PopEquus is a predictive population modeling tool to support management decisions for free-roaming horse populations. The application simulates how different management actions influence the size of horse populations, while measuring metrics related to the amount of management performed and management costs. Users can specify features of a horse population and select from among six management actions to be applied to the population, either alone or in combination with other actions. The model then projects how population size might be expected to change through time, given the selected management alternatives, and useful metrics describing the results are summarized in figures and tables. In general, PopEquus provides natural resource managers a decision-support tool to estimate trade-offs among management alternatives, so that they might be able to identify effective management solutions for populations.
Background
Domestic horses (Equus caballus) were introduced to North America by European explorers and colonists in the 1500s, and feral horses1 have had a large free-roaming population in western North American rangeland ecosystems for centuries. Horses and humans have experienced a significant co-evolutionary relationship for thousands of years2, and both captive and free-roaming horses remain a valued component of modern society today. In 1971, certain free-roaming horses and burros (Equus asinus) living on lands administered by the Bureau of Land Management (BLM) and the U.S. Forest Service, and their descendants, became protected by federal law in the United States under The Wild Free-Roaming Horses and Burros Act. This law directs the BLM and USFS to manage and conserve those free-roaming horses and burros as “living symbols of the historic and pioneer spirit of the West” 3. Under this law, those specific free-roaming horse populations are referred to as 'Wild Horses', and the law requires that the BLM and USFS manage those horse and burro populations for a "thriving ecological balance” between horses, burros, livestock, native plant and animal communities3, and other natural resources.
Problem
Horse populations largely lack predators in North America, and populations experience rapid population growth rates (due to high survival and reproductive rates), such that populations can double in five years and triple in eight years4. These features have caused many wild horse populations to largely exceed the population size ranges identified as ecologically appropriate by the BLM and USFS natural resource managers (i.e., Appropriate Management Levels), and the entire BLM-managed wild horse population on federal lands tripled in size during 2010-20202,4,5. When horse populations reach exceptionally large sizes, horses can overgraze natural ecosystems, outcompete native wildlife for food and water, and experience density-dependent effects, such as mortality due to dehydration and starvation. These three outcomes are generally undesirable for both natural resource managers and U.S. citizens, who value the well-being of both horses and ecosystems on public lands.
A Tool To Support Management Decisions
The primary purpose of the PopEquus application is to estimate the consequences of management alternatives and tradeoffs among them. This information might be used to support decisions about how to manage populations. To do so, there are two tools for users: a Basic Tool with seven relatively simple management alternatives to simulate, and an Advanced Tool with over 20 management alternatives to choose from and greater opportunity to customize alternatives. The application includes a User Manual which explains how to use each tool and a Mechanics page that explains how population projection simulations are performed, including important assumptions. We recommend reading these pages before using either tool. Written Exercises are also provided, which are meant to illustrate how the application might be used to support different management decisions. The user can navigate among application tools and pages using tabs at the top of the application.
For both tools, simulation outputs provide metrics to understand tradeoffs among alternatives. Metrics relate to the population size that results from management, the number of horses that were gathered, removed, and treated with fertility control treatment, and the cost of management. The metrics can be used as performance measures for different objectives of management, such as: maintain population size within target population size ranges; minimize the number of horses that are gathered, removed, or treated; and/or minimize cost of management. After using either tool, users can download reports (.DOC or .PDF files) that summarize the inputs and outputs of simulation exercises. The tool is not meant to replicate complicated population management that has occurred in the past, nor does it identify a single, 'best' alternative for the user. PopEquus helps describe trade-offs among alternatives, so that the user might make an informed decision for themself about what might be an effective alternative for the future.
Notes
PopEquus was built using currently available information describing horse demography and effects of management actions on horses in North America. The application was produced by the U.S. Geological Survey's Wild Horse and Burro Research Group at the Fort Collins Science Center, with support from the Bureau of Land Management and the U.S. Geological Survey. The application represents an updated and more developed alternative to the WinEquus program produced by Stephen Jenkins in 1996.
Questions or comments about the application can be directed to popequus@usgs.gov.
This software can be cited as: Folt, B., Ekernas, L.S., Edmunds, D., Hannon, M., and Schoenecker, K.A., 2023, PopEquus: A Predictive Modeling Tool to Support Management Decisions for Free-roaming Horse Populations, Version 1.0.1: U.S. Geological Survey software release, https://doi.org/10.5066/P9NMRQDG.
Disclaimer: This software has been approved for release by the U.S. Geological Survey (USGS). Although the software has been subjected to rigorous review, the USGS reserves the right to update the software as needed pursuant to further analysis and review. No warranty, expressed or implied, is made by the USGS or the U.S. Government as to the functionality of the software and related material nor shall the fact of release constitute any such warranty. Furthermore, the software is released on condition that neither the USGS nor the U.S. Government shall be held liable for any damages resulting from its authorized or unauthorized use. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.
The Basic Tool can simulate how six management actions influence changes in horse population size. In the left panel, the user can specify input parameters about the population, simulation, and management actions of interest, then run the simulation. After the simulation is complete, tradeoffs among management scenarios are illustrated with graphs, tables, and a summary.
The Advanced Tool simulates six different management actions which can be implemented as over 25 different management alternatives. With the left panel, enter information about the population, simulation, and management alternatives. In the right panels, customize inputs related to alternatives that are selected. Results are plotted in graphs and tables to evaluate tradeoffs among alternatives.
This panel specifies features related to alternatives that involve gathers, if they are selected.
Gather cost ($ per horse) is calculated during each gather as a consequence of the number of horses gathered using data from the Bureau of Land Management.
This panel specifies features related to alternatives that involve removals, if they are selected.
This panel specifies features related to alternatives that involve GonaCon treatment during a gather, if they are selected.
This panel specifies features related to alternatives that involve PZP-22 treatment during a gather, if they are selected.
This panel specifies features related to alternatives that involve ZonaStat treatment during a gather, if they are selected.
The application assumes that ZonaStat treatment will always involve treating with a booster shot after the first treatment.
This panel specifies features related to alternatives that involve IUD treatment, if they are selected.
This panel specifies features related to alternatives that involve mare sterilization, if they are selected.
This panel specifies features related to vaccine darting alternatives, if they are selected.
The 'ZonaStat (darting)' alternative assumes that all horses are re-treated in the first year after an individual is treated, even during darting.
Use this panel to customize features related to graphing of results (e.g., legend position).
