dynamics under alternative management scenarios (Bartholow, 2007). How the Bureau of Land Management Uses WinEquus As noted previously, the BLM handbook calls for the use of the WinEquus population model for Herd Management Area (HMA) planning that involves management interven- tions. Guidelines for the use of WinEquus have been developed and summarized by BLM for the Wild Horse and Burro Program staff in a document titled “How to Use and Interpret the WinEquus Population Modeling Program” (BLM, email communication, February 17, 2012). The document offers step-by-step instructions for specifying parameters and alterna- tive management scenarios, running the model, and viewing or saving results. The committee reviewed gather plans and environmental assessments of proposed management actions related to a sample of about 10 HMAs or HMA complexes and re- quested additional information from BLM administrators to aid in interpretation of informa- tion presented in the documents to evaluate how BLM uses WinEquus (see Appendix D). As stated variously in gather plans and environmental assessments, population modeling using WinEquus appeared to have two objectives: to evaluate potential population effects of alternative management actions and to determine whether any of the alternatives would crash the population or cause extremely low population numbers or growth rates. At least one gather plan (BLM, 2010b) reported that one of the objectives of population modeling was to assess the effects of different management alternatives on the genetic health of the herd, but WinEquus has no capability for simulating genetic diversity, so it cannot be used to address issues related to genetic health. Presentations of WinEquus results in the HMA gather plans and environmental assess­ ments examined by the committee normally included a brief narrative in the body of the

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POPULATION MODELS AND EVALUATION OF MODELS 181 document and further details and graphic presentations of simulations in an appendix. Notably absent from most of the presentations was adequate information on the input parameter values used and the modeling options. Results of population simulations with WinEquus depend heavily on a large number of decisions that must be made by the user when setting up a simulation. As previously described, the decisions include data on or assumptions about animal abundance, sex and age structure, survival and foaling rates, parameters needed to model environmental stochasticity, and parameters associated with density dependence if it is incorporated into a simulation. In addition to model parameters that establish attributes of the population and the demographic processes to be simulated, the user must provide parameter values for management alternatives, which may include efficacy of fertility treatment, percentage of mares of different ages to be treated, percentage of horses to be removed by sex and age, and removal schedule. There are a large number of combinations of the input parameter values that, in turn, dictate model output. Default parameter values (estimated using data collected from the Garfield Flat, Granite Range, and Pryor Mountain HMAs) and options available in the program can be used; however, it was often not stated whether or which set of default parameter values were used. Results of WinEquus simulations cannot be adequately interpreted without knowledge of input parameters and the many decisions made by the user in setting up the simulations. Despite the importance of describing clearly and explicitly how WinEquus simulations were structured and the input parameter values used for each modeling exercise, there appeared to be no standardization of the amount of information presented in gather plans and environmental assessment documents. Many planning documents provided vague descriptions of input parameter values. For example, the Black Mountain gather plan stated that “data used in the statistical analysis of the Black Mountain and Hardtrigger HMAs was extrapolated from the census, and age and sex structure of the November 2010 CTR [­ apture, treat, release] gather” (BLM, 2012a, p. 79). Without further information, it is c impossible to know how the data referred to in that statement were used to parameterize the WinEquus model or the actual values of any input parameters that might have been derived from the data. An exception in that respect was the High Rock Complex gather plan (BLM, 2011a), which provided a fair amount of relevant detail regarding input parameter values (with appropriate citations) and WinEquus options used. It specifically stated that demographic parameters for the Granite Range herd (a default option) were used, provided values of contraception and removal parameters, and stated that age and sex composition based on data from the High Rock HMA collected during 2006 were used in the results re- ported. However, many BLM planning documents reviewed by the committee, such as the Cold Spring HMA gather plan (BLM, 2010c), failed to provide any information regarding input parameter values or WinEquus options. The lack of relevant information regarding input or management parameters in gather plans or environmental assessments has attracted public attention. For example, multiple public comments were related to some aspects of input parameters or modeling options for the Twin Peak HMA gather plan (BLM, 2010d). In response to one such comment, BLM stated that “the model and parameters therein were developed by Stephen H. Jenkins of the Department of Biology, University of Nevada at Reno. Reference: Wild Horse Population Model, Version 3.2 User’s Guide, Stephen H. Jenkins, University of Nevada, 1996” (BLM, 2010e, p. 24). That response is vague and uninformative but seems to imply that the simu- lations relied on one of the default parameter options available in WinEquus. Although it was rarely stated explicitly in planning documents, the committee concluded that one of the default age-specific survival and foaling rate datasets (Granite Peak, Garfield Flat, and Pryor Mountain HMAs) is typically used for WinEquus simulations. It was unclear whether

