Mathematical Models of Dynamics and Evolution in Structured Populations

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The observed changes and evolution of natural populations are closely influenced by the life history of the organisms involved, and their responses to environmental change. Environments can drive temporal changes in the rates of vital events such as birth, death and growth. They can also result in resource limitations that reveal themselves in density-dependent population responses. This proposal aims to explore the consequences of both of these kinds of environmental effects for dynamics and evolution. One direction of study is the analysis of changing environments as they affect the rate at which organisms develop, and the distribution of reproduction over the lifespan of organisms, with special attention to repeated reproduction and developmental delays. This will be the first systematic analysis of the effect of environmental pattern on the evolution of complex life cycles, and will also explore the relationship between population growth and the components of the life cycle, when the environment is changing unpredictably over time. A second direction of study focuses on resource limitation and density effects in shaping the dynamics of population change; in particular, the ways in which such effects can drive cyclical change in population numbers and composition. These effects have been studied in experimental populations, and the theory will be applied to these data.