Some feral horses whose ancestors lived in 1971 on lands in ten western states administered by the Bureau of Land Management and the U.S. Forest Service are protected by federal law as 'Wild Horses'. The PopEquus application can simulate how six management actions, alone or in combination, might reasonably influence important metrics in horse population management, including the size of the population, the amount and types of management performed, and the direct costs of management. The six management actions are removals, three fertility control vaccines (GonaCon-Equine [GonaCon], PZP-22, and ZonaStat-H), intrauterine devices, and mare sterilization. The application includes two tools to perform simulations and visualize results: the Basic Tool, which allows the simulation of six single-action alternatives and a null model of 'no management', and the Advanced Tool, which allows the simulation of over 25 management alternatives, including compound alternatives with two or three management actions used jointly. Below, we explain how to perform simulations using each tool and describe additional assumptions related to simulation scenarios.
Metrics
The application tracks ten metrics during simulations: population size in the final year of the projection interval ('Final population size'); average population size across all replicates and years ('Overall mean population size'); likelihood that an alternative yielded AML in the final year of the projection ('AML probability'); proportion of simulation replicates that ended beneath a population persistence threshold ('Persistence probability'); total number of horses gathered ('Number gathered'); total number of horses removed ('Number removed'); total number of horses treated ('Number treated'); direct cost of management in the Herd Management Area (HMA) in millions of USD ['On-range cost']; direct costs of transporting, caring for animals in short-term and long-term holding facilities and pastures, and attemping to place animals in private care ['Off-range cost']; and total direct cost of management, including costs incurred at the HMA and also off-range ['Total cost']. Values indicate the mean estimates among replicates for each alternative; costs are calculated in millions of dollars ($).
An important objective of horse population management is to maintain populations within target population size ranges (i.e., 'Appropriate Management Levels'; AML), so that horse populations do not exert excessively large effects on ecosystems and there can be a thriving natural ecological balance between horses, native plant and animal species, and other multiple land uses. Collectively, the metrics 'Final population size', 'Overall mean population size', and 'AML probability' could be used to assess the relative strength of alternatives for maintaining a population within Appropriate Management Levels, minimizing the ecological effects of horses, and maintaining horse populations at a size that allows for that thriving natural ecological balance.
While management often seeks to maintain population size within target ranges (e.g., AML), management might also seek to avoid excessively reducing population size to minimize risk of a population becoming locally extirpated due to demographic, environmental, or genetic stochasticity or a natural distaster (e.g., extreme drought). The metric 'Persistence probability' could be used to assess the relative strength of alternatives for minimizing risk of a population becoming unintentionally extirpated due to random chance.
Some managers and stakeholders may be interested in minimizing the number of horses that are captured, handled, and removed from the range. The metrics 'Number gathered', 'Number removed', and 'Number treated' could be used to assess the strength of alternatives for achieving that objective.
Management efforts cost money, which is often a limited resource for agencies tasked with management. An objective of management agencies might be to minimize direct costs of management, and the metrics 'On-range cost', 'Off-range cost', and 'Total cost' could be used to assess the relative strength of alternatives for minimizing management costs.
Basic Tool
With the Basic Tool, the user can specify seven details about a population:
- Population name - the name of the population being simulated (e.g., Conger Herd Management Area)
- Population size - the number of horses in the population (including foals)
- Population growth rate - the assumed average percent increase in population size per year
- Capture proportion (%) of the population - the percentage of the population that can reasonably be captured during a gather
- Appropriate Management Levels - the population size range (two values; minimum and maximum) that managers seek to achieve with management
- Target population size - the population size that managers seek to achieve during removals
Reasonable starting values are provided, but can be adjusted manually or using arrows in the input boxes. Values must be provided for each the above boxes, except Population name. The user then must specify two details about the simulation:
- Projection interval - the number of years for the simulations to run (e.g., 10 years)
- Number of simulation replicates - the number of independent simulation runs for each alternative (e.g., 10 replicates); outcomes of different simulation replicates differ due to random variation in environmental conditions from year-to-year (i.e., environmental stochasticity)
The user can then select from among seven management alternatives to be simulated and compared:
- No management
- Removals
- Fertility control treatment with GonaCon
- Fertility control treatment with PZP-22
- Fertility control treatment with ZonaStat
- Fertility control with intrauterine devices (IUDs)
- Fertility control with mare sterilization
At least two alternatives must be selected.
The Basic Tool makes a number of assumptions so that the user has a simple interface to perform easy and quick simulations that quickly demonstrate the effect of alternative management actions on horse populations. Most of these assumptions can be changed when using the Advanced Tool. The Basic Tool assumptions are:
- The total population size estimate includes both adults and foals, such as might be estimated from aerial surveys that take place in late summer to early winter ( i.e., a post-breeding census).
- Management is performed using gathers (e.g., helicopter roundups) before the first year of the simulation and every third year thereafter for up to 20 years.
- Removals are not selective; they are a 'gate-cut' removal that does not discriminate by sex, age, or other characteristics.
- The maximum number of horses that can be removed from a single HMA in a year is 1500.
- Fertility control treatment of females with vaccines, IUDs, or sterilization can be given to any non-foal females (age 1 year old or greater).
- All individuals treated with the vaccines GonaCon or ZonaStat are held in short-term holding to apply a booster treatment after a time period that increases the effectiveness of the booster (30 days for GonaCon, 30 days for ZonaStat).
- All individuals receiving PZP-22 treatment were held for 7 days to reflect the time needed for sorting and treatment before being returned to the range.
- IUD treatment involves holding all gathered females for 14 days to ultrasound and treat all eligible, non-pregnant females.
- IUD-treated females have an 86% retention rate (0.86) each year.
- Sterilized mares are held for 14 days to perform the procedure and post-procedure observation.
- The population persistence threshold is 30 horses.
- After a removal, some mares are pregnant and give birth in short-term holding facilities; the proportion of birthing females in short-term holding is assumed to be half of the proportion of birthing females in the wild that year.
- Horses in long-term holding facilities (removed and not adopted) are projected for an additional 25 years after the on-range population projection ends.
- Costs related to gathers, management, and holding are assumed to be: $7.60 per day in short-term holding, $2.02 per day in long-term holding, $1700 administration cost for federal agencies to adopt-out a horse, $300 for mare sterilization, $50 for GonaCon primer or booster, $430 for PZP-22 primer treatment, $30 for PZP-22 booster treatment, $30 for ZonaStat-H primer or booster, $30 for an ultrasound, $60 for an IUD, and $50 for IUD installation by a veterinarian.
After adjusting input values and selecting management alternatives, the user should click the “Perform simulations” button to run the analysis. If all required values have been provided, a progress bar should appear, which indicates that the analysis is working. Run times will vary from short (a few seconds) to long (a minute or two), depending on the projection interval, number of replicates, and number of management alternatives selected. We recommend selecting fewer than six alternatives during a single simulation exercise, because fewer scenarios are easier to compare and interpret. After the run is complete, the tool will produce two graphs and one table that summarize the key results.
