论文标题
人口的生存标准受到选择和突变的约束；应用于时间分段恒定环境
Survival criterion for a population subject to selection and mutations ; Application to temporally piecewise constant environments
论文作者
论文摘要
我们研究了一种抛物线洛特卡 - 沃尔特拉型方程，该方程描述了由表型性状构成的人群的演变，在突变和以非本地反馈为模拟的资源的竞争下。小突变的极限的特征在于汉密尔顿 - 雅各比方程的约束，该方程描述了某些特征上人口的浓度。该结果已经在2008年的Barles-Perthame，2009年Barles-Mirrahimi-Perthame，Lorz-Mirrahimi-Perthame 2011中的2011年，当时在时间基础的环境中，当时人口的渐近性持久性通过假设对生长速率或初始数据确保。在这里，我们放宽了这些假设，将研究扩展到人口可能在极限上灭绝的情况。为此，我们为人口渐近命运的初始数据提供条件。最后，我们展示了这项研究的研究如何允许考虑时间分段的恒定环境。
We study a parabolic Lotka-Volterra type equation that describes the evolution of a population structured by a phenotypic trait, under the effects of mutations and competition for resources modelled by a nonlocal feedback. The limit of small mutations is characterized by a Hamilton-Jacobi equation with constraint that describes the concentration of the population on some traits. This result was already established in Barles-Perthame 2008, Barles-Mirrahimi-Perthame 2009, Lorz-Mirrahimi-Perthame 2011 in a time-homogenous environment, when the asymptotic persistence of the population was ensured by assumptions on either the growth rate or the initial data. Here, we relax these assumptions to extend the study to situations where the population may go extinct at the limit. For that purpose, we provide conditions on the initial data for the asymptotic fate of the population. Finally, we show how this study for a time-homogenous environment allows to consider temporally piecewise constant environments.