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182 USING SCIENCE TO IMPROVE THE BLM WILD HORSE AND BURRO PROGRAM or to what extent the chosen (default) datasets were representative of a specific HMA or HMA complex because no information that addressed this issue is typically provided in planning documents. In response to the committee’s queries, BLM noted that default p ­ arameter values were used because HMA-specific data were not available, and it offered ­ lack of funding to collect HMA-specific data as justification. The committee recognized that limitation, but nearly all HMAs or HMA complexes are periodically gathered and substantial numbers of horses removed, sexed, aged, and placed into holding facilities. Those data, with sex- and age-composition data obtained in previous gathers and esti- mates of abundance from periodic population surveys (see Chapter 2), can provide some site-specific data that can be used in assigning values to parameters in WinEquus, and it is the committee’s impression that this information may have been used in most WinEquus simulations. However, that is an assumption; it was not explicitly stated in most gather plans or environmental assessments. Results of population modeling reported in gather plans or environmental assessments varied substantially, but they generally included graphic or numerical summaries of typical population trajectories, of statistics on population size at the end of the simulation period (usually 11 years), of descriptions of the realized population growth rate during the simula- tion period, and of the numbers of horses gathered, removed, and treated with a fertility-­ control agent under alternative management actions. Most gather plans and environmental assessments, however, simply copied and pasted WinEquus output and gave no explanation or interpretation of the results being reported. Although management options recommended or implemented appeared to be generally consistent with results of population modeling, most of the gather plans conveyed nothing about whether or how results of population model­ ng were used to make management decisions. In rare instances, how results of popu- i lation modeling were used in management decisions was explicitly stated; for example, the Challis HMA gather plan specifically stated that the number, age, and sex of animals pro- posed for removal were based on the results of population modeling (BLM, 2012b). The committee queried BLM to gain additional insight into how results of WinEquus simulations were used in management decisions to determine whether there was a general agency policy on the use of WinEquus results. One BLM field office responded that “[results of population modeling] were not used to make direct management decisions regarding age or sex of horses to return to the range as these decisions were made based on horses actually captured and commensurate with our selective removal criteria” (BLM, email communication, March 20, 2012). A similar question had been submitted to BLM officials by a member of the public during the public-comment period for the Twin Peak envi­ ronmental assessment. It elicited the response that “these modeling prediction numbers are not used for making specific management decisions, however these numbers are useful in making relative comparisons of the different alternatives and of the potential outcomes under different management options” (BLM, 2010e, p. 34). Thus, whether or how results of WinEquus analyses were used in management decisions at the HMA or HMA-complex level is unclear because of the inconsistency in statements found in the planning documents reviewed by the committee. The committee was also asked to determine the type of management decisions that can be appropriately supported by using WinEquus. Such a determination would require the committee knowing how BLM uses, or would like to use, WinEquus to make management decisions, specific questions to be addressed and management alternatives to be evaluated, and the availability of data needed to assign values to parameters in the model. As noted above, the committee could not determine with certitude whether or how BLM uses results of WinEquus population modeling in making management decisions. Specifically, it was

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POPULATION MODELS AND EVALUATION OF MODELS 183 difficult to determine whether results of population modeling were used to make manage- ment decisions or were offered as justification for management decisions that were made independently of modeling results. Furthermore, in the absence of at least some site-specific (or otherwise representative) data and relevant information regarding input parameters and WinEquus options, results of population-modeling exercises would be difficult for a critical reader to accept as pertinent and meaningful. Nonetheless, given appropriate data, WinEquus can be used to simulate free-ranging horse population dynamics without man- agement interventions or under alternative management regimes that are available in the program (removal only, female fertility control only, and both removal and female fertility control). Strengths and Weaknesses of WinEquus The committee understood that WinEquus was developed to fulfill BLM’s need for easy-to-use software for simulating horse population dynamics and its need for manage- ment scenarios that can be used by its staff with minimal training. WinEquus appears to fulfill those needs. The easy-to-use graphical user interface makes it easy to enter baseline demographic data manually or to choose from default datasets available in the program. When a management option is selected, the program offers intuitive data-input windows for relevant parameters. Likewise, the program makes it relatively painless to input a scale parameter to implement environmental stochasticity on age-specific survival and foaling rates or to implement density-dependent effects on foal survival rate. Ease of use, the abil- ity to simulate population effects of management options (female fertility control, removal, or both), and informative outputs were viewed as strengths of WinEquus. However, some modeling options that are not available in WinEquus would potentially be useful to BLM’s Wild Horse and Burro Program (see section “Alternative Modeling Approaches” below). THE WILD HORSE MANAGEMENT SYSTEM