Franco Gabriella Dantas, Marquitti Flavia Maria Darcie, Fernandes Lucas D, Braha Dan, de Aguiar Marcus Aloizio Martinez
Universidade Estadual de Campinas, Departamento de Física da Matéria Condensada, Instituto de Física "Gleb Wataghin", 13083-970 Campinas, São Paulo, Brazil.
Universidade Estadual de Campinas, Instituto de Biologia, 13083-862 Campinas, São Paulo, Brazil.
Phys Rev E. 2021 Aug;104(2-1):024315. doi: 10.1103/PhysRevE.104.024315.
Mutation and drift play opposite roles in genetics. While mutation creates diversity, drift can cause gene variants to disappear, especially when they are rare. In the absence of natural selection and migration, the balance between the drift and mutation in a well-mixed population defines its diversity. The Moran model captures the effects of these two evolutionary forces and has a counterpart in social dynamics, known as the voter model with external opinion influencers. Two extreme outcomes of the voter model dynamics are consensus and coexistence of opinions, which correspond to low and high diversity in the Moran model. Here we use a Shannon's information-theoretic approach to characterize the smooth transition between the states of consensus and coexistence of opinions in the voter model. Mapping the Moran into the voter model, we extend the results to the mutation-drift balance and characterize the transition between low and high diversity in finite populations. Describing the population as a network of connected individuals, we show that the transition between the two regimes depends on the network topology of the population and on the possible asymmetries in the mutation rates.
突变和漂变在遗传学中发挥着相反的作用。虽然突变创造了多样性，但漂变会导致基因变体消失，尤其是当它们很罕见时。在没有自然选择和迁移的情况下，一个充分混合的种群中漂变和突变之间的平衡决定了其多样性。莫兰模型捕捉了这两种进化力量的影响，并且在社会动力学中有一个对应物，即具有外部意见影响者的选民模型。选民模型动力学的两个极端结果是意见的一致和共存，这分别对应于莫兰模型中的低多样性和高多样性。在这里，我们使用香农信息论方法来刻画选民模型中意见一致和共存状态之间的平滑过渡。将莫兰模型映射到选民模型中，我们将结果扩展到突变 - 漂变平衡，并刻画有限种群中低多样性和高多样性之间的过渡。将种群描述为相互连接个体的网络，我们表明两种状态之间的过渡取决于种群的网络拓扑结构以及突变率中可能存在的不对称性。
