Rare mutations limit of a steady state dispersal evolution model
Rare mutations limit of a steady state dispersal evolution model
复制标题
稳态扩散进化模型的罕见突变限制
DOI：
10.1051/mmnp/201611411
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发表时间：
2016
影响因子：
2.2
通讯作者：
P. Souganidis
中科院分区：
文献类型：
--
作者：
B. Perthame;P. Souganidis
扩散演化是进化生态学中的经典问题，已有多种数学模型对其进行了广泛的研究。主要的问题是为有界区域中的种群定义最合适的分散率，最近，为整个空间中的行波定义最合适的分散率。
在本研究中，我们在适应性进化的背景下重新表述了这个问题。我们考虑一个由空间和遗传性状构成的种群，在罕见突变对该遗传性状的影响下，直接作用于扩散(扩散)速度。我们表明，与在更简单的模型中一样，在消失突变的限制下，种群集中在与最低分散率相关的单个特征上。我们还解释了如何计算向这种进化稳定分布的进化速度。对数学的兴趣源于渐近分析，它需要对不同变量进行完全不同的处理。对于空间变量，椭圆性导致使用最大值原理和Sobolev型正则性结果。对于性状变量，狄拉克质量的浓度需要不同的处理。这是基于WKB方法和粘性解，从而得到有效的哈密顿量(人口的有效适应度)和约束的哈密顿-雅可比方程。
The evolution of dispersal is a classical question in evolutionary ecology, which has been widely studied with several mathematical models. The main question is to define the fittest dispersal rate for a population in a bounded domain, and, more recently, for traveling waves in the full space.
In the present study, we reformulate the problem in the context of adaptive evolution. We consider a population structured by space and a genetic trait acting directly on the dispersal (diffusion) rate under the effect of rare mutations on the genetic trait. We show that, as in simpler models, in the limit of vanishing mutations, the population concentrates on a single trait associated to the lowest dispersal rate. We also explain how to compute the evolution speed towards this evolutionary stable distribution. The mathematical interest stems from the asymptotic analysis which requires a completely different treatment of the different variables. For the space variable, the ellipticity leads to the use the maximum principle and Sobolev-type regularity results. For the trait variable, the concentration to a Dirac mass requires a different treatment. This is based on the WKB method and viscosity solutions leading to an effective Hamiltonian (effective fitness of the population) and a constrained Hamilton-Jacobi equation.
从随机的、基于个体的模型到自适应动力学的规范方程 - 一步到位
DOI：
10.1214/16-aap1227
发表时间：
2017
期刊：
arXiv: Probability
影响因子：
--
作者：
M. Baar;A. Bovier;N. Champagnat
通讯作者：
N. Champagnat