MODEL The Humane Society of the United States (HSUS) has suggested to BLM that it use the Wild Horse Management System (WHMS) model as an alternative in the management of free-ranging horses and burros. The model was developed by EconFirst Associates, LLC, initially with HSUS’s financial support. Charles W. de Seve, the company’s president, gave two presentations to the committee (de Seve, 2011a, 2012) explaining how the model simu- lates free-ranging horse population dynamics, management actions, and associated costs. According to de Seve (2011b), the WHMS is “a set of linked computer models to help control wild horse populations on the western rangelands managed by the Bureau of Land Management.” The model is described as a “dynamic management tool useful to guide BLM’s activities toward the dual objectives of humane population control and cost contain- ment.” It has four components: • Dynamic population simulation model: This component is a stochastic population simulation model that projects age and sex composition annually for up to 12 years. A sub-model projects age and sex composition of horses in the holding facilities; • Economic costing model: This component calculates annual costs of horse manage- ment on the range and in holding facilities; • Management intervention and optimization model: This module is described as a supervisory module that controls parameter input, simulation runs, and reports results; and

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184 USING SCIENCE TO IMPROVE THE BLM WILD HORSE AND BURRO PROGRAM • Population and range database system: The database structure includes “current and historical data by range on age-sex counts, gathers, removals, releases and fertility control.” It is argued that the database “is designed to improve the limited management data that are currently available” (de Seve, 2011b). Economic costing and optimization options offered by the WHMS model could be u ­ seful to BLM. For example, the reverse-optimization technique in that model could be used to identify the most effective use of limited funds for managing horses given the simulated population dynamics of the horses, the effects of removals and contraception on horse population dynamics, and the economic costs of removals, contraception, and holding facilities. Other useful features of the model include the ability to model single or multiple HMAs and a built-in database-management system. It is claimed that the popula- tion dynamics submodel is the same as that used in WinEquus, but the committee could not verify that. The description of many aspects of the model provided in the handout and presentations was generally unclear or otherwise vague. The committee did not have access to the program or its user manual, so it could not objectively evaluate the WHMS model developed by EconFirst Associates, LLC, or verify the many claims made about its capabilities. The committee cautions that BLM should not adopt a complex model, such as the WHMS model, without a thorough evaluation of its program and appropriate docu- mentation by independent experts. ALTERNATIVE MODELING APPROACHES The adequacy of a population model depends on a number of factors, including how (and for what purpose) BLM plans to use it, characteristics and processes that are consid- ered important enough to be included, management alternatives that are to be simulated, and availability of data to assign to parameters. If BLM plans to use a population model for short-term population projection and to evaluate potential effects of the management alternatives (female fertility control, removal, or a combination of the two), WinEquus is probably sufficient to support current needs. However, BLM’s Wild Horse and Burro Program faces unique challenges, and population models are potentially valuable tools in devising and implementing both short-term and long-term management plans. Although the committee recognizes that a perfect model does not exist, it is instructive to consider features that would help BLM to meet its unique challenges. Basic Features At the basic level, a good population model would accurately reflect free-ranging horse or burro life-history, social structure, and mating system. It would also incorporate factors and processes that can affect population dynamics, including environmental and demographic variability or stochasticity, and density dependence. Climatic ­ ariability can v substantially affect population growth through its effects on forage availability and sub- sequently, survival and reproduction. Explicit linkages between weather data and demo- graphic vital rates would markedly increase the realism of simulated scenarios. Chapter 3 reveals that several vital demographic rates can be potentially influenced by increased competition for forage at high population densities, especially if the populations are a ­ llowed to increase to food-limited carrying capacity. Thus, options to allow those vital rates to be density-dependent, and perhaps the inclusion of alternative functional forms for d ­ ensity-dependent effects, might be useful. There are, however, surprisingly few studies of

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POPULATION MODELS AND EVALUATION OF MODELS 185 mechanisms that generate density-dependent responses in free-ranging horse and burro populations, and data-based estimates of parameters that define relationships between population density, climatic variables, and demographic vital rates were not available at the time of the committee’s study. Until such data on free-ranging horses and burros be- come available, incorporating the aforementioned features would necessitate extrapolating insights gained from detailed demographic studies of other species, and caution should be exercised when making such extrapolations. The committee understands that fertility control may become a major tool for manage- ment of free-ranging horses. Whereas WinEquus allows simulation of female fertility con- trol, male fertility control cannot be simulated with the current version of it. As described in Chapter 4, male fertility control, perhaps via such minimally invasive methods as chemical vasectomy, remains a viable management option. Fertility control that targets both males and females may be more