Problems in Probability Motivated by Questions in Ecology

由生态学问题引发的概率问题

• 批准号: 9877066
• 负责人: Richard Durrett
• 金额: $ 20.64万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-07-01 至 2002-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9877066&HistoricalAwards=false
• 关键词: Problems; Probability; Motivated; Questions; Ecology

9877066This investigator will study a number of questions that arise from ecology. An important direction of the research will be to prove general results in support of the picture advocated by Durrett and Levin (1994): the behavior of stochastic spatial models can be predicted from that of the mean field ODE obtained by pretending all sites are always independent. He will also continue work on hybrid zones, progressing now to the derivation of PDE limits for these systems as selection tends to 0, and the study of spatially inhomogeneous models to understand the structure of mosaic hybrid zones that have been seen in field work on the cricket species Gryllus firmus and G. pennsylvanicus. Other projects include understanding limits to diversity by analyzing Tilman's competition model on a finite grid, studying the asymptotic behavior of an evolutionary arms race, and demonstrating the existence of chaotic oscillations in a simple discrete time model of gypsy moth populations.The basic question that drives this research is: when does the spatial distribution of individuals change the behavior of a biological system? The comparison is made to a homogeneously mixing system in which each individual interacts equally with all the others. In the past five years the investigator and his collaborators have developed some rules for predicting the answer to this question and have applied them to a variety of biological systems. In the next three years they will apply this theory to some new examples. One of the most important questions they will study is: What are the limits to diversity? They will address this question mathematically by investigating the number of species that can coexist in a stochastic competition model. Other questions will concern the fluctuations of the size of gypsy moth populations and the structure of hybrid zones that result from spatially varying selection.

9877066这位研究者将研究生态学中出现的一些问题。 研究的一个重要方向将是证明支持Durrett和Levin（1994）主张的图像的一般性结果：随机空间模型的行为可以从假设所有站点总是独立的平均场ODE的行为来预测。 他还将继续研究杂交区，现在正在推导这些系统的偏微分方程极限，因为选择趋于0，并研究空间不均匀模型，以了解在蟋蟀物种Gryllus firmus和G. pennsylvania icus。 其他项目包括通过在有限网格上分析Tilman的竞争模型来理解多样性的限制，研究进化军备竞赛的渐近行为，以及证明在一个简单的离散时间模型中存在混沌振荡的舞毒蛾种群。驱动这项研究的基本问题是：个体的空间分布何时改变生物系统的行为？ 与均匀混合系统进行比较，其中每个个体与所有其他个体平等地相互作用。 在过去的五年里，研究人员和他的合作者已经开发出一些规则来预测这个问题的答案，并将其应用于各种生物系统。 在接下来的三年里，他们将把这一理论应用到一些新的例子中。他们将研究的最重要的问题之一是：多样性的极限是什么？ 他们将通过研究在随机竞争模型中可以共存的物种数量来解决这个问题。 其他问题将涉及舞毒蛾种群的大小和结构的混合区，从空间上不同的选择结果的波动。