The population dynamics for the replicator equation has been well studied in continuous time, but there is less work that explicitly considers the evolution in discrete time. The discrete-time dynamics can often be justified indirectly by establishing the relevant evolutionary dynamics for the corresponding continuous-time system, and then appealing to an appropriate approximation property. In this paper we study the discrete-time system directly, and establish basic stability results for the evolution of a population defined by a positive definite system matrix, where the population is disrupted by random perturbations to the genotype distribution either through migration or mutation, in each successive generation.

中文翻译：

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扰动正定复制子方程的离散时间演化动力学

复制器方程的种群动力学已经在连续时间内得到了很好的研究，但很少有工作明确考虑离散时间的演化。离散时间动力学通常可以通过为相应的连续时间系统建立相关的演化动力学来间接证明，然后诉诸适当的近似属性。在本文中，我们直接研究离散时间系统，并建立由正定系统矩阵定义的种群进化的基本稳定性结果，其中种群被通过迁移或突变对基因型分布的随机扰动打乱，在每一代人。