2005 Progress Report: Spatial Demographic Models for the Study of Stress Effects on Wildlife Populations
EPA Grant Number: R829089Title: 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 Period Covered by this Report: December 17, 2004 through December 16, 2005
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 objectives of this research project include the development and analysis of models for the dynamics of spatially distributed populations in different kinds of landscapes: (1) patchy populations; (2) populations distributed across a continuous landscape; and (3) including both deterministic and stochastic, linear (densityindependent), and nonlinear (densitydependent) situations.
Progress Summary:
Work on the project during this period has been successful and productive. During the last 2 years numerous manuscripts have been completed, and results have been presented at several international conferences.
We have made progress on both these goals; the following is a list of accomplishments during the reporting period.
New Developments in 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 lifehistory 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 timeaveraged 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 environmentspecific 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 populationlevel effects of stress in stochastic environments.
The Sensitivity of the Invasion Exponent and Population Size in Nonequilibrium, DensityDependent 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 equilibriumstage densities. The weights measure the effect of the stage on densitydependence and the effect of the densitydependence 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 MarkRecapture Data on Animals
We have developed a new method for estimating a distribution of dispersal displacements (a dispersal kernel) from markrecapture 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 markrecapture 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.
New Advances in Perturbation Analysis
The use of perturbation analysis is fundamental to our approach to the populationlevel consequences of stressors. We are currently writing up results on several new developments in this area. (1) The sensitivity of transient (shortterm) dynamics in constant, timevarying, and densitydependent environments. Transient dynamics are expected to be particularly important parts of population response to shortterm stress events. (2) The sensitivity of equilibrium or cyclic population density in densitydependent models. (3) The sensitivity of extinction probability in models (multitype branching process models) including demographic stochasticity for very small populations. In each of these cases, the theory we have derived is readily applicable to real demographic data, and we are presenting examples from both animal and plant populations.
Invasion Wave Speed in Periodic and Stochastic Environments
A population invading an unoccupied environment (spatially homogenous, timeinvariant, 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 been extending our earlier results supported by this project by considering environments that vary in time. In our last report, we were working on models for environments characterized by periodic (e.g., seasonal) variation. However, we were able to generalize this approach further and have now obtained the theory for both periodically and stochastically varying environments. Stochastic invasions can be linked to explicitly stochastic models for environmental processes (fires, floods, prey availability, etc.). We are writing up these results, using data on plants subject to fire to determine the effect of fire regimes on invasion processes.
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 onethird 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 (19972000). 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 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.
New Understanding of the Connection Between Energy Budgets and Demography
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 supplyside 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 submodels, 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 Population Dynamics of 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 twopatch system, a linear array of patches, a sourcesink 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.
Development of Methods for Maximum Likelihood Estimation of Sensitivity and Elasticity Results From MarkRecapture 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 markrecapture 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 markrecapture methods, linked to matrix population models, will become an increasingly important part of demography, with important applications in conservation biology.
Development of Methods To Estimate Survival and Transition Rates for Models With Unobserveable States
Population dynamics of longlived 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 longlived species survival may depend on the status of an individual (e.g., breeding or nonbreeding), which affects its exposure to both humancaused and natural stressors. However, status categories such as breeding or nonbreeding often lead to unobservable states that make 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 timedependent assumptions. We are applying the method to three albatross species to examine how stressors affect different segments of the populations.
Future Activities:
Planned activities for the next reporting period include: (1) completion of analysis of stochastic integrodifference equation models and writing results; (2) completion of results on perturbation analysis and writing results; (3) completion of results on coupled dynamic energy budget/pharmacokinetic models and writing results; and (4) presentation of our results at several meetings.
Journal Articles on this Report : 18 Displayed  Download in RIS Format
Other project views:  All 80 publications  23 publications in selected types  All 20 journal articles 

Type  Citation  


Caswell H, Lensink R, Neubert MG. Demography and dispersal: life table response experiments for invasion speed. Ecology 2003;84(8):19681978. 
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Caswell H, Fujiwara M. Beyond survival estimation: markrecapture, matrix population models, and population dynamics. Animal Biodiversity and Conservation 2004;27(1):471488. 
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Caswell H, Takada T. Elasticity analysis of densitydependent matrix population models:the invasion exponent and its substitutes. Theoretical Population Biology 2004;65(4):401411. 
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Caswell H, Takada T, Hunter CM. Sensitivity analysis of equilibrium in densitydependent matrix population models. Ecology Letters 2004;7(5):380387. 
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Caswell H. Sensitivity analysis of the stochastic growth rate:three extensions. Australian & New Zealand Journal of Statistics 2005;47(1):7585. 
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Fujiwara M, Anderson KE, Neubert MG, Caswell H. On the estimation of dispersal kernels from individual markrecapture data. Environmental and Ecological Statistics 2006;13(2):183197. 
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Gervais JA, Hunter CM, Anthony RG. Interactive effects of prey and p,p'DDE on burrowing owl population dynamics. Ecological Applications 2006;16(2):666677. 
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Harding KC, Harkonen T, Caswell H. The 2002 European seal plague:epidemiology and population consequences. Ecology Letters 2002;5(6):727732. 
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Hunter CM, Caswell H. Selective harvest of sooty shearwater chicks: effects on population dynamics and sustainability. Journal of Animal Ecology 2005;74(4):589600. 
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Hunter CM, Caswell H. The use of the vecpermutation matrix in spatial matrix population models. Ecological Modelling 2005;188(1):1521. 
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Jacquemyn H, Brys R, Neubert MG. Fire increases invasive spread of Molinia caerulea mainly through changes in demographic parameters. Ecological Applications 2005;15(6):20972108. 
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Klanjscek T, Caswell H, Neubert MG, Nisbet RM. Integrating dynamic energy budgets into matrix population models. Ecological Modelling 2006;196(34):407420. 
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Lesnoff M, Ezanno P, Caswell H. Sensitivity analysis in periodic matrix models: a postscript to Caswell and Trevisan. Mathematical and Computer Modelling 2003;37(910):945948. 
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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):869878. 
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Neubert MG, Klepac P, van den Driessche P. Stabilizing dispersal delays in predatorprey metapopulation models. Theoretical Population Biology 2002;61(3):339347. 
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Neubert MG. Marine reserves and optimal harvesting. Ecology Letters 2003;6(9):843849. 
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Neubert MG, Parker IM. Projecting rates of spread for invasive species. Risk Analysis 2004;24(4):817831. 
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Smith M, Caswell H, MettlerCherry P. Stochastic flood and precipitation regimes and the population dynamics of a threatened floodplain plant. Ecological Applications 2005;15(3):10361052. 
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Supplemental Keywords:
matrix population models, integrodifference equation models, invasion wave speed, LTRE analysis, sensitivity analysis, elasticity analysis, marine protected areas,, 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