Final Report: Spatial Demographic Models for the Study of Stress Effects on Wildlife Populations

EPA Grant Number: R829089
Title: Spatial Demographic Models for the Study of Stress Effects on Wildlife Populations
Investigators: Caswell, Hal , Neubert, Michael
Institution: Woods Hole Oceanographic Institution
EPA Project Officer: Carleton, James N
Project Period: December 17, 2001 through December 16, 2005 (Extended to June 16, 2006)
Project Amount: $500,000
RFA: Wildlife Risk Assessment (2001) RFA Text |  Recipients Lists
Research Category: Ecological Indicators/Assessment/Restoration , Biology/Life Sciences , Ecosystems

Objective:

The objective of this research project was to develop new generalized approaches to assessing risks to wildlife populations, particularly risks characterized by a multiplicity of stressors and by spatial distribution. Our approach was to weave together two threads already spun into the fabric of demographic analysis: models for spatially distributed populations and analyses of the effects of stressors.

Summary/Accomplishments (Outputs/Outcomes):

Our goal was to develop spatial demographic models for use in evaluating effects of stress on wildlife populations. We addressed three problems: model formulation, the calculation of population endpoints, and the development of perturbation theory. Some of our specific accomplishments were theoretical or methodological developments; others were applications to specific populations subject to single or multiple stresses. The following is a list of some of our major accomplishments and findings.

The Sensitivity Analysis of the Stochastic Growth Rate

The perturbation analysis of population growth rate plays an important role in population biology. The sensitivity and/or elasticity (proportional sensitivity) of population growth rate to changes in the vital rates are regularly used to: (1) predict the effects of environmental perturbations; (2) characterize selection gradients on life-history traits; (3) evaluate management tactics; (4) analyze life table response experiments; and (5) calculate the sampling variance in population growth rate. In a stochastic environment, population growth is described by the stochastic growth rate, which gives, with probability 1, the asymptotic time-averaged growth rate of any realization. Tuljapurkar derived the sensitivity and elasticity of the stochastic growth rate to changes in the entries of the stochastic matrices. In our research, we have extended his result to cover three cases, each of which has arisen recently in applications. The first gives the response of the stochastic growth rate to environment-specific perturbations, applied only in a specified subset of the possible environments. The second gives the sensitivity and elasticity of the stochastic growth rate to changes in lower-level parameters. The third applies to stochastic seasonal models, in which the projection matrix for each year is a periodic product of matrices describing seasonal transitions. In this case interest focuses on the sensitivity of the stochastic growth rate to changes in the entries of the seasonal matrices, not entries in the annual matrices. These methods are turning out to be extremely useful in analyzing the population-level effects of stress in stochastic environments.

The Sensitivity of the Invasion Exponent in Nonequilibrium, Density-Dependent Population Models

The invasion exponent plays a critical role in life-history theory. It measures the rate at which a new phenotype would grow if introduced at low densities into a population of a resident phenotype that is on an attractor (equilibrium, cycle, invariant loop, or strange attractor). Only if the invasion exponent is positive will selection favor the phenotypic change represented by the difference between the invader and the resident. The selection gradient on the trait is measured by the sensitivity of the invasion exponent to a change in that parameter. In addition to changing the parameter, a successful invasion will also change the population density. When the resident phenotype is at a stable equilibrium, the sensitivity of the invasion exponent is equal to the sensitivity of an effective equilibrium density, which is a weighted sum of the equilibrium stage densities. The weights measure the effect of the stage on density-dependence and the effect of the density-dependence on population growth rate. Our results present a new analysis that extends these results to invasions when the resident is on a periodic attractor, an invariant loop, or a strange attractor. We have derived formulae for the effective average population density over the attractor and proved that the sensitivity of this equilibrium density is equal to the sensitivity of the invasion exponent.

New Methods for Estimation of Dispersal from Mark-Recapture Data on Animals

We have developed a new method for estimating a distribution of dispersal displacements (a dispersal kernel) from mark-recapture data. One conventional method of calculating the dispersal kernel assumes that the distribution of displacements is Gaussian (e.g., resulting from a diffusion process) and that individuals remain within sampled areas. The first assumption prohibits an analysis of dispersal data that do not exhibit the Gaussian distribution (a common situation); the second assumption leads to underestimation of dispersal distance because individuals that disperse outside of sampling areas are never recaptured. Our method eliminates these two assumptions. In addition, the method can also accommodate mortality during a sampling period. This new method uses integrodifference equations to express the probability of spatial mark-recapture data; associated dispersal, survival, and recapture parameters are then estimated using a maximum likelihood method. We examined the accuracy of the estimators by applying the method to simulated data sets. We then applied the method to data on movement of brown trout at the Sierra Nevada Aquatic Research Laboratory in California.

