Grantee Research Project Results
2006 Progress Report: Model Choice Stochasticity, and Ecological Complexity
EPA Grant Number: R829402C005Subproject: this is subproject number 005 , established and managed by the Center Director under grant R829402
(EPA does not fund or establish subprojects; EPA awards and manages the overall grant for this center).
Center: Solutions for Energy, AiR, Climate and Health Center (SEARCH)
Center Director: Bell, Michelle L.
Title: Model Choice Stochasticity, and Ecological Complexity
Investigators: Dwyer, Greg , Pfister, Cathy , Coram, Marc , Wang, Mei , Wootton, Timothy
Current Investigators: Dwyer, Greg , Elderd, Bret , Pfister, Cathy , Forester, James , Coram, Marc , Wang, Mei , Wootton, Timothy
Institution: University of Chicago
EPA Project Officer: Packard, Benjamin H
Project Period: March 12, 2002 through March 11, 2007
Project Period Covered by this Report: March 12, 2006 through March 11, 2007
RFA: Environmental Statistics Center (2001) RFA Text | Recipients Lists
Research Category: Environmental Statistics , Ecological Indicators/Assessment/Restoration , Human Health , Aquatic Ecosystems , Air
Objective:
To understand human-influenced systems, ecologists have increasingly relied upon mathematical models to describe processes ranging from population growth to ecosystem dynamics. Historically, most ecological models have been deterministic, and thus were of limited usefulness in environmental management. By focusing on incorporating stochasticity into ecological models, the ecology group has been developing methods for quantifying uncertainty and for examining how uncertainty in outcomes changes management decisions. For concreteness, each project focuses on particular organisms, but the models and methods that we are developing are of wide applicability.
Our projects fall into two categories: population growth and species interactions. The population growth project is in collaboration with EPA scientists Drs. Diane Nacci and Jason Grear at the Atlantic Ecology Division of the National Health and Environmental Effects Research Laboratory (NHEERL). During the upcoming year, we expect to build upon these collaborations with EPA. In fact, the collaboration with the Atlantic Ecology Division has produced a manuscript that is nearing submission (Grear and Elderd, in preparation). In addition to these collaborations, we will continue to submit articles to a wide variety of journals (see Publications), and our expectation is that the articles that are currently in review or in revision will be published.
Progress Summary:
Population Growth
In the population growth project, we are attempting to assess the impact of variation among individuals on population growth rates, by extending simple models and assessing their general usefulness. First, Principal Investigators Cathy Pfister and Mei Wang have been adapting population matrix models to account for variation among individuals. Matrix models are widely used in ecology and environmental management and are often helpful in quantifying the effects of pollutants on population growth rates. Such models, however, typically lump individuals into a small number of age or stage groups, which may bias estimates of population growth. Pfister and Wang (2005) have therefore developed a method of incorporating variability in growth rates among individuals into matrix population models. The usefulness of this method is that it allows for a major complication without greatly complicating the underlying model; in particular, the increase in the number of parameters that must be estimated is quite modest. Moreover, Mei Wang and a colleague have developed an algorithm that can be applied to this and related models to exhaustively categorize the different possible impacts that a given change in a life-history parameter can have on population growth rates (Sun and Wang, 2007).
An important issue in the use of matrix models, including in Pfister and Wang’s work, is the tradeoff between the higher realism afforded by more complex models and the smaller amount of data needed to parameterize less complex models. Indeed, one of the reasons why ages or stages in matrix models are often lumped together is that there are not enough data available to calculate survival rates or fecundities for more than a few age or stage classes. Models with lumped classes, known as partial life cycle (PLC) models, may thus be useful when data are lacking, even though their predictions are less accurate. To assess the relative importance of systematic error versus higher data requirements in such models, Bret Elderd, a former postdoctoral research associate with the Ecology Group, has been working with Jason Grear of the EPA to explore the usefulness of PLC models (Grear and Elderd, in preparation). PLC models are more likely to be useful if survivorship changes little over the course of an organism’s lifetime. If survivorship varies significantly over multiple age classes, the PLC approach can drastically overestimate or underestimate population growth rate, whether the model in question is deterministic or stochastic. To correct for this error in population growth rate, Grear and Elderd (in preparation) propose a simple solution based on the shape of the organism’s survivorship curve. The resulting approach can provide reasonable estimates of population growth, even when data are quite limited.
