## Abstract

Population models can be useful tools for evaluating management strategies and risks for a given species. A major, but often overlooked, component of endangered or threatened species management and recovery is the incidental take allowance of many endangered species laws. In the United States population models are seldom applied to address specific incidental take scenarios. We believe it is prudent for wildlife management agencies like the U.S. Fish and Wildlife Service to embrace explicit predictive tools to assess the possible effects of incidental take actions and to set standards for what constitutes unacceptable levels of incidental take in terms of predicted effect on population viability, recovery, and extinction. We briefly give recommendations for incorporating simulation models into jeopardy evaluations in ways that would dovetail with legislative language and provide a simple example model. Using explicit predictive models to support jeopardy determinations and incidental take decision-making would lead to transparent decisions rooted in measurable quantities such as changes in extinction probability or abundance projections.

## Introduction

Predicting the future of an endangered or threatened species is a key part of planning management actions and recovery (National Research Council 1995). In 1995 the National Research Council concluded that predictive population models were extremely useful tools for evaluating listing and delisting of an endangered species, assessing management strategies, and evaluating risks to the species. The National Research Council (1995) recommended that population models be used wherever possible for those purposes in endangered species management and policy decisions. Population models and population viability analyses have a long history and have grown in importance for managing rare and endangered species (Boyce 1992; Beissinger and McCullough 2002; Morris and Doak 2002).

A major, but often overlooked, component of endangered or threatened species management and recovery is incidental take (hereafter, “take”) allowances, which are defined as exceptions to the prohibitions and protections under endangered species laws. For example, Section 10 of the U.S. Endangered Species Act (ESA), as amended, states “The Secretary may permit…any taking otherwise prohibited… if such taking is incidental to, and not the purpose of, the carrying out of an otherwise lawful activity,” and if “the taking will not reduce appreciably the likelihood of the survival and recovery of the species in the wild” (ESA 1973). Similar exceptions exist in endangered species legislation of other countries. For example, the Bern Convention on the conservation of European wildlife and natural habitats prohibits destruction of protected species but permits exceptions “to prevent serious damage to crops, livestock, forest, fisheries, water and other forms of property…” as long as “the exception will not be detrimental to the survival of the population concerned” (E.U. Convention on the Conservation of European Wildlife and Natural Habitats, 1981, Bern, 19.IX.1979, Article 9). The National Research Council's book, “Science and the Endangered Species Act” (1995), has entire chapters and sections dedicated to listing decisions, critical habitat designations, and habitat conservation planning, but only addresses take within the context of other regulatory or management issues. The National Research Council (1995) did, however, call for the use of population viability analyses when evaluating take decisions wherever possible. The language of the legislative documents (i.e., “probability of survival…in the wild”) is well-suited for use with population projection models that produce predictions regarding extinction probability and future population growth and abundance.

The legislative phrase “reduce appreciably the likelihood of survival and recovery of the species in the wild” is often referred to as “causing jeopardy” in U.S. legislative and government documents (U.S. Fish and Wildlife Service [USFWS] 1998). Jeopardy determinations come under the Section 7 Consultation process, which (in theory) is a straight forward process. If, during the planning stages for any action, a Federal agency determines that the actions “may affect” a listed species, the agency requests the initiation of a Section 7 consultation. If the action agency determines that the action “may adversely affect” a listed species or designated critical habitat, it requests “formal consultation.” To analyze an action and the effects on any listed species and critical habitat, the USFWS writes and issues a “biological opinion.” A biological opinion consists of a review of relevant literature and data to assess the status of the species in question and to assess the effects of the proposed actions and whether they will cause jeopardy for the listed species. Biological opinions conclude with an “incidental take statement” that articulates what levels of take are anticipated and how much take is permissible (USFWS 1998). Section 7 of the ESA and the pursuant determination of what actions amount to jeopardy can have major implications for management and recovery of a listed species (Rohlf 2001).

Jeopardy decisions for any take situation provide opportunities to apply predictive quantitative models that could evaluate the effects of the proposed actions in terms of extinction probability or population growth of the protected species (National Research Council 1995). The phrasing “reduce the probability of survival…in the wild” implies that some evaluation of future extinction risk and the changes in extinction risk due to the proposed actions is conducted in making jeopardy decisions. But, thus far, to our knowledge there have been few attempts to use population models to evaluate take effects on endangered or threatened populations (McGowan 2008; McGowan and Ryan 2009).