Sensitivity Analysis of Transient Population Dynamics

Short-term, transient population dynamics can differ in important ways from long-term asymptotic dynamics. Just as perturbation analysis (sensitivity and elasticity) of the asymptotic growth rate reveals the effects of the vital rates on long-term growth, the perturbation analysis of transient dynamics can reveal the determinants of short-term patterns. We have developed a completely new approach to transient sensitivity and elasticity analysis, using methods from matrix calculus. Unlike previous methods, this approach applies not only to linear time-invariant models but also to time-varying, subsidized, stochastic, nonlinear, and spatial models. It is computationally simple and does not require calculation of eigenvalues or eigenvectors. The method is presented along with examples of plant and animal populations.

Invasion Wave Speed in Periodic and Stochastic Environments

A population invading an unoccupied environment (spatially homogenous, time-invariant, and infinite in extent), from an initial condition restricted to a finite region, will, under some mild assumptions, eventually expand as an invasion wave of fixed shape moving at a constant speed. This invasion wave speed depends on both demography (i.e., on the rates of survival, development, reproduction, etc.) and on dispersal (i.e., on the probability distribution of distances dispersed by individuals at each stage of their life cycle). Because the wave speed integrates demography and dispersal into a single index of population spread, it plays a role analogous to that played by the population growth rate in demographic analysis. We have developed models for environments characterized by periodic (e.g., seasonal) and/or stochastic variation. Stochastic invasions can be linked to explicitly stochastic models for environmental processes (fires, floods, prey availability, etc.).

Effects of Fire on Invasiveness

We investigated the effects of fire on population growth rate and invasive spread of the perennial tussock grass Molinia caerulea. During the last decades, this species has invaded heathland communities in Western Europe, replacing typical heathland species such as Calluna vulgaris and Erica tetralix. M. caerulea is considered a major threat to heathland conservation. In 1996, a large and unintended fire destroyed almost one-third of the Kalmthoutse Heide, a large heathland area in northern Belgium. To study the impact of this fire on the population dynamics and invasive spread of M. caerulea, permanent monitoring plots were established both in burned and unburned heathland. The fate of each M. caerulea individual in these plots was monitored over 4 years (1997-2000). Patterns of seed dispersal were inferred from a seed germination experiment using soil cores sampled 1 month after seed rain at different distances of seed producing plants. Based on these measures, we calculated projected rates of spread for M. caerulea in burned and unburned heathland. Elasticity and sensitivity analyses were used to determine vital rates that contributed most to population growth rate (λ) and c*. Invasion speed was on average three times larger in burned compared to unburned plots. Dispersal distances, on the other hand, were not significantly different between burned and unburned plots, indicating that differences in invasive spread were mainly caused by differences in demography. Elasticities for fecundity and growth of seedlings and juveniles were higher for burned than for unburned plots, whereas elasticities for survival were higher in unburned plots. Finally, a life table response experiment analysis revealed that the effect of fire was mainly contributed by increases in sexual reproduction (seed production and germination) and growth of seedlings and juveniles. Our results clearly showed increased invasive spread of M. caerulea after fire and call for active management guidelines to prevent further encroachment of the species and to reduce the probability of large, accidental fires in the future. Mowing of resprouted plants before flowering is the obvious management tactic to halt massive invasive spread of the species after fire.

Effects of Selective Harvest and Bycatch on the Sooty Shearwater

Selectivity of harvest influences harvest sustainability because individuals with different characteristics contribute differently to population growth. We investigated the effects of selection based on chick weight on a traditional harvest of the sooty shearwater (Puffinus griseus) by Rakiura Maori in New Zealand. We developed a periodic stage-structured matrix population model and incorporated seasonal harvest of three weight classes of chicks. Intensity and selectivity of harvest are defined in terms of weight-specific hazard functions. We investigated the effect of harvest intensity and selectivity on λ and the chick exploitation rate, E. We also considered the interaction of chick harvest and adult mortality. λ decreases and E increases as harvest intensity increases. At low harvest intensities, selection has little effect on λ. At high harvest intensities, λ increases as selectivity increases because of the nonlinear relationship between harvest intensity and the probability of being harvested. λ is determined almost completely by E, irrespective of the combination of harvest selectivity and intensity producing E. This is true for both general patterns of selectivity and specific patterns estimated from empirical data. The elasticities of λ, the net reproductive rate, and the generation time are unaffected by selectivity and show only small responses to harvest intensity. Adult sooty shearwaters are killed as bycatch in long-line and driftnet fisheries. Such mortality of adults has an effect on λ about ten-fold greater than an equivalent level of chick harvest. The sustainability of any combination of chick harvest and adult mortality depends on the resulting reduction in λ. We explored these results in relation to indices of sustainability, particularly the U.S. Marine Mammal Protection Act standards.