effective in reducing population growth than a strategy that tar- gets only one sex. In addition, fertility control can trigger unintended consequences such as increased survival and longevity, changes in ages at first and last reproduction, and alteration of populations’ age structure (see Chapter 4). Many HMAs and HMA complexes hold fairly small numbers of horses, and Chapter 5 suggests that genetic diversity remains a concern. Maintenance of genetic diversity is especially important in the context of global climate change because further loss of genetic diversity may compromise free-ranging equids’ ability to respond to global climate change evolutionarily. Thus, the capacity to model population effects of fertility control that targets both males and females (and the ensuing compensatory responses) and options that allow simulation of allelic diversity (e.g., Gross, 2000; Lacy, 2000) might prove useful for short-term population management and the long-term goal of maintaining genetic diversity and evolutionary potential. The earth’s climate is changing (IPCC, 2007). Most models of global climate change predict that the mean and variance of rainfall and temperature will be affected and that the frequency of extreme climatic events, such as severe drought, will increase. Thus, global climate change will undoubtedly affect free-ranging horses and burros because it will ­affect the arid environment that horses and burros inhabit (McLaughlin et al., 2002; Saltz et al., 2006; IPCC, 2007). Population models that would allow simulation of climate-change effects and catastrophic events (e.g., disease outbreaks) would be helpful in the long run. Asymptotic and transient sensitivity analyses (sensitivity of asymptotic population growth rate, projected population size, or probability of extinction to vital demographic rates and other input parameters) are useful tools and have been used in setting priorities for research and making management decisions (Crowder et al., 1994; Caswell, 2001, 2005, 2007). WinEquus and other models developed for free-ranging horses do not offer options for sensitivity analysis. Options to perform transient and asymptotic sensitivity analyses would be helpful to BLM’s Wild Horse and Burro Program. A “Metapopulation” Perspective and Budgetary Considerations BLM’s Wild Horse and Burro Program manages free-ranging horse and burro popula- tions on public rangelands, but it also manages captive populations of horses that have been removed from the rangelands. Horses and burros removed from public rangelands are processed in short-term holding facilities where a subset of animals are made available for adoption by the public and unadoptable horses are transferred to long-term hold- ing facilities, where they are maintained indefinitely. Each of those populations has its own characteristic dynamics, and all three are linked inasmuch as BLM moves horses among the populations on the basis of management policies and actions, budgets, and

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186 USING SCIENCE TO IMPROVE THE BLM WILD HORSE AND BURRO PROGRAM other considerations that influence maintenance of the captive horses and burros. A major dilemma for the Wild Horse and Burro Program over the last decade has been the rapid increase in the number of horses removed from public rangelands that cannot be placed into private ownership through the Adopt-a-Horse Program and must be maintained in long-term holding facilities. WinEquus and most other models developed for free-ranging horses are focused on capturing the dynamics of individual free-ranging horse populations and the influence of removals and various contraceptive interventions to alter growth rates of free-ranging horse herds (Garrott, 1991; Garrott et al., 1991, 1992; Garrott and Siniff, 1992; Gross, 2000; Roelle et al., 2010). An alternative model structure that could complement those efforts would use a metapopulation type of model that captures the dynamics of the free-ranging, short-term holding, and long-term holding populations and the movement of horses among these three populations—in essence, a model that captures the dynamics of all horses managed by the Wild Horse and Burro Program. Such a model could • Elucidate the basic processes operating in the Wild Horse and Burro Program and help to address BLM’s current programmatic challenges. • Project the changes in the numbers of horses maintained in short-term and long- term holding facilities and the budgets that would be required under current and potential future management alternatives. • Include economic costing, and possibly cost-optimization and population-­ optimization, options. • Project the longevity of horses in the long-term holding facilities to plan for the long-term budgetary requirements to maintain them. • Project changes in the number of horses in each subpopulation and the entire metapopulation4 and budgets that would be required if best available contracep- tive tools are more aggressively used to reduce the growth rates of free-ranging populations as outlined in the 2011 Wild Horse and Burro Program strategic plan (BLM, 2011b). • Explore additional combinations of management actions that may help to meet the challenges of stabilizing the budget of the Wild Horse and Burro Program and to address the multiple goals of the program. If BLM finds that current management alternatives cannot meet program objectives within the budgetary constraints, it may be necessary to explore additional alternatives. The WHMS model described above presumably has some of those capabilities and the capacity to calculate the economic costs incurred by keeping animals in holding facilities. However, the committee could not verify that because it did not have access to the WHMS software program. An Ecosystem Modeling Approach The population dynamics of free-ranging horses and burros are inextricably linked to ecosystem processes through their interactions with vegetation and other herbivore species, including livestock. Horse and burro populations respond to the quantity and quality of vegetation used as forage; their herbivory and trampling affects vegetation composition, 4  metapopulation is a collection of smaller subpopulations that are connected through movement of individual A animals.

