Discrete-Time Population Models: The Combined Effects of Dispersal and Stage Structure

9527400卡斯威尔扩散是种群生态学中的一个基本过程。包括扩散在内的人口增长数学模型帮助科学家解决了栖息地碎片化、外来物种入侵和流行病传播等重要的生态、经济和公共卫生问题。个人的生活史也会对人口统计学产生重要影响。生命率(即出生、生长、发育和死亡率)在一个人的一生中都会发生变化。包含与年龄或大小相关的生命率的数学模型是研究生活史演变和保护濒危物种的最重要工具之一。该项目将在一个基于积分差分方程组(IDE‘s)的简单建模框架中开发和分析同时包含扩散和种群结构的模型。IDE有许多优点：(1)IDE不是使用标准的扩散近似，而是可以模拟各种扩散机制；(2)作为离散时间方程，IDE自然地与矩阵总体模型相联系；(3)IDE很容易与数据连接，因为其中心成分--扩散分布--适合于经验测量。研究人员对这些模型的分析将重点放在特定阶段的驱散和特定阶段的生命率之间的相互作用。他们将把数学分析和数值模拟结合起来。研究结果将在种群生态学、进化生物学、保护生物学和生物防治中发挥重要作用。

9527400 Caswell Dispersal is a fundamental process in population ecology. Mathematical models of population growth that include dispersal have helped scientists to address such important ecological, economic, and public health issues as habitat fragmentation, invasions of exotic species, and the spread of epidemics. The life history of individuals also has important demographic consequences. Vital rates (i.e., birth, growth, development, and mortality rates) change throughout an individual's life. Mathematical models that incorporate age- or size-dependent vital rates are among the most important tools for studying the evolution of life histories and for protecting endangered species. This project will develop and analyze models that incorporate both dispersal and population structure in a simple modeling framework based upon integrodifference equations (IDE's). IDE's have a number of advantages: (1) rather than using a standard diffusion approximation, IDE's can model a variety of dispersal mechanisms; (2) as discrete-time equations, IDE's link naturally to matrix population models and (3) IDE's connect easily with data because their central component, the dispersal distribution, lends itself to empirical measurement. The investigators' analyses of these models will focus on the interaction of stage-specific dispersal and stage-specific vital rates. They will combine mathematical analysis and numerical simulation. The results will be useful in population ecology, evolutionary biology, conservation biology, and biological control.