论文标题
突变选择平衡中的祖先谱系，最佳移动
Ancestral lineages in mutation-selection equilibria with moving optimum
论文作者
论文摘要
我们研究了在表型中构成的种群的进化动力学，并以线性移动的最佳和无性繁殖方式受到性状依赖性选择。我们的模型由非本地和非线性抛物线PDE组成。我们的主要目标是衡量人口围绕平衡时的特征历史。我们根据中性分数的概念来定义祖先过程。它使我们能够随着时间的流逝而得出人口多样性的演变定量信息。首先，我们研究祖先过程的长期渐近学。我们表明，最适合的人可以推动适应。然后，我们应对自适应动力学制度，其中突变的效果渐近地很小。在此限制中，我们为一些相关优化问题（汉密尔顿雅各比方程）作为典型的祖先血统提供了一种解释。我们根据基于单个的模拟检查理论结果。
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.