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POPULATION MODELS AND EVALUATION OF MODELS 187 quantity, and quality. Vegetation dynamics are in turn linked to climate, hydrology, nutri- ent cycling, and decomposition of plant matter in the soil. Ultimately, equid population dynamics are driven by forage abundance and forage dynamics. Forage abundance affects forage intake, which affects animal body condition, which then affects survival and foaling rates. Survival and foaling rates affect horse and burro abundance, which affects forage abundance. An ecosystem modeling approach (Coughenour, 1999, 2000, 2002; Weisberg et al., 2006) would capture these linkages between horse and burro population dynamics and eco­ system dynamics. It would go beyond the simple representations of fixed parameter ­values for survival and foaling rates, stochastic variation in the values of the parameters as rep- resented in some models, or even correlative or regression-based linkages to climatic vari- ables. Such a modeling framework would explicitly consider how or why horse and burro population sizes vary in response to forage, climate, and competition from other herbivore species over time and across the landscape. Density-dependent population controls could be represented mechanistically. In contrast with the traditional approach of invoking a carrying-capacity term such as the “K” term in a logistic or theta-logistic population growth model (see section “Density- Dependent Factors” in Chapter 3), density dependence would be represented by simulat- ing competition for forage among equids and other wildlife and livestock and the effects of forage limitation on body condition and the subsequent effects of body condition on population processes. As the herbivore population increases, available forage per animal decreases, average forage intake rate decreases in response to the decreased forage biomass, body condition begins to decline in response to decreased intake, survival and foaling rates decrease, and population growth slows. Density-independent population controls could also be represented mechanistically. The primary source of density-independent controls is climatic controls on forage biomass. An ecosystem model therefore would represent plant-productivity responses to climate in a realistic fashion. A second major source of density-independent population fluctuations for horse and burro populations occupying higher elevations and more northerly latitudes is variation in winter severity, particularly snow cover (Berger, 1986; Garrott and Taylor, 1990). Snow cover affects forage availability and energetic costs of foraging for large herbivores because of the need for animals to displace snow while moving and foraging (Parker and Robbins, 1984; Parker et al., 1984). To simulate that effect, the model would have to simulate snow cover and its effect on forage intake rate. A third major source of density-independent population fluctuations for horses and burros occupying more southerly latitudes is varia- tion in the availability of drinking water. Because such climatic variables as precipitation, temperature, snow cover, and water are not affected by population density of horses and burros, their effects on forage abundance and, later, on forage intake, body condition, sur- vival, and foaling rates are density-independent. Horses and burros are mobile and wide-ranging animals, capable of moving large distances daily. Consequently, they derive forage from landscapes that are spatially hetero- geneous with respect to climate, soils, topography, water, and vegetation. It matters where horses and burros are on the landscape because forage biomass is spatially heterogeneous. If horses and burros have access to portions of the landscape that have increased forage, their forage intake will increase, with favorable effects on population dynamics as de- scribed above. Conversely, if they do not have access to forage areas because, for example, these areas are too far from a drinking-water source, there will be negative consequences for population growth. Thus, an ecosystem model would represent spatial variations in soil and climate and their effects on forage productivity. It would represent spatial variations

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188 USING SCIENCE TO IMPROVE THE BLM WILD HORSE AND BURRO PROGRAM in densities of horses or burros as they select habitats that have suitable forage, topogra- phy, water, snow, and vegetation cover. It would also represent spatial variations in forage offtake, inasmuch as this affects the spatial distribution of forage. Forage, drinking ­ ater, w snow, and animal distributions are, of course, temporally variable. Some parts of the land- scape can function as “key resource areas” that provide critical forage and drinking water during times of drought when most of the rest of the landscape is devoid of these resources. Consequently, an ecosystem model would need to be spatially explicit (that is, it would rep- resent the spatial distributions of forage, water, and equids on the landscape); it should also represent the seasonal and annual changes in climatic variables and the spatial distribution of horses or burros and key resources to predict equid population responses to variability in their environments accurately. Spatially explicit ecosystem models are useful for a mechanistic understanding of critical linkages involved in climate-vegetation-consumer dynamics and to capture spatial heterogeneity at various levels of ecological organization adequately. Such models would also be required for exploring short-term and long-term effects of