Stochastic Processes in Ecology and Population Genetics

Neuhauser博士的这项研究涵盖三个领域：(1)群落生态学，(2)进化生态学，(3)种群遗传学。将开发数学工具来解决下列问题：(1)空间结构对植物群落的原因和影响，特别是明确的空间如何影响植物群落的多样性和稳定性；(2)抗药性的演变和抗药性等位基因的传播，特别是对于表达对害虫有毒的化学物质的转基因作物；(3)交配结构如何影响雌雄异株植物的空间结构；(4)时间变异性如何影响系谱。空间过程将使用相互作用粒子系统的框架来模拟，该相互作用粒子系统是无限维格子上的连续时间马尔可夫过程，其特征是站点之间的局部相互作用。将使用祖先选择图作为建模框架来研究谱系过程。提出这项研究的动机是为了更好地了解空间和时间因素如何影响植物群落中相互作用的结果。由于在分析这类模型时遇到的困难，大多数生态和农业模型传统上没有考虑显式空间的影响。最近，已经开发了一些工具，可以对空间模型进行严格的分析。Neuhauser博士的这项研究旨在阐明空间如何影响植物群落；这对于理解自然和管理(农业)群落的结构都很重要。她的结果应该有助于制定管理策略，以维持自然群落的生物多样性，并减缓抗性基因在转基因作物作物系统中的传播。

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.