The first figure is a line graph that illustrates predicted population size through time for each management alternative. The tool projects the population under each alternative with independent simulation replicates, depending on the number entered by the user. Simulation replicates appear as individual lines on the graph; each line describes a different trajectory for the population, because each replicate experiences different demographic rates due to random environmental variation through time (i.e., environmental stochasticity). Predicted patterns of population projections will also vary among alternative scenarios, because management actions have different effects on demographic vital rates, such as population size, reproduction, or survival. The upper and lower target population size ranges (i.e., Appropriate Management Levels) are plotted in black dashed lines. The target population size range represents a key objective of managers (achieving AML), and the purpose of this graph is to illustrate how well each management alternative might achieve the objective of managing the population to within this population size range.
The second figure is a table that summarizes the ten metrics for each management alternative over the projection interval. Values indicate the mean estimates among replicates for each alternative; costs are calculated in millions of dollars ($). The table summarizes potential trade-offs among alternatives, based on variation in resulting population size, the amount of management performed, and direct costs of management. However, the model does not explicitly account for or consider multiple uses on public lands, local land use planning considerations, or other important considerations.
The third figure provides a more detailed illustration of one specific trade-off: the relationship between predicted outcomes for mean population size and overall direct cost of management (the sum of on-range and off-range costs) among simulated alternatives. Managers often seek to reduce and/or maintain population size (x-axis) to be within Appropriate Management Levels (AML), while also saving money. However, management alternatives vary in their effectiveness at achieving AML and minimizing cost, and the third figure illustrates this trade-off. Each management alternative is plotted with a point (colored as in the first figure); the horizontal and vertical lines adjacent to points indicate the 95% confidence intervals for predicted population size and total management cost, respectively. Vertical black dashed lines indicate Appropriate Management Levels (minimum, left; maximum, right). The purpose of this figure is to identify the cost-effective alternatives that achieve AML.
At the end of the page, results are summarized briefly in text.
After running a simulation, the user can save the results using a few options. First, the results can be downloaded to the user's local computer using the 'Save results' buttons on the left panel. Downloadable reports include summaries of the inputs specified the user and the results generated by the application. Summary report tables also include 95% confidence intervals for metrics. Reports can be saved as a Word document or PDF file. Second, if the user wants to copy the figures or tables exactly as they appear on the PopEquus interface, the user can use the 'Snipping Tool' application on most PCs or the 'screen-capture' function on Macs (click and hold: “command + shift + 4” on the keypad) to save an image of results. Third, the output table also has buttons to copy the table or save it as a .CSV, .XLS, or .PDF file. We recommend using the 'Save results' buttons, because they save summaries of input values in addition to the results.
Advanced Tool
The Advanced Tool operates similar to the Basic Tool (the same base-line assumptions from the 'Mechanics' page are made for both tools) but combinations of management actions can be selected and management action is highly customizable. In the left panel, users can specify estimates for population and simulation parameters and select alternatives. As with the Basic Tool, the user must provide values for most inputs for the tool to run.
Unique to the Advanced Tool are the abilities to specify: the proportion of the population that is female, whether foals are included as part of the population estimate (i.e., whether it is from a pre-breeding census typical of January-April or a post-breeding census typical of July-December), a population persistence threshold to monitor for low population size during projections, and an additional 19 Management Alternatives to choose from (26 total alternatives).
In addition to being customizable, a main strength of the Advanced Tool is that it permits simulation of compound alternatives (i.e., management strategies that employ two or three actions concurrently).
In the right panel, there are nine grey boxes that, when clicked, drop-down to reveal additional input boxes that allow the user to customize features related to gathers, management actions, and minor cosmetics for graphs. Initial estimates are provided for each parameter, based on conversations with wildlife managers (i.e., Wild Horse and Burro Specialists), but the user can customize estimates as they may deem reasonable. In the bullets below, customization options are explained.
Gather Options: the user can specify the short-term cost of holding horses that have been gathered (e.g., $7.60 per horse per day). The per-horse cost of gathers cannot be specified by users; rather, this value is estimated during each gather year using the best available information describing how gather size influences per-head gather cost provided by the Bureau of Land Management.
Removal Options: The 'Removal years' input box allows the user to specify a fixed removal schedule; removals will be performed before any year entered in the box if the population size exceeds maximum AML before that year. The second box ('Reactive removals') allows the user to specify an alternative form of removals, where removals are performed before any year when the population exceeds maximum AML if sufficient time has passed since the previous gather ('Minimum gather interval'). If the 'Reactive removals' box is not selected, the 'Minimum gather interval' value will be ignored; alternatively, if the 'Reactive removals' box is selected, the 'Removal years' values will be ignored. For the 'Removal years' input, the order of values does not matter and values will only be used that are less than or equal to the user-defined 'Projection interval'.
The 'Selective removals' box will specify whether removals will involve adjusting the sex ratio of any animals being returned to the range in ways that would decrease future population growth. Sex-ratio adjustment requires gathering sufficient horses so that (1) a removal can be performed to reduce the population size to the target population size, and (2) the sex-ratio of horses to be returned to the range can be adjusted to be male-biased. Releasing more males than females can decrease population-wide reproduction in the short term relative to releasing individuals at random. The sex-ratio adjustment of horses being returned to the range can be adjusted with the 'Male proportion of population returned after a removal' input. The 'Selective removals' box must be ticked for the sex-ratios of removed and released horses to be manipulated with the 'Male proportion of population returned after a removal' input. If the 'Selective removals' box is not ticked, removals are not selective and horses are removed independent of sex (i.e., 'gate-cut' removal).
Additional inputs related to removals include: the maximum number of individuals that can be removed from a population in a single year ('Maximum number removed per year'), the number of years that removed animals will be projected in 'off-range' holding facilities ('Number of years to project holding population'), the long-term holding cost of each horse ($2.02 per day) ('Long-term holding cost'), the proportion of horses in holding that are adopted out to private citizens each year ('Proportion of horses adopted each year'; e.g., 0.69; see above), the cost of federal agencies to adopt out a horse (e.g., $1700) ('Net adoption cost to agency'), and the percent reduction of females that give birth in captivity the first year after removal (when compared to the proportion of females give birth that year in the wild; e.g., 25%) ('Foaling reduction [%] of removed females in captivity the first year after removal').
GonaCon Options: the user can specify the years that females are treated with GonaCon ('Treatment years'), the ages of females that are treated (ranging from 0 [foals] to 20 [all individuals 20 years old and up]) ('Treatment ages'), the percentage of age-eligible females that will be treated with GonaCon (0, 0.25, 0.5, 0.75, or 1) ('Treatment percentage'), the cost of each GonaCon treatment (e.g., $50 per shot) ('Treatment cost per shot'), whether females are kept in short-term holding to receive a booster treatment ('Hold to give booster'), and the number of days to keep females in holding before giving a booster treatment (e.g., 30 days) ('Days in holding until booster'). Primer and booster shots of GonaCon are identical and have the same cost. As with 'Removal years', the order of input values for 'Treatment years' and 'Treatment ages' does not matter and values will only be used that are less than or equal to the user-defined 'Projection interval'.