Elderd has also expanded the usefulness of matrix population models for analyzing experimental data through collaboration with Dr. Dan Doak at the University of California at Santa Cruz. Matrix models often figure in ecological experiments in the form of Life-Table Response Experiment (LTRE) analyses. LTRE analyses allow investigators to quantify the impact of experimental treatments on population growth in order to better understand how changes in life-history parameters—due, for example, to anthropogenic change—are likely to affect population growth. Most LTRE studies, however, use only single-factorial experiments and deterministic models. Elderd and Doak (2006) have extended this method to include nested multiple-factorial experiments, and they have shown how the method can incorporate stochastic models.
James Forester is collaborating with Dr. Andrea Graham (from the University of Edinburgh) and others to model the disease dynamics of rodent malaria (Plasmodium chabaudi chabaudi) as a predator-prey process within individual mice (Mus musculus). Understanding the factors that limit parasite population growth is important for developing improved methods of disease intervention that may be used to treat human infections. To this end, this group is trying to determine if the magnitude and timing of peak parasite density is limited by top-down (immune response), bottom-up (red blood cell limitation), or hybrid processes. They are using hierarchical Bayesian methods to confront population models with data and to explicitly characterize the uncertainty in estimated parameters. This project is still in the early analysis phase; however, preliminary models have proved very effective at capturing important characteristics of within-animal disease dynamics.
Pfister, Wang, and graduate students Ole Shelton and Li Ma (now at Stanford) are examining a long term fisheries dataset of Pacific herring (Clupea palasii) from southeastern Alaska. They are working to understand the bias associated with current survey techniques for herring populations and to develop techniques to improve the precision of population estimates. A second goal of this work is to fit dynamic models to 30 years of survey data to look for the signature of density-dependence and inter-annual environmental variation in mortality and growth rates. This research has direct implications for the management of herring fisheries.
Species Interactions
The work being carried out in the population-growth projects essentially assumes that interactions among species are weak. For many organisms, this assumption is a useful simplification, but for just as many or more, it is not. A second focus of our group thus lies in the development and application of models of species interactions, whether those interactions are between pairs or instead involve complex networks of many species. Our approach involves the incorporation of stochastic elements into species-interaction models in order to use data to estimate the likelihood of each model. In turn, the likelihood of each model will be used in a model-selection criterion in order to determine which model is the best. Our immediate goal is thus to develop methods by which ecologists and environmental managers can determine how complex a model is required to describe a given set of ecological interactions. Such assessments are almost always necessary, because typically we do not know which model is most appropriate. Model-selection criteria allow the investigator to rigorously identify the model that does the best job of describing the data and is thus the most appropriate description of the process. For example, in applications, researchers may have to choose between a model that includes differential effects of pollution on species interactions and one that does not. Our longer term goal is thus to provide models that can help us to predict how anthropogenic perturbations may influence communities and ecosystems.
Results to Date
Population Growth. As we have described, by incorporating variability among individuals into matrix population models, Pfister and Wang (2005) have developed a method of accounting for autocorrelation in growth among individuals. That is, in real populations, some individuals consistently grow more rapidly, while others grow more slowly, but such effects are typically ignored in matrix models (see Progress Summary/Accomplishments for the Population Growth project). An account of the mathematical details of this method can be found in a CISES technical report by Wang and Sun, which is also published in a peer-reviewed journal ( Sun and Wang, 2007). Drs. Nacci and Grear of EPA’s Atlantic Ecology Division recognized that the method could be used to examine the impact of pollution on the population demography of the common loon (Gavia immer), which is an indicator species for environmental health in the Northeast and Midwest. Dr. Grear has been contacting other EPA personnel in order to collect survival and fecundity estimates for the common loon. In addition, Dr. Grear has been collaborating with Dr. Elderd on another intriguing aspect of population demography. Specifically, Elderd and Grear have investigated the importance of stochasticity in correctly forecasting population growth using PLC models (see Progress Summary/Accomplishments for the Population Growth project ). Elderd has also developed a method for determining the impacts of nested experimental treatments on population growth by extending LTRE analysis to include nested components and stochasticity (Elderd and Doak, 2006). Each of these analyses represents a substantial contribution within the study of population ecology, and our hope is that each will find application in environmental management problems, especially those examining environmental stressors and ecosystem health.
