Invasion and adaptive evolution for individual-based spatially structured populations
Invasion and adaptive evolution for individual-based spatially structured populations
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DOI：
10.1007/s00285-007-0072-z
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发表时间：
2007-08-01
影响因子：
1.9
通讯作者：
Meleard, Sylvie
中科院分区：
文献类型：
--
作者：
Champagnat, Nicolas;Meleard, Sylvie
空间和进化之间的相互作用是种群动态学中的一个重要问题，在多态性和空间格局的出现中尤为重要。近年来，生物学研究表明，入侵与进化密切相关。在这里，我们模拟空间和进化之间的相互作用，以个人为基础的方法开始，并显示聚类和入侵的重要作用的参数缩放。考虑一类具有出生、死亡、竞争、突变和空间扩散的随机离散模型，其中所有的参数既依赖于个体的位置又依赖于个体的表型特征。空间运动由有界域中的反射扩散驱动。在给定的空间相互作用范围内的相互作用被建模为个人之间的特质竞争。首先，我们给出了一个算法的建设过程。其次，我们得到了大种群近似，作为非线性反应扩散方程的弱解。当空间相互作用范围固定时，非线性是非局部的。然后，我们使相互作用范围减小到零，并证明了空间局部化的非线性反应扩散方程的收敛性。最后，讨论了三个具体的例子，提出了基于微观个人为基础的模型的模拟。这些例子说明了空间相互作用范围对空间和表型多样性（聚类和多态性）的出现以及入侵和进化之间的相互作用的强烈影响。模拟的重点是本地和非本地的相互作用之间的定性差异。
The interplay between space and evolution is an important issue in population dynamics, that is particularly crucial in the emergence of polymorphism and spatial patterns. Recently, biological studies suggest that invasion and evolution are closely related. Here, we model the interplay between space and evolution starting with an individual-based approach and show the important role of parameter scalings on clustering and invasion. We consider a stochastic discrete model with birth, death, competition, mutation and spatial diffusion, where all the parameters may depend both on the position and on the phenotypic trait of individuals. The spatial motion is driven by a reflected diffusion in a bounded domain. The interaction is modelled as a trait competition between individuals within a given spatial interaction range. First, we give an algorithmic construction of the process. Next, we obtain large population approximations, as weak solutions of nonlinear reaction-diffusion equations. As the spatial interaction range is fixed, the nonlinearity is nonlocal. Then, we make the interaction range decrease to zero and prove the convergence to spatially localized nonlinear reaction-diffusion equations. Finally, a discussion of three concrete examples is proposed, based on simulations of the microscopic individual-based model. These examples illustrate the strong effects of the spatial interaction range on the emergence of spatial and phenotypic diversity (clustering and polymorphism) and on the interplay between invasion and evolution. The simulations focus on the qualitative differences between local and nonlocal interactions.