Prey, Pesticides, and Burrowing Owl Populations

We used population models to explore the effects of the organochlorine contaminant p,p’-DDE and fluctuations in vole availability on the population dynamics of burrowing owls (Athene cunicularia). Previous work indicated an interaction between low biomass of voles in the diet and moderate levels of p,p’-DDE in burrowing owl eggs that led to reproductive impairment. We constructed periodic and stochastic matrix models that incorporated three vole population states observed in the field: average, peak, and crash years. We modeled varying frequencies of vole crash years and a range of impairment of owl demographic rates in vole crash years. Vole availability had a greater impact on owl population growth rate than did reproductive impairment if vole populations peaked and crashed frequently. However, this difference disappeared as the frequency of vole crash years declined to once per decade. Fecundity, the demographic rate most affected by p,p’-DDE, had less impact on population growth rate than adult or juvenile survival. A life table response experiment of time-invariant matrices for average, peak, and crash vole conditions showed that low population growth under vole crash conditions was caused by low adult and juvenile survival rates, whereas the extremely high population growth under vole peak conditions was the result of increased fecundity. Our results suggest that even simple models can provide useful insights into complex ecological interactions. This is particularly valuable when temporal or spatial scales preclude manipulative experimental work in the field or laboratory.

The Links Between Energetics, Food Supply, Toxicants, and Demography in Marine Mammals

Food and toxicants often are bound to each other and have interacting effects on populations that consume them. To begin to disentangle these effects we are investigating coupled energy budget/pharmacokinetic/population models. In a first step, we have figured out how to construct a simple matrix population model from a dynamic energy budget model in a constant or seasonally variable environment. The matrix model accurately predicts asymptotic population dynamics for a wide range of parameter values and environmental conditions. The model captures some transients well, but more elaborate stage structure is necessary when the initial age distribution within stages is far from the stable age distribution.

In a second step, we have constructed a more elaborate supply-side dynamic energy budget model coupled with a pharmacokinetic model that accounts for the vertical transfer of toxicants. It is a compartmental model with two linked sub-models, one of which models the energetics, and the other models the pharmacokinetics of persistent lipophilic substances in a marine mammal. We are using the model to investigate the effects of energy availability and exposure to toxicants on the North Atlantic right whale.

Effects of Local Dynamics and Dispersal on Patchily Distributed Populations

Populations living in spatially structured environments are influenced by landscape structure (e.g., patch size and isolation), population dynamics within individual patches (e.g., survival and reproductive rates), and dispersal or movement among patches. We constructed and analyzed matrix projection models for four different landscape structures: a simple two-patch system, a linear array of patches, a source-sink system, and a system of patches of varying sizes separated by varying distances. Using these models we evaluated the effects of life history and dispersal patterns on the contribution of individual patches to population growth and structure of a metapopulation. In general, the patch with the highest local growth rate makes the greatest contribution to metapopulation growth rate through both demography and dispersal. More restrictive connection patterns preserve the metapopulation growth rate as dispersal increases but patch structure becomes skewed. Removing a single patch has little effect. As additional patches are removed the contribution of remaining patches to dynamics of the system becomes more even. Our results provide a general theoretical framework to study the effect of landscape structure on spatial population distribution and growth rate.

New Methods for Maximum Likelihood Estimation of Sensitivity and Elasticity Results From Mark-Recapture Data

Survival probability is of interest primarily as a component of population dynamics. Only when survival estimates are included in a demographic model are their population implications apparent. Survival describes the transition between living and dead. Biologically important as this transition is, it is only one of many transitions in the life cycle. Others include transitions between immature and mature, unmated and mated, breeding and nonbreeding, larva and adult, small and large, and location x and location y. The demographic consequences of these transitions can be captured by matrix population models, and such models provide a natural link connecting multistage mark-recapture methods and population dynamics. We have explored some of those connections at length, with examples taken from an ongoing analysis of the endangered North Atlantic right whale (Eubalaena glacialis). Formulating problems in terms of a matrix population model provides an easy way to compute the likelihood of capture histories. It extends the list of demographic parameters for which maximum likelihood estimates can be obtained to include population growth rate, the sensitivity and elasticity of population growth rate, the net reproductive rate, generation time, and measures of transient dynamics. In the future, multistage mark-recapture methods, linked to matrix population models, will become an increasingly important part of demography, with important applications in conservation biology.

