Stochastic Processes in Ecology and Population Genetics

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0072262Neuhauser This research of Dr. Neuhauser covers three areas: (1) community ecology, (2) evolutionary ecology, and (3) population genetics. Mathematical tools will be developed to address questions of (i) the causes and effects of spatial structure on plant communities, in particular the question of how explicit space affects diversity and stability of plant communities; (ii) the evolution of resistance to insecticide and the spread of resistant alleles, in particular for a genetically engineered crop that expresses chemicals that are toxic to its insect pests; (iii) how mating structure affects spatial structuring in gynodioecious plants; and (iv) how temporal variability affects genealogies. The spatial processes will be modeled using the framework of interacting particle systems, which are continuous time Markov processes on the infinite D dimensional lattice, characterized by local interactions between sites. The genealogical processes will be investigated using the ancestral selection graph as a modeling framework. The motivation for the proposed research is to gain a better understanding of how spatial and temporal factors affect the outcome of interactions in plant communities. Most of ecological and agricultural modeling traditionally did not take into account effects of explicit space due to the difficulties encountered in the analysis of such models. More recently, tools have been developed that allow rigorous analysis of spatial models. This research of Dr. Neuhauser is intended to shed light on how space affects plant communities; this is important in understanding the structure of both natural and managed (agricultural) communities. Her results should help devise management strategies for maintaining biodiversity in natural communities and for slowing the spread of resistance genes in crop systems of genetically engineered crop.