Pfister and Wootton have co authored a paper with Dr. Handojo Kusumo (Kusumo, et al., 2006) in which they describe the small-scale population genetics of the sea palm (Postelsia palmaeformis). Genetic clustering analyses identified distinct populations that were separated by as little as 5 m. The results of this analysis suggest that the dispersal distances of sea palm spores are very short (1 – 3 m), and thus population dynamics are most likely driven by local phenomena, rather than long-distance dispersal events.
Graduate student Pauline Fujita is working with Dwyer and Coram to study the population genetics and population dynamics of the nucleopolyhedrosis virus (LdNPV), a pathogen associated with the gypsy moth (Lymantria dispar). Most mathematical models of host-pathogen coevolution assume that the populations under study are at ecological equilibrium; however, pathogens and their hosts can impose such strong selection pressure that evolutionary dynamics can occur on an ecological time frame. This group collected virus strains from L. dispar populations across the Midwest and sequenced loci across the LdNPV genome to quantify genetic variation with respect to host density and geographic location. They found varying levels of polymorphism at the loci surveyed, and surprisingly, most alleles were at intermediate frequencies in each population. They used data from all these loci to quantify the degree of spatial structuring among these natural populations and to estimate gene flow. Initial results suggest that viral gene flow is high enough to prevent strong spatial structure. Research is ongoing to determine if observed variation in levels of polymorphism are the result of selection imposed by host ecology.
Species Interactions. Work in the species interactions project has focused on: (1) disease dynamics; and (2) intertidal community dynamics. First, Bret Elderd, Vanja Dukic, and Greg Dwyer have developed a Bayesian framework for forecasting a disease’s rate of spread (Elderd, et al., 2006). The basis of this approach is to, first, construct prior distributions on each model parameter, using data from the literature on observations of infected individuals. Second, one uses maximum likelihood to fit the model to epidemic data. Finally, one combines the likelihood and the priors to calculate the joint posterior distribution of the parameters. This method allows researchers to combine data from multiple sources to predict future epidemics. Elderd, et al. (2006) used this approach to assess the effectiveness of different public health interventions for reducing the severity of epidemics of introduced diseases, notably those due to bioterrorist smallpox attacks.
Beyond its usefulness in public health, this approach can be of widespread usefulness in environmental management, because it allows a rigorous assessment of how uncertainty in a model’s parameter values is translated into uncertainty in the model’s predictions. One obstacle to direct application to wildlife diseases, however, is that the model does not allow for stochastic fluctuations in transmission rates. To address this problem, Elderd and Dwyer, in collaboration with Principal Investigator Marc Coram, have developed a stochastic epidemic model, as well as a method of fitting this model to epidemic data (Dwyer, et al., in preparation). In early work, the group assumed simply that the effects of stochasticity on transmission were due only to Gaussian white noise, representing the effects of random fluctuations due to weather. In nature, however, such fluctuations are likely to be auto correlated, as weather fronts move in and out of the region in which the epidemic is proceeding. Over the past year, the group has therefore extended the model so that transmission on any given day is an autoregressive process of order 1. A useful feature of the resulting model is that it combines classical autoregression with mechanistic differential equation models, thereby unifying two very different approaches to disease spread.
To fit the model to data, the group next generated many realizations of the model, calculated the likelihood of each realization under the assumption of Gaussian measurement errors, and maximized the average likelihood across realizations. A difficulty with this procedure, however, is that the likelihood is dominated by a small number of good-fitting realizations. To get around this problem, Coram has constructed an importance-sampling scheme, which permits a reduction in the variance of the likelihoods by preferentially sampling parameter values from regions of parameter space that provide better fits to the data. Scientists at EPA’s Western Ecology Division have expressed interest in the applicability of these models for other diseases of concern .
