Lewis Mark A, Marculis Nathan G, Shen Zhongwei
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada.
Department of Biological Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada.
J Math Biol. 2018 Dec;77(6-7):1649-1687. doi: 10.1007/s00285-018-1206-1. Epub 2018 Jan 13.
To understand the effects that the climate change has on the evolution of species as well as the genetic consequences, we analyze an integrodifference equation (IDE) models for a reproducing and dispersing population in a spatio-temporal heterogeneous environment described by a shifting climate envelope. Our analysis on the IDE focuses on the persistence criterion, travelling wave solutions, and the inside dynamics. First, the persistence criterion, characterizing the global dynamics of the IDE, is established in terms of the basic reproduction number. In the case of persistence, a unique travelling wave is found to govern the global dynamics. The effects of the size and the shifting speed of the climate envelope on the basic reproduction number, and hence, on the persistence criterion, are also investigated. In particular, the critical domain size and the critical shifting speed are found in certain cases. Numerical simulations are performed to complement the theoretical results. In the case of persistence, we separate the travelling wave and general solutions into spatially distinct neutral fractions to study the inside dynamics. It is shown that each neutral genetic fraction rearranges itself spatially so as to asymptotically achieve the profile of the travelling wave. To measure the genetic diversity of the population density we calculate the Shannon diversity index and related indices, and use these to illustrate how diversity changes with underlying parameters.
为了理解气候变化对物种进化的影响以及遗传后果，我们分析了一个积分差分方程（IDE）模型，该模型用于描述在由移动气候包络所刻画的时空异质环境中进行繁殖和扩散的种群。我们对IDE的分析聚焦于持续性准则、行波解以及内部动态。首先，根据基本再生数建立了刻画IDE全局动态的持续性准则。在持续性的情况下，发现一个唯一的行波支配全局动态。还研究了气候包络的大小和移动速度对基本再生数的影响，进而对持续性准则的影响。特别地，在某些情况下找到了临界域大小和临界移动速度。进行了数值模拟以补充理论结果。在持续性的情况下，我们将行波和一般解分离为空间上不同的中性部分来研究内部动态。结果表明，每个中性遗传部分在空间上重新排列自身，以便渐近地达到行波的轮廓。为了测量种群密度的遗传多样性，我们计算了香农多样性指数及相关指数，并利用这些指数来说明多样性如何随潜在参数变化。