global climate change and can be used to simulate the effect of management actions. On the basis of the com­ ittee’s m evaluation of how BLM uses population models, basic outputs provided by WinEquus a ­ ppear to satisfy the agency’s needs. However, spatially explicit, process-driven ecosystem models would provide capabilities for assessing population responses to climate, spatial distributions of accessible forage and water, density dependence, and consequences for vegetation as described in Chapter 7. CONCLUSIONS The committee views population models as tools that can be useful but are never per- fect. The usefulness of the information obtained from population modeling is directly re- lated to the reliability of the data that are used to assign values to parameters in a model and depends on how adequately the model structure reflects the life-history of the study organ- isms and whether and to what extent deterministic and stochastic factors and management actions that affect the study population are considered. Models that capture free-ranging horse or burro life-history, genetics, social structure, and behaviors adequately or that simu- late ecosystem processes are likely to be more complex and require more parameters than simpler models, but HMA managers are often constrained by a lack of that information. Consequently, it is difficult for the committee to recommend specific modeling frameworks. A suitable modeling framework, or suite of models, would have to simulate life history; social behavior; mating system and genetics; forage limitation; use of forage, water, and space; and effects of alternative management actions throughout horse or burro life spans to meet the challenges outlined in the preceding paragraphs and to incorporate appropriately the factors and processes that influence free-ranging equid population dynamics. Possibly, different models could be used to address different aspects of the overall problem. As dis- cussed previously, BLM’s current practice of using default datasets for population model- ing is relatively uninformative and potentially misleading in that free-ranging horse and burro populations are distributed over a wide geographic area that encompasses ­varied cli- matic conditions and ecoregions, states of rangeland vigor, and herd management histories. All those factors almost certainly interact to influence demographic vital rates and other model parameters that would be needed to reflect horse or burro population ­ ynamics in d any HMA or HMA complex accurately. Efforts should be made to ensure that future model- ing exercises use data from the target HMA or HMA complex or a sentinel population that closely resembles the target population being modeled.

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POPULATION MODELS AND EVALUATION OF MODELS 189 The free-ranging horse and burro populations under BLM management are unusual in that they are composed of a multitude of HMAs or HMA complexes, horses and ­ urros b in short-term holding facilities, and horses in long-term holding facilities; animals are moved among the free-ranging population and short-term and long-term holding facili- ties. In addition, horses exhibit strong social organization, and age-sex composition is likely to be important in modeling the projected outcomes of management actions. BLM faces management constraints and must work within the 1971 Wild Free-Roaming Horses and Burros Act (P.L. 92-195 as amended), budgetary constraints, and other congressional or administrative restrictions, which leave the agency with few management options (pri- marily fertility control and removal). As summarized in Chapter 4, some fertility-control treatments are suitable only for males and others are suitable only for females. Furthermore, some fertility-control measures sterilize treated animals for life, whereas others are effec- tive only for a limited period and have changing degrees of efficacy over time. To make the matter more complicated, both fertility control and removal (the two management options available to BLM at the time of the committee’s review) can alter individual and population demographic attributes, social organization, behavior, and genetic diversity. As discussed in Chapter 5, loss of genetic variation remains a concern in connection with free-ranging horse and burro populations and cannot be ignored. In light of those complexities and budgetary constraints, population models could serve as helpful tools. Although the committee appreciated BLM’s efforts to use population models in its Wild Horse and Burro Program, it also identified several shortcomings. Those included a lack of transparency regarding how values were assigned to model parameters in WinEquus and what information was used to determine those values, how (or whether) results were used in management decisions, and failure to make full use of the available capabilities of WinEquus. When the same default datasets are used to model population dynamics of most or all HMAs or HMA complexes, results will necessarily be similar (give or take the effect of environmental stochasticity and initial age and sex structure). It is therefore not surpris- ing that most gather plans and environmental assessments arrived at identical conclusions regarding the potential effects of the management alternatives considered. It may not be possible to collect site-specific demographic data because of budgetary constraints, but such site-specific data may not be necessary. Detailed study and monitor- ing of free-ranging horse populations in a few HMAs that are representative of the HMAs or HMA complexes in a given habitat or