Tim Wootton’s research has been focusing on community dynamics and species interactions. During the past year, he used a long-term data set on intertidal communities to investigate an emerging ecological theory about community assemblage (i.e., Hubbell’s neutral theory). This study tested for the effects of variation in species and their interactions on community composition (Wootton, 2005). As such, it is the first empirical analysis of the neutral theory of community assembly, and it demonstrates the need for understanding species interactions in describing community dynamics. Dr. Wootton has also been active in research regarding Lyme disease dynamics and rates of human infection (Tsao, et al., 2004). This work has shown that vaccinating mice—a primary reservoir for this disease—reduces disease incidence among mice. Similar ideas can also be readily applied to other diseases of concern where no human vaccine exists.
James Forester is working with Tim Wootton, Greg Dwyer, and Marc Coram to identify direct and indirect species interactions in intertidal communities using observational time series of fixed quadrats (Forester, et al., in preparation). These data are particularly challenging to work with because they are percent- cover (therefore bounded between 0 and 100) and exhibit variability that changes as a function of the density of the dominant mussel species (Mytilus californianus). This density-dependent stochasticity is of biological interest because it represents variability in immigration at low densities of M. californianus and increased susceptibility to wave disturbances at higher densities. The group has modeled this system as a series of linked, non-linear betabinomial mixture models that describe the system dynamics and identify how species interactions change through time. Initial results indicate that these models successfully capture the density-dependent stochasticity and provide some insights into the species- interaction strengths.
Future Activities:
Population Growth
Future work in the population growth group will continue to explore how variation among individuals is quantitatively described, and how it relates to extinction risk and viability in populations. In particular, Pfister and Wang have come to realize that continued progress is likely to require an accounting of the relative roles of genetic versus environmental factors in the performance of individuals and the viability of populations. Again using data from coastal marine populations, they will continue to develop general models that seek to predict the trajectories of these populations with the least complexity necessary. Pfister and Wang will continue working with Ole Shelton, a graduate student in the Department of Ecology and Evolution at the University of Chicago, to analyze census data of the Alaskan herring population and spawning counts. James Forester will also be collaborating with Cathy Pfister and other CISES researchers to develop new methods of animal movement modeling and will explore how individual variation in movement behavior can affect broad-scale population dynamics. In addition, Forester will continue working on the malaria population model, with results expected in the next quarter.
Species Interactions
The intertidal community dynamics group is working to link single-species betabinomial models using a hierarchical Bayesian approach. The ultimate goal of this work is to develop a general modeling framework in which time series of percent-cover data can be easily analyzed to identify interactions among species and density-dependent stochasticity. Such a framework could be applied to terrestrial systems in the context of small-scale vegetation plots or broad-scale GIS analyses (e.g., monitoring the change in abundance of land-cover types through time).
An important future direction for the disease-dynamics group is to extend the stochastic host-pathogen model. As we have described, a useful feature of the model is that it incorporates an autoregressive model into a differential equation model. Because the underlying assumption is that the stochasticity is due to weather effects on disease transmission rates, the next step is to extend the autoregressive model to include weather covariates, such as temperature or rainfall. The group then plans to fit the resulting model to Dwyer’s data on a fungal pathogen of insects, which is very sensitive to rainfall. Over the longer term, the group hopes to use the model to understand data on wasting disease in white-tailed deer, as suggested by Drs. Fairbrother and Orme-Zavaleta of EPA’s Western Ecology Division. Also, the group plans to further develop the methods used in Elderd, et al. (2006) to consider the importance of spatial correlation between disease outbreaks and rates of spread within populations (Elderd, et al., in preparation).
