Stochastic Processes with Applications to Ecology and Theoretical Population Genetics

小行星9703694诺伊豪泽 这些项目分为两个主要研究领域，相互作用粒子系统背景下的生态模型的理论研究，以及理论种群遗传学中的谱系过程。相互作用的粒子系统是整数格上的连续时间马尔可夫过程，其中每个点处于几个状态之一。局部规则决定了系统的动态。它们提供了一个理想的框架来研究生态学模型中空间结构的作用。在与Stephen Pacala博士（普林斯顿大学）的联合工作中，首席研究员将考虑生态学经典模型中空间结构的后果，例如种间竞争的Lotka-Volterra模型。非空间的版本非常好理解。包括空间成分可能会产生新的现象。在与Stephen Krone博士（爱达荷州大学）的联合工作中，首席研究员将通过在随机环境中使用二维接触过程来研究种群在异质环境中的传播。在理论群体遗传学方面，诺伊豪泽博士计划研究各种选择方案下的系谱，例如，频率依赖选择和超显性选择。计划严格推导系谱，并使用它们来调查空间和非空间环境中的样本属性。 空间结构的原因和影响一直是种群和群落生态学的中心议题。首席研究员将与Stephen Pacala博士（普林斯顿大学）共同研究竞争对社区空间结构的影响。空间群落中的局部相互作用和竞争可能导致同一物种的个体聚集，从而导致生物多样性的减少。在与斯蒂芬·克朗博士（爱达荷州大学）的联合工作中，首席研究员将考虑种群在异质环境中的传播，以及破坏和随后的恢复如何影响种群恢复的能力。系谱学是群体遗传学中研究基因样本性质的重要工具。诺伊豪泽博士计划研究频率依赖和超显性选择。已知这两种选择模式都能够保持高度的遗传多样性。在这种选择方案下的系谱，例如在植物育种系统或主要组织相容性复合体中是很重要的，人们对此知之甚少。

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.