As we see it, the benefits of models for the type of assessments related to endangered species take decision-making are three-fold. First, the resulting decisions are based on mathematical and probabilistic predictions. A model can tell the decision maker what is likely to happen in future and how some proposed take is likely to affect the endangered population. Second, a formalized model is explicit and open for review from other scientists. Decisions based on a model (if well-crafted and reasonable) are immediately scientifically defendable because there are no hidden assumptions. In an appropriately documented explicit model, the assumptions used to make the predictions can be clearly articulated so that all involved with and affected by the decision can see and understand the basis on which the decision was made. All models contain some assumptions about the system or process represented by the model and all management decisions involve some model or method for making predictions about how the management actions will affect the system (Williams et al. 2002). We are advocating for a process that transparently articulates the methods used to make those predictions and the assumptions embedded within that predictive model. Lastly, models can account for uncertainty in predictions and incorporate that uncertainty into the decision-making process. All decisions in natural resource management are subject to uncertainty, whether it is environmental stochasticity (e.g., unpredictable weather events), partial controllability (e.g., a prescribed fire gone awry), partial observability (e.g., sampling or parameter estimation errors), or ecological uncertainty (e.g., lack of knowledge about system function or population dynamics; Williams et al. 2002). Appropriately crafted models can mimic some or all of that uncertainty and make probabilistic predictions about the outcomes of take proposals and the probable effects of take on population abundance, extinction probability, or recovery probability. Objective-driven decision-making (e.g., maximizing species recovery probability, or minimizing species extinction probability) supported by appropriate population models is transparent, defendable, and robust to uncertainty. Models that acknowledge and incorporate uncertainty can also allow decision-making to proceed under the uncertainty, and can provide opportunities to learn about system function to reduce uncertainty in the future. Effective monitoring of the effects of take on an endangered population and comparisons to model predictions can lead to insights on population dynamics and model accuracy. We argue that projection models should be used wherever possible for take decisions and that a standardized approach for the use of those models should be adopted.

## An Example—Piping Plover Biological Opinions

McGowan (2008) looked at 11 biological opinions for piping plovers *Charadrius melodus* from throughout the species' range and examined and evaluated the use of population models in those opinions. Piping plovers are small migratory shorebirds that breed on beaches of the Atlantic Coast of North America, on beaches in the Great Lakes, and on rivers, lakes, and wetlands in the northern Great Plains (Elliott-Smith and Haig 2004). The piping plover was listed as threatened in the Atlantic Coast and the Great Plains and endangered in the Great Lakes in mid-1980s (USFWS 1985). The piping plover is a representative species for this evaluation because its ecology and population dynamics have been studied extensively. Furthermore, it has been listed under the ESA for over 20 y and there have been numerous biological opinions filed on many different federal projects throughout the species' range (Sidle et al. 1991). There have also been several attempts to model piping plover populations, each with varying methodologies and results for the USFWS to evaluate and chose among.

The use of piping plover population models and the results of the models varied across opinions, time, and geographic range. For the Atlantic Coast breeding population, the 1996 Recovery Plan (USFWS 1996) included a population model that set target fledge ratios (the number of chicks successfully produced per breeding pair) to guide management. All the opinions from that region examined the proposed take in terms of the target fledge ratios, and determined permissibility based on some assessment of whether those target ratios would be reached when the action took place.

For the Great Plains population there have been three published models since 1993 (Ryan et al. 1993; Plissner and Haig 2000; and Larson et al. 2002), which vary in mathematical structure and complexity. McGowan (2008) reported that opinions from that region primarily determined jeopardy by determining whether or not action would result in meeting the desired fledging target from the first published model, which had the lowest required fledge ratios to maintain a stable population size. McGowan (2008) reported that only one of the examined biological opinions discussed the effects of the proposed action on the extinction probability of the population. All others discussed the effects of the proposed actions in terms of achieving target fledge ratios that the population models concluded were necessary for maintaining stable population growth. The recovery criteria for this population are stated in terms of regional population size targets and not in terms of fledge ratios. In those opinions, McGowan (2008) found no discussion of how not achieving the prescribed fledge ratios would decrease or change the probability of survival in the wild or of reaching the proposed delisting criteria.