PZP-22 Options: the user can specify similar input parameters as with GonaCon, but PZP-22 treatment involves different treatments for primer and booster doses. The initial primer treatment of PZP-22 involves one dose of PZP pellets (e.g., $400 per shot) and one dose of ZonaStat-H (e.g., $30), but subsequent booster treatments in later years only involves one dose of ZonaStat-H. The user can adjust costs for primer and booster treatments as necessary. The ‘Days in holding’ option represents the number of days a mare is held for sorting and treatment before being released back to the range.
ZonaStat-H Options: the user can specify the same input parameters as with GonaCon. Howeer, all ZonaStat treatments are assumed to be identical in cost (e.g., $30).
Intrauterine Device (IUD) Options: the user can specify the years ('Treatment years') and ages of females ('Treatment ages') for IUD-treatment. Only non-pregnant females can be given an IUD; a veterinary exam (e.g., ultrasound) is required for all gathered, age-eligible females to determine which females can receive an IUD. Because relatively few females will not be pregnant during gathers, the models assume that all non-pregnant females are treated. The user can specify cost of ultrasound (e.g., $30 per female) ('Ultrasound cost'), the number of days mares are held to treat and observe all age-eligible, non-pregnant females (e.g., 14 days) ('Total holding days for screening, treatment, and observation'), cost of each IUD (e.g., $60) ('Materials cost'), cost of veterinary work to place each IUD (e.g., $50) ('Treatment cost'), and the proportion of IUDs that are retained among treated females each year ('Retention rate (per year)'; e.g., 0.87; i.e., 87% of IUDs are retained each year).
Mare Sterilization Options: similar to vaccine-treatment options, the user can specify the percentage of mares to be treated, the years and ages of females for mare sterilization treatment, cost (e.g., $500), and number of days for post-treatment observation before mares are released (e.g., 14 days).
Darting Options: the user can specify the years ('Treatment years') and ages ('Treatment ages') for females that will be treated with vaccine by darting, the proportion of the female population that can reasonably be treated by dart in a year ('Proportion of female population (%) that can be darted'), the percentage of age-eligible females that are available for darting and will be darted ('Treatment percentage'), whether darting scenarios will attempt to boost GonaCon-treated individuals during the individual's first treatment year ('Are individuals re-treated with GonaCon by dart…'), and the per-animal cost to deliver vaccine by dart (e.g., $250 per treatment). There is no booster option for the 'ZonaStat (darting)' alternative, because that function assumes that all horses are re-treated in their first treatment year, regardless of treatment by hand or dart. Note: if the booster option is clicked for GonaCon, this assumes that all individuals darted for the first time will be darted again that year as a booster; it may be difficult to retreat the same individuals in a year. For compound alternatives with 'Removal (year 1) and fertility control', the alternative will ignore (1) inputs from 'Removal years' beneath Removal Options drop-down and (2) inputs specifying 'Treatment years' beneath the GonaCon or ZonaStat-H drop-downs; instead, a removal will be performed in the first year and age-eligible females will be treated with vaccine according to the 'Treatment years' beneath the Darting Options drop-down.
Graphing Options: the user can specify whether the minimum and maximum Appropriate Management Levels and persistence threshold are included on graphs, and whether the first figure's legend is in the top left or bottom left of the graph.
After examining or adjusting values within a drop-down box, boxes can be minimized again by clicking the grey box, which we recommend.
For the Advanced Tool to run, at least two alternatives must be selected (and no more than nine). We recommend selecting 2-5 alternatives, so that the results are easy to read and evaluate.
There are a few details and assumptions relating to the Advanced Tool that are important to mention:
- Management is performed using gathers (e.g., helicopter roundups) for all scenarios, except for alternatives with vaccine darting.
- Vaccine darting alternatives assume that vaccine is delivered to age-eligible females by ground darting. When darting scenarios are simulated, the input variable 'Proportion of population (%) that can be darted' within the 'Darting Options' drop-down is used to specify the proportion of the population that will be treated with vaccine by dart during darting years.
- We specified an initial value for IUD retention rate as 0.86 (86% per year), following averaged annual results from a study of Y-design flexible IUDs (Holyoak et al. 2021).
- For compound scenarios with IUDs and a second form of fertility control treatment, it is assumed that all gathered females are examined by a veterinarian with ultrasound equipment to determine if they are pregnant and all non-pregnant females are given an IUD; pregnant females that are unavailable for IUDs are then treated with other forms of fertility control treatment (e.g., vaccine).
- For compound scenarios with mare sterilization and vaccine treatment, females are treated first with mare sterilization; any non-sterilized, age-eligible females remaining after that will then receive vaccine. In other words, vaccine is only treated to age-eligible females that are not mare sterilized. Therefore, if the mare sterilization percentage is set to 100 and if mare sterilization ages and vaccine treatment ages are the same, then no females will receive vaccine treatment, and the scenarios function identical to the mare sterilization-only scenario. If mare sterilization percentage is less than 100 or if ages are changed to differ from vaccine treatment ages, then compound alternatives with mare sterilization and vaccine treatment will differ in outcomes from the mare sterilization-only scenario.
Summary Reports
As with the Basic Tool, the Advanced Tool simulation results can be downloaded as summary reports using the “Save results” buttons. Each tool has its own “Save results” buttons (either .DOC or .PDF), and each tool can only save results from its own simulations. The user must first run a simulation to completion using the “Perform simulation” button. The date and time (Mountain Standard Time) are saved with the summary.
The reports summarize the input parameters and alternatives, provide figures and tables (with explanatory text), and conclude with simple language that summarizes key results. The tables include 95% confidence intervals around mean estimates for each metric.
Notes
To change the interface window or text size, press “ctrl shift +” or “ctrl -” on your keyboard to zoom in or out, or adjust the width of the window using your mouse. The interface may not be aesthetically pleasing on a cell phone or tablet; it is best viewed on a regular computer.
Questions or comments about the application can be directed to popequus@usgs.gov.
Last, we note that simulations made by PopEquus are model predictions and are not perfect representations of future reality. This model does not account for many ecological, logistical, administrative, or budgetary factors that may be important considerations for management decisions. Nonetheless, the framework for comparing potential population and cost outcomes under different management alternatives, produced by the currently available demographic and cost data, may help illustrate tradeoffs among management alternatives and assist in decision making.
References
Holyoak, G. R., C. C. Lyman, S. Wang, S. S. Germaine, C. O. Anderson, J. M. Baldrighi, N. Vemula, G. B. Rezabek, and A. J. Kane. 2021. Efficacy of a Y‐Design Silastic Elastomer Intrauterine Device as a Horse Contraceptive. The Journal of Wildlife Management 85(6):1169-1174.
