Yerevan Physics Institute, Alikhanian Brothers Street 2, Yerevan 375036, Armenia.
Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan.
Phys Rev E. 2019 Sep;100(3-1):032401. doi: 10.1103/PhysRevE.100.032401.
Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric payoffs reduces to the Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic (fine-grained) environment, the time-averaged population frequencies are shown to obey a replicator dynamics with a nonlinear fitness that is induced by environmental changes. The nonlinear terms in the fitness emerge due to populations tracking their time-dependent environment. These terms can induce a stable polymorphism, though they do not spoil the polymorphism that exists already without them. In this sense polymorphic populations are more robust with respect to their time-dependent environments. The overall fitness of the problem is still given by its time-averaged value, but the emergence of polymorphism during genetic selection can be accompanied by decreasing mean fitness of the population. The impact of the uncovered polymorphism scenario on the models of diversity is exemplified via the rock-paper-scissors dynamics, and also via the prisoner's dilemma in a time-periodic environment.
在时变环境中进行选择可以通过连续时间双玩家复制者动力学来建模，对于对称报酬，这简化为数理遗传学中的 Fisher 方程。对于足够快速和循环（细粒度）的环境，平均时间的种群频率被证明服从具有由环境变化引起的非线性适应度的复制者动力学。适应度中的非线性项是由于种群跟踪其时变环境而产生的。这些项可以诱导稳定的多态性，尽管它们不会破坏没有它们就存在的多态性。从这个意义上说，多态性种群对其时变环境具有更强的鲁棒性。问题的整体适应度仍然由其平均时间值给出，但是在遗传选择过程中多态性的出现可能伴随着种群平均适应度的降低。通过石头剪刀布动态和时变环境中的囚徒困境，揭示了多态性情景对多样性模型的影响。