From this limited and brief examination of biological opinions written as part of Section 7 Consultation in U.S. law to evaluate the effects and permissibility of take, we conclude that wider and more standardized use of population models should be used. Population viability analysis–type population models are well-suited to evaluate extinction risk (Morris and Doak 2002) and, potentially, changes in extinction risk due to take (McGowan and Ryan 2009). We argue that models are the only tools available to thoroughly evaluate the effects of management actions and take allowances that can account for and incorporate the variety of sources of uncertainty that factor into a jeopardy decision. In fact, making any prediction about the effect of some action on an ecosystem or species requires a model of the system or population dynamics (Williams et al. 2002).

## Developing Models

Developing predictive models of system dynamics does not require tremendous data sets and detailed knowledge of system dynamics (Starfield 1997), but rather some notion of system processes and the ecology and population dynamics of the species concerned. Models need to be only as complex as necessary to make adequate predictions about the issue being modeled. Some situations require very complex models, such as the loggerhead sea turtle *Caretta caretta* model developed by Crouse et al. (1987) and Crowder et al. (1994). Those studies used stage-based matrix models to simulate turtle populations and their models required significant complexity because the issue being studied was the effect of fishing bycatch mortality of juvenile turtles on population viability. The models required isolating the juvenile age class from other stages of development and applying bycatch to that stage specifically. Alternatively, models could be as simple as linear regression of a time series of abundance data (e.g., Dennis et al. 1991; Morris and Doak 2002) where the regression slope parameter is equivalent to the finite population growth rate. Predictions about future population size and extinction risk would be as simple as multiplying the population size by the estimated growth rate to return the expected population size in the future. Applying variability to the growth rate parameter and replicating the projection numerous times could represent uncertainty about future environmental variation and growth-rate estimation uncertainty. However, even deterministic simulations (explicit predictions with no variability) would be a more transparent approach than intuition or undefined unarticulated processes for evaluating take. These models can easily be implemented in statistical programs such as R (R Development Core Team 2009), but could also be developed in spreadsheet-type programs such as Microsoft® Excel, a program widely used for data management in the field of natural resources.

## A Simple Population Model Example

To exemplify the benefits of modeling we have crafted a very simple population model to represent a threatened or endangered species similar to the count-based population viability analysis presented in Morris and Doak (2002). The equation to predict future population size simply multiples current population size by the estimated population growth rate to predict the population size at the next time step:

where *N* is the population abundance, *t* is time, and λ is the population growth rate. Initial *N* is estimated from ongoing monitoring, counting surveys, or mark–recapture studies, and λ is estimated by examining a time series of population counts.

And after a number of successive population counts the geometric mean of λ can be estimated:

where *y* is the number of years for which λ is estimated. Our approach assumes that past population growth rate will continue into the future and that population size can be estimated with some accuracy. Variability and uncertainty about future population growth can be incorporated by simply calculating the variance or the standard deviation of the mean (a simple task in Microsoft Excel), and replicating the population projection numerous times with new values of λ for each year in each replication.

Again, this approach to incorporating variation and uncertainty assumes that past variability is a reasonable approximation of future variability. Calculating extinction from this simulation is simply a matter of counting the number of replications where *N* falls below 1 and dividing by the total number of replications. The model must have some restrictions applied so that the populations cannot recover from an abundance of less than two individuals. It is also important to not simulate the population too far into the future because a model like this has no limits on growth and could, theoretically, grow to infinity if given enough time, or conversely the probability of extinction also increases over time in a stochastic model. There is no rule of thumb for determining good simulation duration, but (depending on the species) simulating on the order of a few decades is likely sufficient to avoid the problems of unimpeded growth and make model predictions relevant to take decision-making.

Consider a case where a wind power company wants to build a wind farm facility in an area where an endangered bird species lives. Based on other wind farm projects, they estimate that their actions will likely take between 5 and 10 adult breeding birds of the endangered species each year. Using our simple model described above, applying this take is simply a matter of subtracting the annual take from the projection equation:

Simultaneous simulations with equations (4 and 5) can show the expected difference in abundance between a take and a no-take scenario, and extinction probability could easily be derived and compared for these two sets of simulations. If no estimates of λ or *N* are available, it may be appropriate to simulate multiple values of these parameters to see how the population responds to the proposed take under different conditions.