This software can be cited as: Folt, B., Ekernas, L.S., Edmunds, D., Hannon, M., and Schoenecker, K.A., 2023, PopEquus: A Predictive Modeling Tool to Support Management Decisions for Free-roaming Horse Populations, Version 1.0.1: U.S. Geological Survey software release, https://doi.org/10.5066/P9NMRQDG.
This page describes the mechanics of how horse population projections are performed by the PopEquus simulation tools and how management actions, such as fertility control treatment, are simulated in that framework.
Population projection
The PopEquus application projects horse populations through time using matrix multiplication (Caswell 2001). It conceptualizes horse population structure using an age-based, two-sex, post-breeding census population model, where horse populations have 21 age classes for each sex: one age class for each year of age from 0 (foals) to 19 years old, and a final stage with all individuals ≥20 years old. During a given time-step, individuals in each age class have a probability of surviving and transitioning to the next age class, until they reach age 20; all individuals ≥20 years old are modeled as a single stage class with a probability of surviving and staying within that stage. Females of age ≥2 years old have a probability of reproducing (foaling) and recruiting individuals into the foal age class. Individuals that do not survive and transition during a time-step are assumed to have died.
The model uses demographic matrices containing population vital rates (age-based survival and reproductive rates) to project populations (Table 1). Some demographic matrices are based on studies of wild horse populations from western North American ecosystems (Berger 1986, Garrott and Taylor 1990, Jenkins 2002, Roelle et al. 2010). Other matrices were built to approximate the wide range of potential population growth rate (λ) values experienced by horses (range: 0.84–1.39) (Ransom et al. 2016). In total, the model uses ten demographic matrices representing variable demographic conditions that might be experienced by horse populations in space and time. Each demographic matrix yields a different deterministic value of λ. Seven of the matrices create λ values ranging from 1.066-1.196 (i.e., 6.6-19.6% increases in population size per year). Two matrices yield larger λ values (1.231, 1.317) that might occur during years or in places with particularly high productivity. One matrix yields a λ value of 0.53, where the population decreases in size (approximately halves); this might happen during years where environmental conditions cause extremely low adult survival, such as during an unusual blizzard event (Garrott and Taylor 1990). Populations are projected by multiplying a demographic matrix by a population size vector, which is a single column, 42-row describing the number of female and male horses in each age classes in a given year (below).
Table 1: Population vital rates and demographic matrices used to project horse populations with the PopEquus simulation tool. The 'Summary' tab summarizes all population vital rates (survival, S; reproduction, R) and resulting measures of deterministic population growth rates (λ) from ten demographic matrices used to project horse populations. Reproduction of females (i.e., foaling) is denoted by the variable R. Additional tabs (e.g., 'Matrix 1') include the exact demographic matrices used by the application. Each demographic matrix is a square matrix with 42 rows and 42 columns that correspond to 21 age classes for females (F) (age 0-20+) and males (M) (age 0-20+). Columns and rows are labeled by F for females, M for males, and numbers to represent ages (e.g., F1 is 1-year old females). Each matrix cell describes probability that an individual will transition (or reproduce) from column state to row state during one time step. For example, in Matrix 1, the value in column 1, row 2 (0.948) is the probability that an age 0 female that will survive and transition to become an age 1 female at the end of the year. Values along the subdiagonal describe the transition rates (i.e., survival) among age classes. Alternatively, horizontal values in rows 1 and 22 of columns 1-21 describe reproductive rates from the column state to the row state. For example, in Matrix 1, the value in column 4, row 1 (0.244) describes the rate at which age 3 females (column) will produce age 0 females (row) at the end of year. Similarly, the value in column 4, row 22 (0.163) is the rate at which age 3 females (column) will produce age 0 males (row). See Caswell (2001) for a thorough introduction to matrix population models.
Stochasticity
The application projects populations forward in time each year by multiplying a demographic matrix by a vector of population size. However, horse population vital rates can vary annually due to random variation in the environment (i.e., environmental stochasticity), which can cause changes in population size to vary from year-to-year. For this reason, using the same demographic matrix each year during projections may not be appropriate. To this end, the application accounts for environmental stochasticity by randomly drawing and using one of the ten demographic matrices during each year of a projection. Because the matrices differ in the magnitude of population growth that they cause, the likelihood that each matrix is drawn will influence the resulting population trajectory during simulations. Therefore, the application allows the user to specify a baseline value for population growth (e.g., λ = 1.18 or 18% increases per year), which is assumed to represent the natural growth of the population in the absence of any management (i.e., previous sex-ratio adjusted removals, previous fertility control treatment). Depending on the value provided for population growth, the application uses a vector of probability values associated with the ten demographic matrices, where each matrix is assigned a weighted probability value and the sum of the product of each matrices’ λ value and its weighted probability generated a mean λ for the provided population growth value (Table 2). With this system, a user can enter a population growth rate (%) between 1-32%, and the application will randomly draw different demographic matrices each year to simulate random, stochastic variation in population growth from year-to-year that approximates the user-specified baseline population growth value.
Table 2: Probability vectors describing the likelihood that each of ten demographic matrices (Table 1) are drawn each year during population projections under different values of Population growth (%) (or Population growth rate [λ]).
Additional sources of stochasticity in demographic rates are built into the application. Populations are projected each year by multiplying the demographic rate matrix by a vector of age-based population size using the 'multiresultm()' function from the R package 'popbio' (Stubben and Milligan 2007). The 'multiresultm()' function takes random draws from statistical distributions on reproduction and survival parameters, which simulates additional stochasticity from year-to-year (i.e., temporal stochasticity).
While horse populations have occasionally been observed to decline in size between consecutive years, no study has documented horse populations in western North America to decline over long-term, multi-year periods (i.e., mean λ < 1.00 over multiple years). For this reason, the application assumes increasing population growth values over multi-year time scales, and user-specified values for population growth are constrained between 1-32%.
Population structure
The application requires the user to input an estimate for initial population size. To project the population using demographic matrices, the initial population size is multiplied by a population structure vector to partition individuals into different age classes. The application uses population structure data from a study at Garfield Flat, Nevada, where no recent gathers or management had occurred (data from WinEquus; Jenkins 2002).
Table 3: Initial vectors of population age structure used by the application. Vectors describe the proportion of a population that is assumed to be within each age class.
Management actions
The PopEquus application can simulate how six management actions, alone or in combination, might reasonably influence horse populations. The six management actions are removals, three fertility control vaccines (GonaCon-Equine [GonaCon], PZP-22, and ZonaStat-H), intrauterine devices, and mare sterilization.
Because the model is based on a post-breeding census, management actions are assumed to occur immediately after reproduction (i.e., late summer).
