Grantee Research Project Results
Final Report: Individual Variability, Environmental Stressors, and Sampling Uncertainty in Wildlife Risk Assessment
EPA Grant Number: R829088Title: Individual Variability, Environmental Stressors, and Sampling Uncertainty in Wildlife Risk Assessment
Investigators: Kendall, Bruce E. , Fox, Gordon A.
Institution: University of California - Santa Barbara , University of South Florida
EPA Project Officer: Packard, Benjamin H
Project Period: September 1, 2001 through August 31, 2004 (Extended to December 31, 2005)
Project Amount: $426,954
RFA: Wildlife Risk Assessment (2001) RFA Text | Recipients Lists
Research Category: Biology/Life Sciences , Ecological Indicators/Assessment/Restoration , Aquatic Ecosystems
Objective:
The original proposal had two broad objectives, each with four specific questions:
- Determine the statistical power of field assessments to predict demographic performance from environmental variables. Specifically:
- Under what circumstances do life table response experiments (LTREs) have the power to detect responses to meaningful environmental variation?
- Under what circumstances do correlation analyses of field data have the power to detect responses to meaningful environmental variation?
- How are these predictions affected by multiple, unmeasured stressors?
- How is the power of these approaches changed by measuring organism condition?
- Examine the importance of variability in the expected demographic performance of individuals (“demographic heterogeneity”). Specifically:
- What is the net affect of a spatially heterogeneous stressor?
- How does this heterogeneity affect the power of LTRE and correlation analyses?
- What is the pattern of demographic variability in fecundity?
- What is the magnitude of individual variability in demography?
We succeeded in addressing Objectives 1a (“Power analysis for demographic models”), 2c (“A general model for demographic stochasticity in fecundity”), and 2d (“Demographic heterogeneity in wildlife populations”). In addition, we made major theoretical advances on the effects of demographic heterogeneity on extinction risk (“Demographic heterogeneity and extinction risk”); this was not a proposal objective but is arguably more important than some of our proposed objectives.
There were three main reasons that we did not make substantial progress on the other proposed objectives. The first was that the initial programming for the power analysis (Objective 1) took longer than expected. Second, we had difficulty hiring Ph.D. students for the project, as our students already were well funded (most of the students on the project were Master’s students, who brought fewer skills and less initiative to the project). Finally, the data set that we used for a case study (Florida scrub-jay) proved to be far richer than we expected; we spent much more time than planned analyzing these data but were able to extract a remarkable amount of information about the sources of demographic heterogeneity in this population.
Summary/Accomplishments (Outputs/Outcomes):
Introduction
The core of wildlife risk assessment is demographic analysis: are birth and survival rates high enough that the population can sustain itself? Understanding and predicting the effects of stressors (both natural and anthropogenic) requires building the connections between the effects of the stressor on individual behavior and physiology and the resulting changes in population dynamics. A variety of factors—including the sensitivity of the population growth rate to changes in affected demographic process, interactions among stressors, density dependence, and animal movement rates—affect whether a measurable effect on individuals is translated into a meaningful effect on populations. The objectives of this study were to determine when stressors are likely to be important and what experimental design we need to have the power to detect these effects as a function of life history, ecological context, stressor mode of action, and stressor magnitude. We examined these issues both in the framework of conventional demographic analysis and in the context of emerging insights about the importance of demographic heterogeneity in demographic processes.
Power Analysis for Demographic Models
Under this grant, we have developed computer programs that make it possible to conduct statistical power analyses for matrix transition models, as well as for particular applications of matrix models, such as LTREs. A crucial assumption to these power analyses—common to all statistical analysis—is that the basic underlying form of the model is correct. In other words, given that population growth is described correctly by the matrix model, how large a sample does one need to draw conclusions with a sufficiently small error?
In all cases we studied, estimates of the long-term population growth rate λ are approximately normally (Gaussian) distributed. This means that many standard statistical methods are appropriate for examining hypotheses about λ, and that reports of estimated values of λ with a standard error are meaningful.
On the other hand, we found that it is common for estimates of other quantities—especially the sensitivities of λ to changes in individual matrix elements (∂λ /∂ aij) and the related elasticities (proportional sensitivities, [∂ ln(λ) /∂ ln(aij)])—to have strongly platykurtic (flat) distributions. The reason for this is simple: mean estimates of λ frequently are close to 1. As a result, many individual estimates are greater than 1, and many are less than 1. Because the former predict a growing population, and the latter a shrinking population, they frequently lead to divergent diagnoses as to what to do to protect a population from extinction. We believe that the solution is not primarily to have larger samples but rather to develop new approaches to decisionmaking for management that take this basic uncertainty into account.
The conclusion regarding LTREs follows logically from this: in a broad sense, current methods of analysis of LTREs have the power to detect meaningful environmental changes when the distribution of both estimates of λ (i.e., assuming a single comparison between a polluted and an unpolluted site) has little overlap with 1. It will be important to develop new methods to augment current LTRE approaches for the case where one or both estimates are close to 1.
