Population models provide estimates of such important quantities as population growth rate, short- and long-term population dynamics, population structure, and extinction risk. In all these cases, it is important to evaluate the sensitivity of model results to changes in parameters, such as rates of birth, growth, death, and movement. Such changes can result from environmental change, evolutionary change, management actions, or revised estimates from new data. This project will produce new mathematical tools for the sensitivity analysis of nonlinear population models. The results will be developed using matrix calculus, and will be applied to spatial models, epidemic models, harvest models, and models for breeding and pair formation.
Sensitivity analysis is significant to several areas of population biology. In evolutionary biology, sensitivity analysis shows the fitness consequences of changes in life histories. In population management (including the conservation of threatened species, the control of pests, and the harvest of resources) it is used to evaluate the effects of management strategies. The mathematical methods developed here will also be of value in many other areas of ecology. The project will have broader impacts through educational outreach, advice to government agencies concerned with population management, and training of a post-doctoral researcher.
The goal of this study was to develop new mathematical tools for sensitivity analysis in ecology. When ecologists study populations, communities, and ecosystems, they almost always begin by measuring the values of some parameters, and then calculate the implications of these parameters. They might, for example, measure reproductive rates and calculate the effects on population growth, or measure environmental temperature and calculate the effects on extinction probability. The parameters, of course, do not remain constant; they change for many reasons. The changes may be due to natural processes, or due to human actions, either intentional (e.g., conservation actions or pest control strategies) or unintentional (e.g., pollution or habitat destruction). Parameters also change due to the action of natural selection, and because of improvements in statistical estimation or accumulation of more data. Sensitivity analysis calculates the effects of such changes in parameters. The measured parameters serve as a baseline against which to evaluate the effects of change, and this study provided new mathematical analyses to do so. It focused on 8 different kinds of ecological models: density-dependent models for populations limited by resources, two-sex models for populations limited by the availability of mates, stochastic models for the effect of random environmental fluctuations, spatial models for ecological invasions, epidemic models for populations subject to infection, food web models for communities of interacting consumers and resources, Markov chain models for survival and health status, and periodic models for seasonal variation. New mathematical methods were developed for the sensitivity analysis of each of these types of models. In the course of the study, new analytical methods were also applied to a number of ecologically important cases. The effects of climate change on polar bear populations in the southern Beaufort Sea were analyzed by connecting population models to the predictions of climate models developed by the IPCC. A similar, but more detailed analysis was applied to emperor penguins in Terre Adelie, Antarctica. In both cases, the best available predictions of future climate conditions imply crashes of the population within the next century, due to reductions in sea ice. An analysis of the Verreaux's sifaka (a dramatically colored lemur from Madagascar) revealed how its populations respond to changing rainfall conditions. An analysis of garlic mustard, an introduced invasive plant that is a pest in forests of eastern North America, showed how management strategies, interacting with seasonal growth patterns, might help to control the species. Outreach activities to broaden the impacts of this project included workshops and intensive courses, presented both nationally and internationally. Because the results of this research were inherently highly mathematical, educational efforts were critical to make the new tools accessible to a wide range of scientists, both within and outside of ecology. Educational activities included workshops at the Ecological Society of America, the International Max Planck Research School of Demography (Germany), and the European Doctoral School of Demography, and participating in the training of undergraduate and graduate students and postdoctoral investigators.
