Evolutionarily Stable Dispersal Strategies in Spatial Models

揭示自然选择影响扩散进化的机制是理解生物体生命史的关键。物种分选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？河流生物能否随着河流流量的增加而持续存在？如果这种情况持续下去，它的区间限制将如何改变？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。研究者在进化博弈论的框架下研究这些问题和相关问题。自20世纪70年代创立以来，进化博弈论已经证明自己在解释生物过程的许多复杂和具有挑战性的方面是无价的。然而，直到最近，大多数进化博弈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所产生的数学困难。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，本项目研究扩散模型中的进化稳定策略。进化稳定策略是一种策略，如果一个种群在给定的环境中采用这种策略，它可以确保种群不会被最初罕见的突变入侵。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)以往的研究表明，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扩散策略。另一方面，研究也表明，离散时间和离散空间模型的平衡扩散策略可能无法取代某些不平衡扩散策略。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）水柱的单向流动往往使个体远离有利的环境，也导致个体从栖息地的净损失。先前的研究表明，平流通常会使缓慢的分散器处于不利地位。研究人员将研究在同质或异质、开放或封闭的环境中，是否总是会有较大的扩散速率进化，或者是否会选择一些中间的扩散速率。研究物种扩散演化与范围限制之间的关系。数学工具包括变分方法、椭圆和抛物正则性理论、单调动力系统理论和数值模拟。

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.