Journal Articles on this Report : 8 Displayed | Download in RIS Format
Other subproject views: | All 14 publications | 13 publications in selected types | All 12 journal articles |
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Other center views: | All 120 publications | 74 publications in selected types | All 52 journal articles |
Type | Citation | ||
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Dwyer G, Morris WF. Resource-dependent dispersal and the speed of biological invasions. The American Naturalist 2006;167(2):165-176. |
R829402 (Final) R829402C005 (2006) R829402C005 (Final) |
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Elderd BD, Doak DF. Comparing the direct and community-mediated effects of disturbance on plant population dynamics:flooding, herbivory, and Mimulus guttatus. Journal of Ecology 2006;94(3):656-669. |
R829402 (Final) R829402C005 (2004) R829402C005 (2006) R829402C005 (Final) |
Exit Exit Exit |
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Elderd BD, Dukic VM, Dwyer G. Uncertainty in predictions of disease spread and public health responses to bioterrorism and emerging diseases. Proceedings of the National Academy of Sciences of the United States of America 2006;103(42):15693-15697. |
R829402 (Final) R829402C005 (2004) R829402C005 (2006) R829402C005 (Final) |
Exit Exit Exit |
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Kusumo HT, Pfister CA, Wootton JT. Small-scale genetic structure in the sea palm Postelsia palmaeformis Ruprecht (Phaeophyceae). Marine Biology 2006;149(4):731-742. |
R829402C005 (2006) |
Exit Exit |
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Pfister CA, Wang M. Beyond size: matrix projection models for populations where size is an incomplete descriptor. Ecology 2005;86(10):2673-2683. |
R829402 (Final) R829402C005 (2004) R829402C005 (2006) R829402C005 (Final) |
Exit Exit |
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Sun L, Wang M. An algorithm for a decomposition of weighted digraphs: with applications to life cycle analysis in ecology. Journal of Mathematical Biology 2007;54(2):199-226. |
R829402 (Final) R829402C005 (2004) R829402C005 (2006) R829402C005 (Final) |
Exit Exit |
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Tsao JI, Wootton JT, Bunikis J, Luna MG, Fish D, Barbour AG. An ecological approach to preventing human infection: vaccinating wild mouse reservoirs intervenes in the Lyme disease cycle. Proceedings of the National Academy of Sciences of the United States of America 2004;101(52):18159-18164. |
R829402 (Final) R829402C005 (2006) R829402C005 (Final) |
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Wootton JT. Field parameterization and experimental test of the neutral theory of biodiversity. Nature 2005;433(7023):309-312. |
R829402 (Final) R829402C005 (2006) R829402C005 (Final) |
Exit Exit |
Supplemental Keywords:
RFA, Scientific Discipline, Health, Economic, Social, & Behavioral Science Research Program, PHYSICAL ASPECTS, Air, Geographic Area, Ecosystem Protection/Environmental Exposure & Risk, Applied Math & Statistics, particulate matter, Health Risk Assessment, Ecosystem/Assessment/Indicators, Ecological Effects - Environmental Exposure & Risk, Monitoring/Modeling, Risk Assessments, Environmental Monitoring, Ecological Effects - Human Health, Physical Processes, Ecological Risk Assessment, Environmental Statistics, Environmental Engineering, Engineering, Chemistry, & Physics, Ecological Indicators, EPA Region, particulates, risk assessment, ecological effects, monitoring, health risk analysis, watersheds, emissions monitoring, ecological health, ozone , particulate, stratospheric ozone, ozone, sediment transport, computer models, exposure, air pollution, chemical transport modeling, chemical transport, trend monitoring, statistical models, human exposure, ecological risk, water, ecosystem health, environmental indicators, PM, ecological models, chemical transport models, Region 5, data models, air quality, statistical methodology, human health risk, stochastic modelsRelevant Websites:
http://galton.uchicago.edu/~cises/ Exit
Progress and Final Reports:
Original AbstractMain Center Abstract and Reports:
R829402 Solutions for Energy, AiR, Climate and Health Center (SEARCH) Subprojects under this Center: (EPA does not fund or establish subprojects; EPA awards and manages the overall grant for this center).
R829402C001 Detection of a Recovery in Stratospheric and Total Ozone
R829402C002 Integrating Numerical Models and Monitoring Data
R829402C003 Air Quality and Reported Asthma Incidence in Illinois
R829402C004 Quasi-Experimental Evidence on How Airborne Particulates Affect Human Health
R829402C005 Model Choice Stochasticity, and Ecological Complexity
R829402C006 Statistical Approaches to Detection and Downscaling of Climate Variability and Change
The 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.
Project Research Results
12 journal articles for this subproject
Main Center: R829402
120 publications for this center
52 journal articles for this center