Network Dynamics Group, Max Planck Institute for Dynamics and Self-Organization, Bunsenstrasse 10, 37073 Göttingen, Germany.
J R Soc Interface. 2012 Dec 7;9(77):3387-96. doi: 10.1098/rsif.2012.0464. Epub 2012 Aug 8.
Evolution is simultaneously driven by a number of processes such as mutation, competition and random sampling. Understanding which of these processes is dominating the collective evolutionary dynamics in dependence on system properties is a fundamental aim of theoretical research. Recent works quantitatively studied coevolutionary dynamics of competing species with a focus on linearly frequency-dependent interactions, derived from a game-theoretic viewpoint. However, several aspects of evolutionary dynamics, e.g. limited resources, may induce effectively nonlinear frequency dependencies. Here we study the impact of nonlinear frequency dependence on evolutionary dynamics in a model class that covers linear frequency dependence as a special case. We focus on the simplest non-trivial setting of two genotypes and analyse the co-action of nonlinear frequency dependence with asymmetric mutation rates. We find that their co-action may induce novel metastable states as well as stochastic switching dynamics between them. Our results reveal how the different mechanisms of mutation, selection and genetic drift contribute to the dynamics and the emergence of metastable states, suggesting that multistability is a generic feature in systems with frequency-dependent fitness.
进化同时受到多种过程的驱动，如突变、竞争和随机抽样。理解这些过程中哪些在依赖于系统特性的情况下主导着集体进化动态，是理论研究的一个基本目标。最近的工作从博弈论的角度出发，定量研究了具有线性频率依赖性相互作用的竞争物种的共进化动力学。然而，进化动力学的几个方面，例如有限的资源，可能会导致有效的非线性频率依赖性。在这里，我们研究了非线性频率依赖性对模型类中进化动力学的影响，该模型类涵盖了线性频率依赖性作为特例。我们专注于两个基因型的最简单非平凡设置，并分析了非线性频率依赖性与不对称突变率的共同作用。我们发现，它们的共同作用可能会诱导新的亚稳态以及它们之间的随机切换动力学。我们的结果揭示了突变、选择和遗传漂变的不同机制如何促进动力学和亚稳态的出现，表明多稳定性是具有频率相关适应性的系统的一个通用特征。