Using Microsoft Excel and beginning with a population size of 500 individuals, modeling λ as a normally distributed random variable with mean 0.995 (SD = 0.02; NORMINV(RAND(), 0.995, 0.02), code for a normally distributed random variable in Microsoft Excel) and applying annual take as a uniform random variable varying between 5 and 10 individuals/y (RANDBETWEEN(5,10), Microsoft Excel code for a uniform random variable between the upper and lower value), we simulated the population 50 y into the future and replicated the simulation 5,000 times (see *Supplemental Material*, Table S1, http://dx.doi.org/10.3996/062010-JFWM-014.S1). The model predicted that median abundance at 50 y for the population with the wind farm take will be ∼ 65 individuals compared to ∼ 385 individuals for the simulations with no take (Figure 1). The model also predicted that extinction probability will increase from 0.00 to 0.03 when the proposed take is applied to the system. With this modeling approach it is straightforward to see the effects that the proposed take will have on the system, given the assumptions and the uncertainty about population growth rates in the future. Even if uncertainty in model parameters is high we can still examine the relative abundance across the simulation scenarios and see that the proposed take is likely to have some negative impact on the population. We can also look at population growth predictions and see that allowing the proposed take leads to a decrease in predicted population growth from a nearly stable population (λ ¯ = 0.995) to a rapidly declining population (λ ¯ = 0.956). McGowan and Ryan (2009) showed that simulations can be conducted to compare projected population growth and extinction probability with and without the proposed actions. Subsequently managers can evaluate the predicted change in extinction probability and the changes in the probability of a population reaching its recovery criteria to determine whether an action appreciably affects those probabilities.

## Conclusions

We believe there is a dovetail between legislative language and well-established population ecology modeling tools in the case of evaluating jeopardy in relation to take permitting. We cannot envision good reasons for not using an explicit model to make predictions and evaluate take proposals. We realize that time and budgets are limited and that take assessments are numerous. However, even simple models will make predictions as accurate as (and often more accurate than) intuition, and a modeling approach is more transparent and scientifically defendable. All decisions in natural resource management involve some prediction about the future and how some action will affect the managed system (Williams et al. 2002). A take assessment and decision, with or without an explicit model, must make some prediction about how the proposed take will affect the protected population. An explicitly articulated model allows the decision maker, the stakeholders, and other scientists to understand the basis for the predictions that informed the decision. Models do not need to be complex to assist with decision-making, as was demonstrated herein with a simple Excel spreadsheet model, which took only a few hours to construct and error-check. A quantitative model only needs to suit the decision at hand and fit the available data. If data on abundance and population trend are not available, models can still be constructed though expert opinion on model parameters. Models can be constructed to account for uncertainty in population size, population growth rate, or any model parameter due to lack of data, and sensitivity analyses or multiple scenarios could be simulated to understand how that parameter uncertainty affects the decision outcome.

Putting the criteria for jeopardy in some form of a population viability analysis context related to extinction probability will avoid arbitrary definitions of the term “appreciable.” We conclude that using predictive population models to make take management decisions in conjunction with a standardized definition of jeopardy, could move these decisions from an ad hoc, case-by-case realm (where it currently resides) toward a structured decision-making realm that is more transparent, understandable, and defensible (Gregory and Keeney 2002; Gregory and Long 2009). Objectives could be defined as maximizing take with the constraint that extinction probability not be increased, and population models could then be use to evaluate alternative take scenarios. Population models would greatly contribute to increasing transparency regarding the scientific basis of take decisions.

## Supplemental Material

Please note: The *Journal of Fish and Wildlife Management* is not responsible for the content or functionality of any supplemental material. Queries should be directed to the corresponding author.

**Table S1.** Sample simulation model.

Found at DOI: 10.3996/062010-JFWM-014.S1 (6423 KB XLS).

## Acknowledgments

We thank the U.S. Geological Survey, the U.S. Fish and Wildlife Service, and the department of Fisheries and Wildlife Sciences at the University of Missouri for financial and logistical support of this work.

We are grateful to M.A. Larson, J.J. Millspaugh, F.R. Thompson III, E. Zipkin, two anonymous referees, and the editors of the *Journal of Fish and Wildlife Management* for reviewing and helping us to improve this manuscript. We are also grateful to J.S. Rikoon, M.C. Runge, J. Szymanski, and J. Cochrane for many lengthy discussions on this subject of incidental take and endangered species policy.

## References

## Author notes

Conor P. McGowan,* Mark R. Ryan

McGowan CP, Ryan MR. 2010. Arguments for using population models in incidental take assessments for endangered species. *Journal of Fish and Wildlife Management* 1(2):183–188; e1944-687X. doi: 10.3996/062010-JFWM-014

Present address of C.P. McGowan: U.S. Geological Survey, Alabama Cooperative Fish and Wildlife Research Unit, School of Forestry and Wildlife Sciences, Auburn University, Auburn, Alabama 36849