9419716 Abrams This project will use mathematical models of food webs to explore the interactions between changes in population densities and changes in the traits that determine individuals' feeding and anti-predator characteristics. It builds on a previous project that explored the population dynamical effects of rapid behavioral adaptation and developed a simple method of approximately modeling the dynamics of quantitative traits. The present project is centered on an analysis of the dynamics of simple food webs in which one or more species is characterized by feeding and/or predator-avoidance traits that change adaptively over time. Most of the food webs to be studies consist of groups of two to six species. Two different models of trait dynamics will be explored to reveal differences between traits whose distribution has a relatively inflexible shape and those whose distribution can have any shape within the bounds of possible trait values. The analysis of these models, and their extensions, will advance our understanding of several problem areas ecology. Extensions of the basic models will examine the dynamic consequences of species having two or more modes of adaptive change in trait values, and will explore how the results of these simple models are changed by spatially subdivided environments or more complex population structures, such as size and/or age classes. %%% This mathematical theory will provide a basis for predicting long-term changes in the populations of species in ecological communities. Such long-term changes are almost always affected by natural selection, which is absent from almost all ecological models. By working out the potential consequences of adaptive change for community dynamics, this analysis of simple models will provide a guide to what types of adaptively flexible traits empirical community ecologists need to study.
