Stochastic Processes with Applications to Ecology and Theoretical Population Genetics

点击翻译按钮获取中文摘要

9703694 Neuhauser The projects are divided into two primary research areas, the theoretical investigation of ecological models in the context of interacting particle systems, and genealogical processes in theoretical population genetics. Interacting particle systems are continuous time Markov processes on the integer lattice in which each site is in one of several states. Local rules determine the dynamics of the systems. They provide an ideal framework to investigate the role of the spatial structure in models in ecology. In joint work with Dr. Stephen Pacala (Princeton University) the principal investigator will consider the consequences of spatial structure in classical models in ecology, such as the Lotka-Volterra model of interspecific competition. The nonspatial version is very well understood. Including a spatial component will likely yield new phenomena. In joint work with Dr. Stephen Krone (University of Idaho) the principal investigator will study the spread of a population in a heterogeneous environment by using the two-dimensional contact process in a random environment. In theoretical population genetics, Dr. Neuhauser plans to study genealogies under various selection schemes, for instance, frequency-dependent selection and overdominant selection. It is planned to rigorously derive genealogies and to use them to investigate sample properties in both spatial and nonspatial settings. The causes and effects of spatial structure have long been central topics in population and community ecology. In joint work with Dr. Stephen Pacala (Princeton University) the principal investigator will study the effects of competition on the spatial structure of communities. Local interactions and competition in spatial communities can cause clumping of individuals of the same species which can lead to a reduction in biodiversity. In joint work with Dr. Stephen Krone (University of Idaho) the principal investigator will consider the spread of populations in heterogeneous environments and how habi tat destruction and subsequent restoration affects the ability of populations to recover. Genealogies are an important tool in population genetics to investigate properties of samples of genes. Dr. Neuhauser plans to investigate frequency-dependent and overdominant selection. Both modes of selection are known to be able to maintain a high degree of genetic diversity. Little is known about genealogies under such selection schemes which are important, for instance, in plant breeding systems or in the major histocompatibility complex.