Removals
- Removals involve gathering horses and gather cost estimates are based on information from helicopter gathers. The application assumes that the per-horse cost ($) during gathers depends on the number of horses are gathered, with larger gathers having cheaper costs per horse than smaller gathers. For example, a gather of 1000 horses costs $668 per horse, whereas a gather of 100 horses costs $1074 per horse. The model uses information provided from the Bureau of Land Management to calculate per-horse gather costs each year depending on the size of the gather.
- Removals are only performed when the population size of a replicate exceeds the maximum AML. If a removal is specified during a year but the population size is below maximum AML, no removal will be performed in that year.
- During a removal, it is assumed that managers know the true total population size and aim to remove horses to reduce the true population size to be as close as possible to the user-specified target population size. They may not be able to collect enough horses, however, which depends on the population size in that year and the 'Capture proportion (%) of the population'.
- Removed animals are taken to a short-term holding facility (off-range corral), then made available for adoption or sale with restrictions. While female and male horses are separated in captivity, some females are pregnant upon being removed from the wild and give birth in captivity after approximately one year. To this end, the model projects removed horses for the first year in short-term holding with 95% survival rate for all age classes but while assuming that reproductive rates will be reduced relative to the wild population that they came from. Reproductive rates during the first year in holding are assumed to be 50% less than that experienced by the wild population in that year in the Basic Tool; this breeding reduction percentage is adjustable in the Advanced Tool.
- Among horses removed from populations in a given year, the model assumes that a percentage of them will be adopted that year. Animals that are not adopted in the first year after being removed from the range go to long-term holding facilities (e.g., off-range pastures), where they live out their lives. The percentage of animals adopted each year actually reflects all private care placements: adoptions, sales with limitation, and transfers to government agencies. For simplicity, this overall placement rate is referred to as adoptions for shorthand.
- Population dynamics in long-term holding facilities are characterized by no reproduction and 95% survival of all ages each year in holding (e.g., 'Holding' matrix; Table 1).
GonaCon
- GonaCon treatment was modeled using results from published field trials in Theodore Roosevelt National Park (Baker et al. 2018) that described treatment-driven reductions in reproduction. We modeled GonaCon as having relatively weak effects when individuals are only given one treatment (e.g., ca. 37% and 29% reductions in fertility after one and two years, respectively), but substantially stronger effects when individuals are treated with a booster shot (i.e., a second shot; 100%, 85%, and 50% reductions in fertility during 1, 2–4, and 5–7 years after two or more shots; Baker et al. 2018, Bureau of Land Management reasonable expectation for effects in years 5-7).
- Mares treated with fertility control treatment have higher survival than untreated females (Kirkpatrick and Turner 2007). The application assumes that any mare treated with GonaCon or any other form of fertility control treatment would have increased survival rate during years that the treatment is active. This is done by is multiplying survival rates by 1.02 for treated mares, but with maximum annual survival rates of 100% per year.
PZP-22
- The application assumes that PZP-22 treatment involves an initial treatment of mares with one dose each of PZP-22 and ZonaStat-H and subsequent retreatment with an additional dose of ZonaStat-H in each future treatment year.
- We modeled PZP-22 treatment efficacy using results describing treatment reductions in reproduction from Rutberg et al. (2017). We assumed minimum and maximum percent reductions in fertility from PZP-22 treatments were 33–72% one year and 20–40% two years after receiving a primary treatment with PZP-22 and ZonaStat-H, respectively; 68–85%, 70–75%, and 60–72% reductions one, two, and three years after receiving a booster retreatment with ZonaStat-H; and 78–95% one-, 80–85% two-, and 70–82% three-years after receiving another booster(s) of ZonaStat-H. Effectiveness rates for the hypothetical third or more treatment are suppositions based on a reasonable expectation of somewhat increased efficacy (Paul Griffin, Bureau of Land Management). Because PZP-22 batches can vary in effectiveness, we modeled a stochastic effect where batch effectiveness was a randomly drawn value between the observed or inferred minimum and maximum effectiveness of receiving one treatment, two treatments, or three treatments.
- The application assumes that PZP-22 is not delivered by dart, because that has not been common BLM practice.
ZonaStat-H
- The application assumes that ZonaStat-H treatment involves an initial treatment of mares with two-doses of ZonaStat-H; females are held in short-term captivity to receive the second dose 30 days after they received the primer dose, so as to achieve maximum reductions of fertility (95%) for one year (Kirkpatrick and Turner 2008). Retreatment involves a single dose of ZonaStat-H in each additional treatment year. We modeled ZonaStat treatment efficacy at reducing reproduction as: 95% and 19% reductions on reproduction one and two years after the first two doses, respectively (Turner et al. 1997, Kirkpatrick and Turner 2008); 95% and 19% reductions one and two years after receiving a third dose, respectively (Turner et al. 1997, Kirkpatrick and Turner 2008); 95%, 72%, 58% and 30% reductions one, two, three, and four years after receiving a fourth dose, respectively (Kirkpatrick and Turner 2008, Nuñez et al. 2017); and a persistent 95% reduction after receiving a fifth dose (Kirkpatrick and Turner 2008, Nuñez et al. 2017).
- For scenarios with ZonaStat-H application via darting, we assumed that all females treated for the first time in a given year would be darted a second time in that same year to administer a booster shot.
Intrauterine devices (IUDs)
- The application assumes that IUDs can only be given to non-pregnant females that are gathered. The number of non-pregnant females each year is estimated by taking the complement of reproductive rates (i.e., 1 - reproductive rate) for each age class of horses from the randomly-drawn demographic matrix for that year, multiplying the rate of non-breeding females by the number of females gathered from each respective age class that year, and rounding to the nearest whole number. These horses are then classified as non-pregnant and are meant to represent horses that would be identified as non-pregnant (via ultrasound) and given an IUD.
- IUDs are 100% effective at preventing pregnancy while the device is within a mare; however, IUDs are subject to an imperfect retention rate each year (e.g., 86% per year; Holyoak et al. 2021).
Mare sterilization
- There are a number of potential methods that could cause mare sterilization from a single handling occasion (such as minimally invasive physical methods, pharmacological, immunological, or surgical methods). The application assumes that Mare sterilization is 100% effective at preventing pregnancy and this effect lasts the duration of the treated individual's life.
The code for the PopEquus web application and its constituent functions will be available through a USGS Software Release.
Questions or comments about the application can be directed to Brian Folt (bfolt@usgs.gov) and Kate Schoenecker (schoeneckerk@usgs.gov).
References
Baker, D. L., J. G. Powers, J. I. Ransom, B. E. McCann, M. W. Oehler, J. E. Bruemmer, N. L. Galloway, D. C. Eckery, and T. M. Nett. 2018. Reimmunization increases contraceptive effectiveness of gonadotropin-releasing hormone vaccine (GonaCon-Equine) in free-ranging horses (Equus caballus): limitations and side effects. PLoS One 13:e0201570.
