Discrete-Time Population Models: The Combined Effects of Dispersal and Stage Structure

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9527400 Caswell Dispersal is a fundamental process in population ecology. Mathematical models of population growth that include dispersal have helped scientists to address such important ecological, economic, and public health issues as habitat fragmentation, invasions of exotic species, and the spread of epidemics. The life history of individuals also has important demographic consequences. Vital rates (i.e., birth, growth, development, and mortality rates) change throughout an individual's life. Mathematical models that incorporate age- or size-dependent vital rates are among the most important tools for studying the evolution of life histories and for protecting endangered species. This project will develop and analyze models that incorporate both dispersal and population structure in a simple modeling framework based upon integrodifference equations (IDE's). IDE's have a number of advantages: (1) rather than using a standard diffusion approximation, IDE's can model a variety of dispersal mechanisms; (2) as discrete-time equations, IDE's link naturally to matrix population models and (3) IDE's connect easily with data because their central component, the dispersal distribution, lends itself to empirical measurement. The investigators' analyses of these models will focus on the interaction of stage-specific dispersal and stage-specific vital rates. They will combine mathematical analysis and numerical simulation. The results will be useful in population ecology, evolutionary biology, conservation biology, and biological control.