A microscopic interpretation for adaptive dynamics trait substitution sequence models
A microscopic interpretation for adaptive dynamics trait substitution sequence models
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DOI：
10.1016/j.spa.2006.01.004
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发表时间：
2006-08-01
影响因子：
1.4
通讯作者：
Champagnat, Nicolas
中科院分区：
文献类型：
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作者：
Champagnat, Nicolas
我们考虑一个非常数种群规模的无性种群中达尔文进化的相互作用粒子马尔可夫过程，涉及线性出生率，密度依赖的Logistic死亡率，和突变的概率μ在每个出生事件。我们引入了一个重整化参数K来缩放种群的大小，当K --> +无穷大时，这导致了持有给定性状的个体密度的确定性动力学。以非标准的方式结合人口众多的限制，（K --> +无穷大）和小突变（mu --> 0），我们证明了在出生和死亡事件与突变事件之间存在时间尺度分离，并且相互作用的粒子微观过程对于有限维分布收敛于被称为“单态性状替代序列”的生物进化模型。适应动力学模型，它描述了在一个无性种群的达尔文进化为一个马尔可夫跳跃过程的特征空间。(C)2006 Elsevier B. V.保留所有权利。
We consider an interacting particle Markov process for Darwinian evolution in an asexual population with non-constant population size, involving a linear birth rate, a density-dependent logistic death rate, and a probability mu of mutation at each birth event. We introduce a renormalization parameter K scaling the size of the population, which leads, when K --> +infinity, to a deterministic dynamics for the density of individuals holding a given trait. By combining in a non-standard way the limits of large population (K --> +infinity) and of small mutations (mu --> 0), we prove that a timescale separation between the birth and death events and the mutation events occurs and that the interacting particle microscopic process converges for finite dimensional distributions to the biological model of evolution known as the "monomorphic trait substitution sequence" model of adaptive dynamics, which describes the Darwinian evolution in an asexual population as a Markov jump process in the trait space. (C) 2006 Elsevier B.V. All rights reserved.