New Methods To Estimate Survival and Transition Rates for Models With Unobservable States

Population dynamics of long-lived species are most strongly influenced by survival of mature individuals. Our ability to understand population dynamics is therefore greatly determined by our ability to estimate survival rates. For many long-lived species, survival may depend on the status of an individual (e.g., breeding or nonbreeding), which affects its exposure to both human-caused and natural stressors. However, status categories such as breeding or nonbreeding often lead to unobservable states that makes survival estimation more challenging. For example, in many seabird species nonbreeding birds do not attend the breeding colonies and, so, are not available for capture. Inclusion of unobservable states makes it more difficult, and in many cases impossible, to estimate some parameters. Constraints among parameters and/or over time are usually required to make all parameters in a model identifiable and thus interpretable. These constraints can provide interesting biological hypotheses. We are investigating which survival and transition parameters can be estimated for models with unobservable nonbreeding states. In particular, we are evaluating which parameters and parameter combinations can be estimated under different constraints and time-dependent assumptions. We are applying the method to three albatross species to examine how stressors affect different segments of the populations.

Response of a Threatened Plant to Flood and Precipitation Stress

Boltonia decurrens is an endangered plant restricted to the Illinois River Valley. Its life cycle, somewhat more complex than that of a typical winter annual, has evolved in response to the dynamics of the historic flood regime. We developed deterministic and stochastic matrix population models to explore the effects of the environment on Boltonia demography. We used periodic matrix models to incorporate intra-annual seasonal variation. We estimated parameters for all four combinations of early and late spring flood recession and high- and low-growing season precipitation and used these matrices to project population growth in a hypothetical constant environment. Late floods and/or low precipitation reduce λ. Early floods and high precipitation lead to explosive population growth. Elasticity analysis shows that changes in floods and precipitation alter the life-history pathways responsible for population growth, from annual to biennial and eventually perennial (clonal) pathways. We constructed and analyzed a stochastic model in which flood timing and precipitation vary independently, and computed the stochastic growth rate (log λs) and the variance growth rate (σ2) as functions of the frequency of late floods and low precipitation. We used historical data on floods and rainfall to estimate trends in these frequencies over the last 100 years. We found that log λs has declined as a result of hydrological changes accompanying the regulation of the river. Since the 1930s, when navigation dams and levees were completed, log λs has been negative. Stochastic elasticity analysis showed that, over that time, the contribution of annual life-history pathways to log λs has declined as the contributions of biennial and clonal pathways have increased. Over the same time period, σ2 has increased, in agreement with observations of large fluctuations in local B. decurrens populations. This is the first time that a stochastic model has been coupled with historical data on a stochastic environment. Undoubtedly, many plant and animal species evolved in concert with dynamic habitats and are now threatened by anthropogenic changes in those dynamics. The data and analyses used in this study can be applied to management and development strategies to preserve other dynamic systems.

Analyses of Populations Subject to Stress

In addition to our theoretical developments, we analyzed aspects of the response of a number of populations to single or multiple stresses. Some of these are described above, but here we list them for reference.

  • Effects of prey shortage and pesticides on the growth rate burrowing owl populations.
  • Effects of fire on dispersal, population growth, and spatial spread of the grass M. caerulea.
  • Effects of harvest and bycatch on population growth and sustainability of the sooty shearwater.
  • Effects of precipitation and flood stress on deterministic and stochastic population growth of the plant B. decurrens.
  • Effects of epidemics on the stochastic growth rate of the harbor seal.

Effects of human impacts (ship strikes, fishing gear entanglements) and food supply on the North Atlantic right whale.


