Evolutionarily Stable Dispersal Strategies in Spatial Models

空间模型中的进化稳定扩散策略

• 批准号: 1411476
• 负责人: Yuan Lou
• 金额: $ 25万
• 依托单位: Ohio State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-09-01 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1411476&HistoricalAwards=false
• 关键词: Evolutionarily; Stable; Dispersal; Strategies; Spatial

Unraveling the mechanism with which natural selection influences the evolution of dispersal is the key to understanding the life history of organisms. A key component in the study of species sorting is to understand how local abiotic factors influence the behavior as well as composition of resident communities. For instance, how does the increase in turbulent diffusion in water columns affect the persistence of phytoplankton populations? Can a river organism persist with increased river discharge? If it persists, how will its range limit be changed? Understanding the answers to these questions can facilitate the development of better management strategies for natural resources. The investigators study these and related questions in this project under the framework of evolutionary game theory. Since its inception in the 1970s, evolutionary game theory has proven itself to be invaluable in explaining many complex and challenging aspects of biological processes. However, most studies in evolutionary game theory have, until recently, ignored the effect of space. This is partly due to the mathematical difficulty arising from the analysis of spatially explicit models. The investigators and their colleagues will undertake the investigation of the evolution of dispersal, via discrete as well as continuous mathematical modeling approaches. More precisely, this project studies the evolutionarily stable strategies in dispersal models. An evolutionarily stable strategy is a strategy which, if adopted by a population in a given environment, assures that the population cannot be invaded by a mutant that is initially rare. This project focuses on finding evolutionarily stable dispersal strategies in homogeneous or heterogeneous environments in two distinct directions: (i) Previous studies have shown that a balanced dispersal strategy for continuous-time and discrete-space models can replace any other unbalanced dispersal strategy. On the other hand, studies have also shown that a balanced dispersal strategy for discrete-time and discrete-space models may not be able to replace some unbalanced dispersal strategies. This project seeks a unified approach to study the evolutionary stability of balanced dispersal in discrete, continuous and nonlocal models, and to resolve the disparities between different modeling approaches; (ii) Unidirectional flow in water columns often pushes individuals away from favorable environments and also induces a net loss of individuals from the habitat. Previous studies show that advection often puts slow dispersers at a disadvantage. The investigators will study whether larger dispersal rates will always evolve or if some intermediate dispersal rate will be selected, in homogeneous or heterogeneous, open or closed environments. Connections between the evolution of dispersal and range limit of species will be investigated. The mathematical tools include variational method, elliptic and parabolic regularity theory, monotone dynamical system theory, and numerical simulations.

了解自然选择影响物种扩散演化的机制，是理解生物生活史的关键。物种分类研究的一个关键组成部分是了解当地非生物因素如何影响居民群落的行为和组成。例如，水体中湍流扩散的增加如何影响浮游植物种群的持久性？河流生物能够在河流流量增加的情况下持续存在吗？如果持续下去，它的范围限制将如何改变？了解这些问题的答案有助于制定更好的自然资源管理战略。研究人员在进化博弈论的框架下对这些问题及相关问题进行了研究。自20世纪70年代创立以来，进化博弈论在解释生物过程的许多复杂和具有挑战性的方面已经证明了自己的宝贵价值。然而，直到最近，进化博弈论中的大多数研究都忽略了空间的影响。这在一定程度上是由于分析空间上明确的模型所引起的数学困难。研究人员和他们的同事将通过离散和连续的数学建模方法，对扩散的演变进行调查。更准确地说，这个项目研究了扩散模型中的进化稳定策略。进化稳定的策略是一种策略，如果在给定的环境中被种群采用，它可以确保种群不会被最初罕见的突变所入侵。本项目致力于在同质或异质环境中从两个不同的方向寻找进化稳定的扩散策略：(I)先前的研究表明，连续时间和离散空间模型的平衡扩散策略可以取代任何其他不平衡的扩散策略。另一方面，研究也表明，用于离散时间和离散空间模型的平衡扩散策略可能不能取代一些不平衡的扩散策略。本项目寻求一种统一的方法来研究离散、连续和非局部模型中平衡扩散的进化稳定性，并解决不同建模方法之间的差异；(Ii)水柱中的单向流动经常将个体推离有利的环境，并导致个体从栖息地净损失。以前的研究表明，平流通常会使缓慢的分散者处于不利地位。研究人员将研究在同质或非均质、开放或封闭的环境中，是否总是会进化出更大的扩散速度，或者是否会选择一些中间的扩散速度。将研究物种扩散演化和物种范围限制之间的联系。数学工具包括变分方法、椭圆和抛物线正则性理论、单调动力系统理论和数值模拟。

项目成果

Evolution of dispersal in closed advective environments

• DOI: 10.1080/17513758.2014.969336
• 发表时间: 2015-06
• 期刊: Journal of Biological Dynamics
• 影响因子: 2.8
• 作者: King-Yeung Lam;Y. Lou;F. Lutscher

Multiple steady-states in phytoplankton population induced by photoinhibition

• DOI: 10.1016/j.jde.2014.12.012
• 发表时间: 2015-04
• 期刊: Journal of Differential Equations
• 影响因子: 2.4
• 作者: Yihong Du;S. Hsu;Y. Lou

The Role of Advection in a Two-species Competition Model: A Bifurcation Approach

• DOI: 10.1090/memo/1161
• 发表时间: 2017-01
• 期刊: 2016 13th Web Information Systems and Applications Conference (WISA)
• 作者: Isabel Averill;King-Yeung Lam;Y. Lou

Global Existence and Uniform Boundedness of Smooth Solutions to a Cross-Diffusion System with Equal Diffusion Rates

• DOI: 10.1080/03605302.2015.1052882
• 发表时间: 2015-08
• 期刊: Communications in Partial Differential Equations
• 影响因子: 1.9
• 作者: Y. Lou;M. Winkler

A remark on the global dynamics of competitive systems on ordered Banach spaces

• DOI: 10.1090/proc12768
• 发表时间: 2015-03
• 作者: King-Yeung Lam;Daniel S. Munther