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

离散时间种群模型：扩散和阶段结构的综合影响

• 批准号: 9527400
• 负责人: Hal Caswell
• 金额: $ 28万
• 依托单位: Woods Hole Oceanographic Institution
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 2000-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9527400&HistoricalAwards=false
• 关键词: Discrete; Time; Population; Models; Combined

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.

[9527400] Caswell扩散是种群生态学的基本过程。包括扩散在内的人口增长的数学模型帮助科学家解决了诸如栖息地破碎、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。个人的生活史也有重要的人口统计结果。生命率（即出生、生长、发育和死亡率）在人的一生中都是变化的。包含年龄或体型依赖的生命率的数学模型是研究生命史进化和保护濒危物种的最重要工具之一。该项目将开发和分析在基于积分差分方程（IDE’s）的简单建模框架中包含扩散和种群结构的模型。IDE有许多优点：(1)IDE可以模拟各种扩散机制，而不是使用标准的扩散近似；(2)作为离散时间方程，IDE自然地与矩阵人口模型联系在一起；(3)IDE很容易与数据联系在一起，因为它们的中心组成部分——分散分布——适合于经验测量。研究人员对这些模型的分析将集中在特定阶段的扩散和特定阶段的生命率的相互作用上。他们将结合数学分析和数值模拟。研究结果在种群生态学、进化生物学、保护生物学和生物防治等领域具有重要意义。