Berger, J. 1986. Wild Horses of the Great Basin. University of Chicago Press, Chicago, USA.
Caswell, H. 2001. Matrix population models. Second Edition edition. Sinauer Associates, Sunderland, MA.
Garrott, R. A., and L. Taylor. 1990. Dynamics of a Feral Horse Population in Montana. Journal of Wildlife Management 54:603–612.
Government Accountability Office. 2008. Effective Long-Term Options Needed to Manage Unadoptable Wild Horses. Bureau of Land Management, Washington, D.C., USA, Report to the Chairman, Committee on Natural Resources, House of Representatives, GAO-09-77.
Holyoak, G. R., C. C. Lyman, S. Wang, S. S. Germaine, C. O. Anderson, J. M. Baldrighi, N. Vemula, G. B. Rezabek, and A. J. Kane. 2021. Efficacy of a Y‐Design Silastic Elastomer Intrauterine Device as a Horse Contraceptive. The Journal of Wildlife Management 85:1169-1174.
Jenkins, S. H. 2002. Feral horse population model, WinEquus. University of Nevada.
Kirkpatrick, J. F., and A. Turner. 2007. Immunocontraception and increased longevity in equids. Zoo Biology 26:237–244.
Kirkpatrick, J. F., and A. Turner. 2008. Achieving population goals in a long-lived wildlife species (Equus caballus) with contraception. Wildlife Research 35(6):513-519.
Nuñez, C. M. V., J. S. Adelman, H. A. Carr, C. M. Alvarez, and D. I. Rubenstein. 2017. Lingering effects of contraception management on feral mare (Equus caballus) fertility and social behavior. Conservation Physiology 5:1–11.
Ransom, J. I., L. Lagos, H. Hrabar, H. Nowzari, D. Usukhjargal, and N. Spasskaya. 2016. Wild and feral equid population dynamics. Pages 68–86 in J. I. Ransom and P. Kaczensky, editors. Wild equids; ecology, management and conservation. Johns Hopkins University Press, Baltimore, Maryland.
Roelle, J., F. J. Singer, L. C. Zeigenfuss, J. I. Ransom, L. Coates-Markle, and K. A. Schoenecker. 2010. Demography of the Pryor Mountain Wild Horses, 1993–2007. U.S. Geological Survey, Reston, Virginia.
Stubben, C. J., and B. G. Milligan. 2007. Estimating and Analyzing Demographic Models Using the popbio Package in R. Journal of Statistical Software 22:11.
Turner, J. W., Jr., I. K. M. Liu, A. T. Rutberg, and J. F. Kirkpatrick. 1997. Immunocontraception limits foal production in free-roaming feral horses in Nevada. Journal of Wildlife Management 61:873–880.
This software can be cited as: Folt, B., Ekernas, L.S., Edmunds, D., Hannon, M., and Schoenecker, K.A., 2023, PopEquus: A Predictive Modeling Tool to Support Management Decisions for Free-roaming Horse Populations, Version 1.0.1: U.S. Geological Survey software release, https://doi.org/10.5066/P9NMRQDG.
Here we described a series of exercises that demonstrate different contexts for how the PopEquus Advanced Tool might be used to simulate and compare management alternatives for free-roaming horse populations and how these applications might be useful for supporting management decisions. We describe hypothetical situations or management decisions that a decision maker might face and provide suggestions for how the application could be used to inform those decision problems. All suggested values for inputs are hypothetical and are meant to illustrate how the model might be used; they are not necessarily 'correct' values for input variables in specific contexts. In the examples below, we emphasize values for certain input variables to describe the population context in each decision problem; for input variables that we do not mention, the default values of the user interface are assumed.
Exercise 1 — Wild horse populations occur in 177 Herd Management Areas (HMAs) in western North America, and Bureau of Land Management (BLM) staff are tasked with making decisions about how to manage those populations. Because horse populations grow quickly, largely lack top-down effects of predators, and managers may be limited in the resources they have available to perform management, many populations have exceeded target population size ranges (i.e., Appropriate Management Levels; AML) identified in land use plans in recent years (e.g., 79% of HMAs had herd sizes that exceeded maximum AML in 20221). The authorized official (decision maker) may need to decide what methods to use, and at what frequency, to manage a horse population on a HMA that exceeds the AML. However, there are many alternatives to choose from, options within alternatives are numerous and complex, and an alternative that leads to desirable outcomes over time may not be immediately obvious to a decision maker. The PopEquus Advanced Tool can be used to estimate the consequences of different management alternatives and help identify alternatives that are effective at reducing population size, reducing cost, and reducing overall management effort.
Within the Advanced Tool, the user could specify a horse population with 500 individuals, AML of 200–300 horses, a target population size of 200 horses during removals, an assumed population growth rate of 18% per year, and a population projection interval of 10 years (i.e., the default input values). Suppose that the user is interested in estimating the consequences of five management alternatives (removals, GonaCon, intrauterine devices [IUDs], removals and GonaCon, removals and IUDs). In that case, the user could select those five options in the Management Alternatives section. Default values can be left unchanged for all other input variables, which would mean that management activities (e.g., removals, fertility control treatment) will occur at the start of years 1, 4, 7, and 10 of the projection. The user then clicks the ‘Perform simulations’ button and the tool will simulate the population under scenarios representing each of the management alternatives.
The output graphs, tables, and summary are meant to help the user understand the simulated consequences of selected alternatives. Based on those, management with GonaCon and IUDs caused simulated populations to increase in size over the projection interval, while management involving periodic removals generally yielded a population size in year 10 that was within the Appropriate Management Levels, but also incurred the highest long-term off-range costs. Overall mean population size was lowest under the ‘Removals and GonaCon’ alternative. Among the three alternatives that achieved overall mean population size within Appropriate Management Levels, ‘Removals and GonaCon’ achieved the lowest mean population size and was the least costly overall. Therefore, this simulation points toward several alternatives that could be useful for reducing population size and provides information about relative management costs among those alternatives.
List of non-default settings for Exercise 1:
- Management Alternatives: Removals, GonaCon, Intrauterine devices (IUDs), Removals and GonaCon, Removals and IUDs
Exercise 2 — Consider the same population conditions from Example 1 (500 horses, AML of 200–300 horses, target of 200 horses), but with a few changes to the management conditions. Suppose that the population occurs over a vast and rugged landscape, so that the horses are more difficult to locate and gather during helicopter gathers, and that gathers are only able to capture about 55% of the population at a time. Because of those logistical difficulties with collecting horses during gathers, the decision maker may be especially interested in using alternatives that are effective at decreasing reproduction of captured horses for longer time periods. To reflect these realities, the user could adjust the ‘Capture proportion (%) during gathers’ to be 55% and the ‘Management Alternatives’ to include ‘Removals’, ‘Removals and GonaCon’, and ‘Removals and mare sterilization’. Here and always, any mare sterilization is assumed to be humane and safe (such as using a minimally-invasive method) and 100% effective at reducing future reproduction of treated individuals.