ecoregion (see Chapter 2) could, in the long run, provide detailed and representative demographic data. In the interim, a default dataset that is most representative of the target HMA with site-specific sex-structure and age-structure data could be used. However, a clear description of input parameters, including those needed for various management alternatives, and a detailed description of and justifica- tion for the WinEquus options selected would help the general public to determine the reliability of modeling results. Furthermore, a clear explanation of whether or how results of population modeling were used would be helpful. The committee noted that BLM’s population-modeling efforts have focused on the near-term (about 10-year) projection of population size. This modeling (and management) focus is understandable given the mandate that herd size be kept between upper and lower appropriate management levels. In the long run, however, management strategies aimed at reducing population growth to a modest rate (such as 5 percent per year) with methods described in Chapter 4 (e.g., a more aggressive fertility-control program targeting both males and females) might be most effective. Such a strategy would ensure that unpredict- able variation in the environmental factors and catastrophic events and uncertainty in the effects of management interventions would not reduce populations to below acceptable

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190 USING SCIENCE TO IMPROVE THE BLM WILD HORSE AND BURRO PROGRAM size. Because only a small number of horses would have to be removed annually if the growth rate is modest, quick placement of removed horses could be possible. In addi- tion, excessive reliance on a removal-based management strategy could backfire because removal can lead to rapid population increases due to density-dependent compensation (Zipkin et al. 2008, 2009). Compensatory (or overcompensatory) responses to removal may be contributing to the high growth rate realized by the free-ranging horse populations in many HMAs (see Chapters 2 and 3). Population models could identify an optimal mix of management interventions that would help to achieve management objectives in the face of (over)compensatory responses to removal, both in the short term and the long term. Under the management regimes reviewed by the committee, BLM will have to remove free-ranging horses from western rangelands indefinitely unless very aggressive fertility- control programs are implemented (Garrott, 1991; Eagle et al., 1992; Garrott and Siniff, 1992; Gross, 2000; Bartholow, 2004, 2007). As briefly discussed in Chapter 2, there may be more horses in the short-term and long-term holding facilities than on the range. An average of more than 8,000 horses are moved from the free-ranging population to holding facilities ­ nnually, and almost 60 percent of the Wild Horse and Burro Program’s budget a was allocated to the care and maintenance of captive animals in fiscal year 2012 (BLM, 2012c). The amount of money needed to care for horses in the long-term holding facilities will continue to increase and, in the long run, could consume the entire budget allocated to the Wild Horse and Burro Program. Thus, BLM may have to consider other management options, including male fertility control. Chapter 3 suggests that self-regulation via density- dependent and density-independent processes is possible if populations are allowed to increase to higher numbers. Virtually all population-modeling efforts under the auspices of BLM have been focused on HMAs or HMA complexes; a modeling study evaluating the entire free-ranging horse population on the range and in holding facilities was not available at the time the report was prepared. A comprehensive modeling study that evaluates population dynamics of horses in the western rangelands and in holding facilities and the costs and consequences of manage- ment alternatives, including those not currently available to BLM, would help in evaluating whether and to what extent stated management objectives are achievable under the cur- rent or projected funding situations and regulatory restrictions. Such a study could help to identify the most effective or cost-effective management options to achieve the objectives or achievable goals given available funding and policy constraints. However, the committee notes that usefulness and reliability of results of modeling exercises depends not only on the adequacy of the model itself but on the quality of data used to parameterize the model. As noted previously (see Chapter 2), data on representative sentinel herds can be used to obtain rigorous and representative estimates of demographic and management parameters. Monitoring of sentinel herds can also provide data that can be used to test models, that is, to evaluate how well predictions of the models under alternative management scenarios match observations. Models can be modified or updated as one learns from the manage- ment experiments and estimates of demographic and management parameters are refined. Consequently, the committee recommends that future modeling efforts be based on rigor- ous and reliable estimates of demographic and management parameters in an adaptive- management framework. Adaptive management is an iterative decision-making process in the face of uncertainty (Williams et al., 2007; Nichols et al., 2011). It aims to reduce uncertainty by monitoring the state of the system, learning, and adjusting management decisions accordingly. Models of system behavior are an important component of adaptive management (Nichols et al., 2011). In the long run, free-ranging horse and burro population dynamics and management are

