非对称再生核的选择-突变动力学
Selection-mutation dynamics with asymmetrical reproduction kernels
摘要：
我们研究了一个由表型性状构成的有性群体的选择突变模型家族。这些模型的主要特征是双亲之间的性状遗传或生殖力的不对称性：我们假设每个个体主要从雌性遗传其性状，或者该性状作用于雌性生殖力，但不影响雄性。根据以前的作品从自适应动力学原理的启发，我们重新调整时间，并假设突变对表型的影响有限。我们的目标是研究总体分布的渐近行为。我们得出的非灭绝条件和BV估计的总人口。我们还获得了对最适合性状的总体分布集中研究中产生的Hamilton-Jacobi方程解的Lipschitz估计。利用李雅普诺夫泛函得到了某些特殊情况下的浓度结果。
英文摘要：
We study a family of selection-mutation models of a sexual population structured by a phenotypical trait. The main feature of these models is the asymmetric trait heredity or fecundity between the parents : we assume that each individual inherits mostly its trait from the female or that the trait acts on the female fecundity but does not affect male. Following previous works inspired from principles of adaptive dynamics, we rescale time and assume that mutations have limited effects on the phenotype. Our goal is to study the asymptotic behavior of the population distribution. We derive non-extinction conditions and BV estimates on the total population. We also obtain Lipschitz estimates on the solutions of Hamilton-Jacobi equations that arise from the study of the population distribution concentration at fittest traits. Concentration results are obtained in some special cases by using a Lyapunov functional.
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