A General Model for Demographic Stochasticity in Fecundity
The two major population viability analysis (PVA) software packages take very different approaches to modeling demographic stochasticity in fecundity. RAMAS uses a Poisson distribution to describe demographic stochasticity in reproductive output; there is no subsequent mortality of the offspring. In contrast, VORTEX requires the analyst to specify a distribution of offspring numbers that then is sampled to obtain the realized number of offspring; these offspring then survive according to a binomial distribution. Most of the independently developed PVA models in the literature apply one or the other of these approaches.
There are shortcomings to both approaches. In general, there is neither biological nor theoretical justification for use of the Poisson distribution, and survival (of either the offspring or their parents, depending on how the model is formulated) is a key component of the reproductive term in these population models. In contrast, custom-defined distributions are adequate to the population at hand, but the nonparametric nature of the model makes it difficult to evaluate the effects of environmental stochasticity, management, or evolutionary change.
In this analysis we considered the biological processes that underlie demographic stochasticity in animal fecundity and used these to develop and analyze a general parametric model of this phenomenon. For simplicity, we use terminology appropriate for birds.
Consider a single breeding attempt. The number of independent offspring depends on: (1) whether nest-building and mating is completed; (2) the number of eggs laid; (3) whether the nest is depredated, destroyed, or abandoned; (4) the nest success and the probability that each offspring survives from egg-laying to independence.
The first item (“egg-laying”), being binary, can be modeled as a Bernoulli process. The second item (“clutch size”) is quite a bit more challenging, as there is no conventionally accepted model for the probability distribution for the number of eggs. We propose that the generalized Poisson distribution often will be appropriate. The third item (“nest failure”) can also be represented as a Bernoulli process (although from the point of view of the offspring, it represents correlated mortality). There are a number of options for the last item (“offspring survival”). Each individual’s survival might be independent of its nestmates; if the survival probabilities are equal, then the number of survivors follows a binomial distribution. However, if fates are not independent (e.g., the instantaneous survival probability is a declining function of the number of currently living nestmates), the distribution might be different (although still computable).
In many species, an individual may attempt multiple broods during the breeding season, with the renesting probability depending on whether the previous breeding attempt was successful or a failure. We have developed the compound probability distributions that describe this set of stochastic processes in reproduction, described their statistical features, and are applying them to a case study of Florida scrub-jays.
Demographic Heterogeneity in Wildlife Populations
We used data from a long-term (35 years) study of the cooperatively breeding Florida scrub-jay (Aphelocoma c. coerulescens) to ask: (1) how much demographic heterogeneity is there in wild populations, (2) how much of it is structured; (3) how much data do we need to estimate these quantities; and (4) what techniques are needed to estimate these quantities?
We found considerable evidence for a strong effect of heterogeneity among maternal families in survival. The estimated variance of the random effect is 0.51; because frailty is defined as having mean 1, this is a large effect. We also found that demographic heterogeneity in reproductive traits (relating primarily to breeding experience and the presence of a helper at the nest) reduced the magnitude of demographic stochasticity 5-20 percent in most years.
In addition to natural sources of environmental heterogeneity, anthropogenic activities have added new sources of heterogeneity that may not have been important forces during most wildlife species’ evolutionary history. We focused on two: anthropogenic chemicals (particularly pesticides and industrial pollutants) and the increasing extent of habitat edges (especially forest edges resulting from forest fragmentation). We searched the literature for studies that contrasted the demographic characteristics of wild animals at different levels of chemical contaminants or at different distances from a forest edge. We have identified 44 studies to date but expect that this is a modest sample of the available literature; we have more than 120 articles still to evaluate from our initial searches and expect that many more remain to be found, especially in the domain of habitat fragmentation and edge effects.
Most of the studies were performed on birds. Demographic effects of chemical pollutants could be substantial. For example, exposure to lead produced a 20 percent reduction in survival and 44 percent reduction in fledging success in mute swans. Most of the studies that we have found to date focus on effects of lead or polychlorinated biphenyls. Most studies of the effects of habitat edges focused on reproductive success; for example, nesting success of ovenbirds and hermit thrush dropped from 52 percent at 500 m from the forest edge to 18 percent within 100 m of an edge.
These results suggest that, when assessing the impact of anthropogenic stressors on extinction risks of small wildlife populations (where demographic stochasticity is important), it is critical to examine the effects of the stressors on the variance of demographic performance as well as on the mean.