Predicted outcomes from simulations suggest that the alternatives produce comparable outcomes in final population size, overall mean population size, and total cost of management. However, many of the simulated herd size projections for ‘Removals and GonaCon’ and ‘Removals and mare sterilization’ have lower final population sizes than ‘Removals’, and ‘Removals and mare sterilization’ is often predicted to be the least costly overall.
After running this simulation and examining the table, note that only a relatively small number of horses were treated and released back into the population for the two alternatives with fertility control treatment over the projection interval. This result occurs because, given the small proportion of the population captured during gathers, most horses are removed to reduce population size to AML during the gathers in years 1 and 4 and only a small number of females are available to be treated and released back into the population during the gathers in years 7 and 10. Also note that due to the random nature of simulations, predicted outcomes can vary among different simulation exercises. Increasing the ‘Number of simulation replicates’ can reduce the chance that the mean values predicted for each alternative are affected by unusual population trajectories.
List of non-default settings for Exercise 2:
- Capture proportion (%) during gathers: 55%
- Management Alternatives: Removals, Removals and GonaCon, Removals and mare sterilization
Exercise 3 — Consider the same conditions from Example 2 (500 horses, AML of 200–300 horses, 55% capture proportion), but with another change. Feral horse populations, globally, have been observed to grow 18% per year on average2, and the BLM generally assumes a 20% annual growth rate for wild horse populations in the western United States. However, suppose that, based on aerial surveys in the last decade, this population has been observed to increase by 23% annually. That growth rate is higher than many other free-roaming horse populations, but it is well within the range of observed values among populations. To reflect this, the user should adjust the estimate for ‘Population growth rate (%)’ to be 23%. The user again selects ‘Removals’, ‘Removals and GonaCon’, and ‘Removals and mare sterilization’ as alternatives to simulate.
Predicted outcomes from simulations suggest that the three alternatives produce comparable outcomes in final population size, overall mean population size, and total cost of management, and the rank order of which alternative performs best at different metrics varies randomly among simulation exercises. This occurs because the low capture proportion during gathers and the high population growth rate require most or all of the horses captured to be removed in an attempt to reach AML. In other words, because annual population growth is so high and because mares are not treated and released unless the herd is within AML, each alternative behaves like the ‘Removals’ alternative.
List of non-default settings for Exercise 3:
- Population growth rate (%): 23%
- Capture proportion (%) during gathers: 55%
- Management Alternatives: Removals, Removals and GonaCon, Removals and mare sterilization
Exercise 4 — Consider the Herd Management Area in exercises above (AML of 200–300 horses; target population size of 200 horses) but back again with just an 18% average annual population growth rate, 75% capture efficiency during management, and now supposing that there might be opportunity to treat mares with immunocontraceptive vaccine through darting at water sources. Assume that there are only a few perennial water sources (i.e., springs) on the landscape and that a gather and removal was performed one year ago that reduced the population to 200 horses; no horses were treated and released with any fertility control method at that time. In the present day, the population has grown to comprise 236 horses, and the user wants to simulate the effects of fertility control treatment through both periodic gathers and regular darting at perennial water sources, to hopefully reduce future reproduction and control the population within AML. Assume that the 75% of the population can be treated with vaccine by dart in a year (i.e., the default value for ‘Proportion of population (%) that can be darted’ under the 'Darting Options' dropdown). Also assume that darting activities could start in year 1 and then happen every year after that. However, given logistical challenges of darting, assume treated females only receive one treatment per year by dart.
Select two alternatives to simulate and compare: ‘GonaCon’ and ‘GonaCon (darting)’. The ‘GonaCon’ alternative assumes that GonaCon is treated as part of helicopter gathers; the default GonaCon treatment years of 1, 4, 7, and 10 can be used to specify the gather years. Navigate to the ‘Darting Options’ dropdown to consider features related to darting. Note that the default inputs include ‘Treatment years’ to include all years from 1–10 and 'Proportion of population (%) that can be darted' is 75%, so that the ‘GonaCon (darting)’ alternative will treat 75% of females with GonaCon by darting during each year of the projection. The option ‘Are individuals darted twice’ should not be selected (the default), given the assumptions above. Project the population under the alternatives for 10 years and compare outcomes.
Results suggest that under both alternatives, simulated populations tend to grow to exceed maximum AML by year 2 or 3, but then population size tends to stabilize going forward in time for the ‘GonaCon (darting)’ alternative. By year 10, the ‘GonaCon (darting)’ alternative may have some simulation replicates that are within AML (e.g., a 0.30 ‘AML probability’ in the table indicates that 30% of simulation replicates for ‘GonaCon (darting)’ were within AML after year 10). Total cost is lower for the ‘GonaCon (darting)’ alternative over 10-years (< $500,000 USD). Changes in population size through time for the ‘GonaCon (darting)’ alternative describe a pattern suggesting that if management were to be extended an additional five years then the population might decrease to be within AML for more replicates.
List of non-default settings for Exercise 4:
- Population size: 236
- Management Alternatives: GonaCon, GonaCon (darting)
Exercise 5 — To test the idea that yearly darting over a 15-year period might better achieve the objective of reducing the population to be within AML, use the same settings as in Exercise 4.1, except adjust the ‘Projection interval (years)’ to be 15 years, adjust the ‘Treatment years’ under GonaCon Options to be years 1, 4, 7, 10, and 13, and the ‘Treatment years’ under Darting Options to be years 1–15, and re-run the simulation.
The results demonstrate that after a 15-year projection, most simulation replicates for the ‘GonaCon (darting)’ alternative fall within AML but not for the ‘GonaCon’ alternative.
List of non-default settings for Exercise 5:
- Population size: 236
- Projection interval (years): 15
- Management Alternatives: GonaCon, GonaCon (darting)
- GonaCon Options:
- Treatment years: 1, 4, 7, 10, 13
- Darting Options:
- Treatment years: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
Exercise 6 — To understand how the amount of the population darted each year influences predicted population size, increase the ‘Proportion of population (%) that can be darted’ from 75% to 90% (under the Darting Options dropdown), decrease the projection interval from 15 back to 10 years, and simulate the ‘GonaCon’ and ‘GonaCon (darting)’ alternatives again. With an additionally 15% of age-eligible females darted each year, the population growth should stabilize and reverse more quickly, most simulation replicates should be within AML by year 10, and overall mean population size should be within AML over the projection interval also. Whether or not it is realistic to treat 90% of mares by darting each year for 10 years in a row is a separate question that might be useful to understand.
List of non-default settings for Exercise 6:
- Population size: 236
- Management Alternatives: GonaCon, GonaCon (darting)
- Darting Options:
- Proportion of population (%) that can be darted: 90