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.

阐明自然选择影响分散的演变的机制是理解生物体生活历史的关键。物种分类研究的关键组成部分是了解局部非生物因素如何影响居民社区的行为和组成。例如，水柱中湍流扩散的增加​​如何影响浮游植物种群的持久性？河流生物可以随着河流排出而持续吗？如果持续存在，如何更改其范围限制？了解这些问题的答案可以促进为自然资源提供更好的管理策略的制定。研究人员根据进化游戏理论的框架研究了该项目中的这些和相关问题。自1970年代成立以来，进化游戏理论已证明自己在解释生物过程的许多复杂而充满挑战的方面是无价的。但是，直到最近，大多数进化游戏理论的研究都忽略了空间的影响。这部分是由于分析空间显式模型引起的数学困难。研究人员及其同事将通过离散和连续的数学建模方法进行分散演变的调查。更确切地说，该项目研究了分散模型中进化稳定的策略。进化上稳定的策略是一种策略，如果在给定环境中被人群采用，可以确保人口不能被最初罕见的突变体入侵。该项目着重于在两个不同的方向上找到均质或异质环境中进化稳定的分散策略：（i）先前的研究表明，连续时间和离散空间模型的平衡分散策略可以替代任何其他不平衡的分散策略。另一方面，研究还表明，离散时间和离散空间模型的平衡分散策略可能无法替代某些不平衡的分散策略。该项目寻求一种统一的方法来研究平衡分散在离散，连续和非本地模型中的进化稳定性，并解决不同建模方法之间的差异。 （ii）水柱中的单向流动通常会使个体远离有利的环境，并引起栖息地的净损失。先前的研究表明，对流通常会使缓慢的分散剂处于不利地位。研究人员将研究较大的分散率是否会始终发展，或者是否将在同质或异质，开放或封闭环境中选择某些中间分散率。将研究分散的演变与物种范围极限之间的联系。数学工具包括变分方法，椭圆和抛物线规则理论，单调动力学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

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

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

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