具有移动最优的突变选择均衡中的祖先谱系
Ancestral lineages in mutation-selection equilibria with moving optimum
摘要：
我们调查的进化动力学的人口结构的表型，进行性状依赖的选择与线性移动的最佳和无性繁殖模式。我们的模型由一个非局部和非线性抛物型偏微分方程。我们的主要目标是测量当种群保持在均衡附近时的性状历史。我们定义了一个祖先过程的基础上的想法中性分数。它使我们能够获得数量上的信息，随着时间的推移，在人口的多样性的演变。首先，我们研究了祖先过程的长时间渐近性。我们表明，极少数最适合的个人驱动适应。然后，我们解决自适应动态制度，突变的影响是渐近小。在这个极限中，我们提供了一个解释的最小值的一些相关的最优化问题，汉密尔顿雅可比方程，作为典型的祖先血统。我们检查的理论结果对个人为基础的模拟。
英文摘要：
We investigate the evolutionary dynamics of a population structured in phenotype, subjected to trait dependent selection with a linearly moving optimum and an asexual mode of reproduction. Our model consists of a non-local and non-linear parabolic PDE. Our main goal is to measure the history of traits when the population stays around an equilibrium. We define an ancestral process based on the idea of neutral fractions. It allows us to derive quantitative information upon the evolution of diversity in the population along time. First, we study the long-time asymptotics of the ancestral process. We show that the very few fittest individuals drive adaptation. We then tackle the adaptive dynamics regime, where the effect of mutations is asymptotically small. In this limit, we provide an interpretation for the minimizer of some related optimization problem, an Hamilton Jacobi equation, as the typical ancestral lineage. We check the theoretical results against individual based simulations.
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