Demographic Heterogeneity and Extinction Risk
Prior to the onset of this project, our theoretical results on demographic heterogeneity focused on “structured” heterogeneity—the traits of individuals are not fully independent of one another—and on survival processes. We had concluded that “unstructured” heterogeneity—where the demographic traits are identically and independently distributed among individuals—had no effect on demographic stochasticity in survival. Subsequently, we have found that for demographic processes that are not well described by the Bernoulli process—such as reproduction in many wildlife species—then unstructured heterogeneity also can impact the magnitude of demographic stochasticity. In contrast to our prior work, which showed that structured heterogeneity in survival traits always reduced the magnitude of demographic stochasticity, we now find that unstructured heterogeneity in fecundity may increase the magnitude of demographic stochasticity, thereby increasing the extinction risk of small populations.
Within a population, factors like variation in exposure to stressors, genetic variation, and spatial environmental variation, all can cause different lineages to have different risks of extinction. By lineage extinction, we mean that at some point, there are no more descendants of particular individuals. We studied how variation in lineage extinction risk affects the extinction risk of a population as a whole. We showed that if there is a phenotypic correlation between parents and their offspring, variation in individual extinction risks always reduces both the long- and short-term population extinction risk, as compared with a population in which all individuals have an identical risk of extinction. This conclusion holds not only for the risk of eventual extinction, but also for the risk at any given time.
These results depend on the assumption that there is a strong correlation in extinction risk between parents and offspring—that the heritability of extinction risk is close to 1. Using a more general approach we have generalized these results for the case of heterogeneity in reproduction. We show that if every individual has the same chance of being a “high quality” or “low quality” individual, and this does not depend on other individuals—that is, if parameters are independently and identically distributed—then heterogeneity in these parameters tends to increase the risk of extinction. However, if (as is generally true) individuals have different chances of getting particular parameters (for example, because they are heritable) or this depends on other individuals in the population, then the effect on extinction risk depends on how heterogeneity is structured and on the underlying form of demographic stochasticity.
One important result from this analysis is that the effect of demographic heterogeneity is likely to depend on the life histories of the organisms involved. In particular, demographic heterogeneity in reproduction and survival of the offspring of long-lived organisms probably has small effects on population viability, whereas the same heterogeneity in short-lived organisms has a much bigger effect. On the other hand, demographic heterogeneity in survival of parents of long-lived organisms is expected to have a larger effect than the same demographic heterogeneity in short-lived organisms, as has been shown in simulation models.
Conclusions:
This project has demonstrated that anthropogenic activities (pollution and habitat fragmentation) can produce demographic heterogeneity in wildlife populations that may substantially impact their risk of extinction. In many cases the extinction risk will be lower than that we would predict simply by assuming that the entire habitat is of “average” quality (although the risk is still higher than it would be in the absence of the anthropogenic impacts). We have developed both a conceptual framework and practical statistical tools that will allow wildlife managers to assess the magnitude and impact of such heterogeneity.
Journal Articles on this Report : 4 Displayed | Download in RIS Format
Other project views: | All 15 publications | 4 publications in selected types | All 4 journal articles |
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Fox GA. Extinction risk of heterogeneous populations. Ecology 2005;86(5):1191-1198. |
R829088 (2002) R829088 (Final) |
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Fox GA, Kendall BE, Fitzpatrick JW, Woolfenden GE. Consequences of heterogeneity in survival probability in a population of Florida scrub-jays. Journal of Animal Ecology 2006;75(4):921-927. |
R829088 (Final) |
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Kendall BE, Fox GA. Variation among individuals and reduced demographic stochasticity. Conservation Biology 2002;16(1):109-116. |
R829088 (2002) R829088 (Final) |
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Kendall BE, Fox GA. Unstructured individual variation and demographic stochasticity. Conservation Biology 2003;17(4):1170-1172. |
R829088 (Final) |
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Supplemental Keywords:
risk assessment, ecological effects, sensitive populations, population, terrestrial, conservation, ecology, mathematics, Florida, FL, modeling, analytical,, RFA, Economic, Social, & Behavioral Science Research Program, Health, Scientific Discipline, Ecosystem Protection/Environmental Exposure & Risk, RESEARCH, Ecology, Applied Math & Statistics, exploratory research environmental biology, wildlife, Ecosystem/Assessment/Indicators, Models, Susceptibility/Sensitive Population/Genetic Susceptibility, Ecological Effects - Environmental Exposure & Risk, Environmental Statistics, genetic susceptability, Ecological Risk Assessment, Ecology and Ecosystems, Ecological Indicators, ecological exposure, risk assessment, predicting risk, sampling designs, stressors, ecosystem assessment, demographic data, environmental stressor, individual variability, Wildlife Risk Assessment, sampling uncertainty, environmental sampling, animal models, statistical models, risk models, data analysis, sampling, life table response experimentsRelevant Websites:
http://www.bren.ucsb.edu/~kendall Exit
http://boojum.cas.usf.edu/index.pl Exit
Progress and Final Reports:
Original AbstractThe perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Conclusions drawn by the principal investigators have not been reviewed by the Agency.