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POPULATION MODELS AND EVALUATION OF MODELS 191 best modeled in an adaptive-management framework (Williams et al., 2001, 2007; Nichols et al., 2011). Chapters 7 and 8 provide details regarding how an adaptive-management framework might be applied to free-ranging horse and burro population management. REFERENCES Andersen, M.C., B.J. Martin, and G.W. Roemer. 2004. Use of matrix population models to estimate the efficacy of euthanasia versus trap-neuter-return for management of free-roaming cats. Journal of the American Veteri- nary Medical Association 225:1871-1876. Ballou, J.D., K. Traylor-Holzer, A.A. Turner, A.F. Malo, D. Powell, J. Maldonado, and L. Eggert. 2008. Simulation model for contraceptive management of the Assateague Island feral horse population using individual-based data. Wildlife Research 35:502-512. Bartholow, J.M. 2004. An Economic Analysis of Alternative Fertility Control and Associated Management Tech- niques for Three BLM Wild Horse Herds. Fort Collins, CO: U.S. Geological Survey. Bartholow, J.M. 2007. Economic benefit of fertility control in wild horse populations. Journal of Wildlife Manage- ment 71:2811-2819. Berger, J. 1986. Wild Horses of the Great Basin: Social Competition and Population Size. Chicago: University of Chicago Press. BLM (Bureau of Land Management). 2010a. Wild Horses and Burros Management Handbook, H-4700-1. W ­ ashington, DC: U.S. Department of the Interior. BLM (Bureau of Land Management). 2010b. North Hills Wild Horse Management Plan Area (WHMPA) Wild Horse Gather Plan. Final Environmental Assessment. Cedar City, UT: U.S. Department of the Interior. BLM (Bureau of Land Management). 2010c. Cold Springs Herd Management Area Wild Horse Gather Plan. Pre- liminary Environmental Assessment. Vale, OR: U.S. Department of the Interior. BLM (Bureau of Land Management). 2010d. Twin Peaks Herd Management Area Wild Horse & Burro Gather Plan. Environmental Assessment. Susanville, CA: U.S. Department of the Interior. BLM (Bureau of Land Management). 2010e. Notice of Field Manager’s Decision for Twin Peaks Herd Management Area and Horse & Burro Gather Plan. Susanville, CA: U.S. Department of the Interior. BLM (Bureau of Land Management). 2011a. High Rock Complex Wild Horse Population Management Plan. Envi­ ronmental Assessment. Cedarville, CA: U.S. Department of the Interior. BLM (Bureau of Land Management). 2011b. Proposed Strategy: Details of the BLM’s Proposed Strategy for Future Management of America’s Wild Horses and Burros. Washington, DC: U.S. Department of the Interior. BLM (Bureau of Land Management). 2012a. Black Mountain and Hardtrigger Herd Management Area Wild Horse Capture, Treat, Release, and Removal Plan. Preliminary Environmental Assessment. Boise, ID: U.S. Depart- ment of the Interior. BLM (Bureau of Land Management). 2012b. Challis Wild Horse Gather Plan. Preliminary Environmental Assess- ment. Challis, ID: U.S. Department of the Interior. BLM (Bureau of Land Management). 2012c. Minutes of the National Wild Horse and Burro Advisory Board Meet- ing, April 23-24, Reno, NV. Bradford, J.B. and N.T. Hobbs. 2008. Regulating overabundant ungulate populations: An example of elk in Rocky Mountain National Park, Colorado. Journal of Environmental Management 86:520-528. Caswell, H. 2001. Matrix Population Models: Construction, Analysis, and Interpretation. Sunderland, MA: Sinauer Associates. Caswell, H. 2005. Sensitivity analysis of the stochastic growth rate: Three extensions. Australian & New Zealand Journal of Statistics 47:75-85. Caswell, H. 2007. Sensitivity analysis of transient population dynamics. Ecology Letters 10:1-15. Choquenot, D. 1991. Density-dependent growth, body condition and demography in feral donkeys: Testing the food hypothesis. Ecology 72:805-813. Coughenour, M.B. 1993. The SAVANNA Landscape Model—Documentation and Users Guide. Fort Collins, CO: Natural Resource Ecology Laboratory. Coughenour, M.B. 1999. Ecosystem Modeling of the Pryor Mountain Wild Horse Range. Final Report to U.S. Geological Survey Biological Resources Division, U.S. National Park Service, and U.S. Bureau of Land Man- agement. Fort Collins, CO: Natural Resource Ecology Laboratory. Coughenour, M.B. 2000. Ecosystem modeling of the Pryor Mountain Wild Horse Range: Executive summary. Pp. 125-131 in Managers’ Summary—Ecological Studies of the Pryor Mountain Wild Horse Range, 1992-1997, F.J. Singer and K.A. Schoenecker, compilers. Fort Collins, CO: U.S. Geological Survey.

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192 USING SCIENCE TO IMPROVE THE BLM WILD HORSE AND BURRO PROGRAM Coughenour, M.B. 2002. Ecosystem modeling in support of the conservation of wild equids: The example of the Pryor Mountain Wild Horse Range. Pp. 154-162 in Equids: Zebras, Asses and Horses: Status Survey and A ­ ction Plan, P.D. Moehlman, ed. Gland, Switzerland: International Union for Conservation of Nature. Crouse, D.T., L.B. Crowder, and H. Caswell. 1987. A stage-based population model for loggerhead sea turtles and implications for conservation. Ecology 68:1412-1423. Crowder, L.B., D.T. Crouse, S.S. Heppell, and T.H. Martin. 1994. Predicting the impact of turtle excluder devices on loggerhead sea-turtle populations. Ecological Applications 4:437-445. Dawson, M.J. 2005. The Population Ecology of Feral Horses in the Australian Alps: Management Summary. Pre- pared for the Australian Alps Liaison Committee. Dawson, M.J. and J. Hone. 2012. Demography and dynamics of three wild horse populations in the Australian Alps. 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