Journal Articles on this Report : 19 Displayed | Download in RIS Format

Other project views: All 80 publications 23 publications in selected types All 20 journal articles
Type Citation Project Document Sources
Journal Article Caswell H, Lensink R, Neubert MG. Demography and dispersal: life table response experiments for invasion speed. Ecology 2003;84(8):1968-1978. R829089 (2003)
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  • Journal Article Caswell H, Fujiwara M. Beyond survival estimation: mark-recapture, matrix population models, and population dynamics. Animal Biodiversity and Conservation 2004;27(1):471-488. R829089 (2005)
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  • Journal Article Caswell H, Takada T. Elasticity analysis of density-dependent matrix population models:the invasion exponent and its substitutes. Theoretical Population Biology 2004;65(4):401-411. R829089 (2003)
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  • Journal Article Caswell H, Takada T, Hunter CM. Sensitivity analysis of equilibrium in density-dependent matrix population models. Ecology Letters 2004;7(5):380-387. R829089 (2003)
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  • Journal Article Caswell H, Neubert MG. Reactivity and transient dynamics of discrete-time ecological systems. Journal of Difference Equations and Applications 2005;11(4-5):295-310. R829089 (Final)
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    Journal Article Caswell H. Sensitivity analysis of the stochastic growth rate:three extensions. Australian & New Zealand Journal of Statistics 2005;47(1):75-85. R829089 (2003)
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  • Journal Article Fujiwara M, Anderson KE, Neubert MG, Caswell H. On the estimation of dispersal kernels from individual mark-recapture data. Environmental and Ecological Statistics 2006;13(2):183-197. R829089 (2005)
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  • Journal Article Gervais JA, Hunter CM, Anthony RG. Interactive effects of prey and p,p'-DDE on burrowing owl population dynamics. Ecological Applications 2006;16(2):666-677. R829089 (2005)
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  • Abstract: Ecological Applications
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  • Journal Article Harding KC, Harkonen T, Caswell H. The 2002 European seal plague:epidemiology and population consequences. Ecology Letters 2002;5(6):727-732. R829089 (2002)
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  • Journal Article Hunter CM, Caswell H. Selective harvest of sooty shearwater chicks: effects on population dynamics and sustainability. Journal of Animal Ecology 2005;74(4):589-600. R829089 (2003)
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  • Abstract: Wiley Interscience Abstract
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  • Journal Article Hunter CM, Caswell H. The use of the vec-permutation matrix in spatial matrix population models. Ecological Modelling 2005;188(1):15-21. R829089 (2003)
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  • Journal Article Jacquemyn H, Brys R, Neubert MG. Fire increases invasive spread of Molinia caerulea mainly through changes in demographic parameters. Ecological Applications 2005;15(6):2097-2108. R829089 (2005)
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  • Journal Article Kraus SD, Brown MW, Caswell H, Clark CW, Fujiwara M, Hamilton PK, Kenney RD, Knowlton AR, Landry S, Mayo CA, McLellan WA, Moore MJ, Nowacek DP, Pabst DA, Read AJ, Rolland RM. North Atlantic right whales in crisis. Science 2005;309(5734):561-562. R829089 (Final)
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  • Journal Article Lesnoff M, Ezanno P, Caswell H. Sensitivity analysis in periodic matrix models: a postscript to Caswell and Trevisan. Mathematical and Computer Modelling 2003;37(9-10):945-948. R829089 (2002)
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  • Journal Article Marvier M, Kareiva P, Neubert MG. Habitat destruction, fragmentation, and disturbance promote invasion by habitat generalists in a multispecies metapopulation. Risk Analysis 2004;24(4):869-878. R829089 (2002)
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  • Journal Article Neubert MG, Klepac P, van den Driessche P. Stabilizing dispersal delays in predator-prey metapopulation models. Theoretical Population Biology 2002;61(3):339-347. R829089 (2003)
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  • Journal Article Neubert MG. Marine reserves and optimal harvesting. Ecology Letters 2003;6(9):843-849. R829089 (2003)
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  • Other: Ecology Letters
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  • Journal Article Neubert MG, Parker IM. Projecting rates of spread for invasive species. Risk Analysis 2004;24(4):817-831. R829089 (2002)
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    Journal Article Smith M, Caswell H, Mettler-Cherry P. Stochastic flood and precipitation regimes and the population dynamics of a threatened floodplain plant. Ecological Applications 2005;15(3):1036-1052. R829089 (2003)
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    Supplemental Keywords:

    environmental monitoring, environmental statistics, mathematics, monitoring/modeling, exploratory research, environmental biology, wildlife, wildlife risk assessment, contaminants, demographic, demographic data, ecological exposure, multiple stressors, population, predicting risk, risk assessment, sensitive population, spatial demographic model, spatial distribution, stress effects on wildlife populations, stressor,, RFA, Scientific Discipline, Economic, Social, & Behavioral Science Research Program, Ecosystem Protection/Environmental Exposure & Risk, Ecosystem/Assessment/Indicators, exploratory research environmental biology, wildlife, Mathematics, Ecological Effects - Environmental Exposure & Risk, Monitoring/Modeling, Environmental Monitoring, Environmental Statistics, Ecological Risk Assessment, ecological exposure, predicting risk, spatial distribution, risk assessment, demographic, stressors, contaminants, demographic data, stress effects on wildlife populations, wildlife populations, multiple stressors, Wildlife Risk Assessment, spatial demographic model, sensitive population

    Progress and Final Reports:

    Original Abstract
  • 2002 Progress Report
  • 2003 Progress Report
  • 2004
  • 2005 Progress Report