Evolution of Conditional Dispersal and Population Dynamics

条件扩散和种群动态的演变

• 批准号: 0615845
• 负责人: Yuan Lou
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-15 至 2010-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0615845&HistoricalAwards=false
• 关键词: Evolution; Conditional; Dispersal; Population; Dynamics

This project investigates the effects of conditional dispersal on dynamics of single and multiple interacting species. A common underlying assumption in theoretical studies of population dynamics is that dispersal rates are uniform across space. However, such simplification can yield misleading results because the surrounding environment can vary both spatially and temporally. Indeed, animals tend to sense and respond to local environmental cues by dispersing directionally, and their movements are often combinations of both random and directed ones. Reaction-diffusion-advection equations serve as one of the major approaches to understanding spatial-temporal processes such as dispersal, and are used in this research to model both random and directed movements of species and population dynamics. Three kinds of conditional dispersal strategies will be studied in this project. The first one is the direct movement of populations along environmental gradients or along density-dependent growth rate gradients, and the goal is to determine the effects of such biased movement on both single population and multiple competing species. The second dispersal strategy concerns area-restricted search of predators, and the purpose is to understand how biased foraging behaviors of predators can induce the aggregation of predators. The third is a dynamical model for ideal free distribution theory, which assumes that species choose habitats in such a way that each individual tries to maximize its reproduction fitness. The aim is to obtain a better understanding of interactions between such dispersal strategy and population dynamics. To address these biological questions, the principal investigator will use mathematical methods which include regularity theory for elliptic and parabolic operators, analysis of eigenvalue problems, maximum principles, bifurcation analysis, monotone system theory, permanence theory, and perturbation analysis.The purpose of this project is to increase our understanding of how populations disperse in response to spatially varying environments, to determine which patterns of dispersal strategy can confer some selective or ecological advantage, and to provide insights on biodiversity issues such as habitat fragmentation and invasions of new species. Preliminary investigations show that the geometry of habitat can play important roles in the evolution of dispersal, and also that strong directed movement of a species can induce coexistence with its competitors. Materials from this project will be modified and used as team projects for a Mathematical Biosciences Institute Summer Program for college teachers and graduate students in mathematics and biology.

该项目研究条件分散对单个相互作用物种的动态的影响。 人口动态的理论研究中的一个共同基础假设是，分散率在整个空间之间是均匀的。 但是，这种简化可以产生误导性的结果，因为周围环境可以在空间和时间上变化。 的确，动物倾向于通过方向分散来感知并应对当地的环境线索，而它们的运动通常是随机和有向动物的组合。 反应扩散 - 辅助方程是理解时空过程（例如分散）的主要方法之一，并在本研究中用于模拟物种和种群动态的随机运动和定向运动。 该项目将研究三种条件分散策略。 第一个是人口沿环境梯度的直接运动或沿密度依赖性生长速率梯度的直接运动，目标是确定这种偏见运动对单人群和多个竞争物种的影响。 第二个分散策略涉及对捕食者的限制性搜索，目的是了解捕食者的觅食行为如何诱导捕食者的聚集。 第三个是理想自由分布理论的动力学模型，该模型假设物种选择栖息地，以使每个人都试图最大化其繁殖适应性。 目的是更好地了解这种分散策略与人口动态之间的相互作用。为了解决这些生物学问题，主要研究者将使用数学方法，包括用于椭圆形和抛物线运营商的规律性理论，特征问题问题的分析，最大原理，分叉分析，单调系统理论，持久性理论，持久性理论和扰动分析。或生态优势，并就生物多样性问题（例如栖息地分裂和新物种的入侵）提供见解。 初步调查表明，栖息地的几何形状可以在分散的演变中起重要作用，而且物种的强烈定向运动可以引起与竞争对手的共存。 该项目的材料将被修改并用作数学生物科学研究所夏季计划的团队项目，用于数学和生物学领域的大学教师和研究生。