de Aguiar Marcus A M, Bar-Yam Yaneer
New England Complex Systems Institute, Cambridge, Massachusetts 02142, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Sep;84(3 Pt 1):031901. doi: 10.1103/PhysRevE.84.031901. Epub 2011 Sep 1.
In population genetics, the Moran model describes the neutral evolution of a biallelic gene in a population of haploid individuals subjected to mutations. We show in this paper that this model can be mapped into an influence dynamical process on networks subjected to external influences. The panmictic case considered by Moran corresponds to fully connected networks and can be completely solved in terms of hypergeometric functions. Other types of networks correspond to structured populations, for which approximate solutions are also available. This approach to the classic Moran model leads to a relation between regular networks based on spatial grids and the mechanism of isolation by distance. We discuss the consequences of this connection for topopatric speciation and the theory of neutral speciation and biodiversity. We show that the effect of mutations in structured populations, where individuals can mate only with neighbors, is greatly enhanced with respect to the panmictic case. If mating is further constrained by genetic proximity between individuals, a balance of opposing tendencies takes place: increasing diversity promoted by enhanced effective mutations versus decreasing diversity promoted by similarity between mates. Resolution of large enough opposing tendencies occurs through speciation via pattern formation. We derive an explicit expression that indicates when speciation is possible involving the parameters characterizing the population. We also show that the time to speciation is greatly reduced in comparison with the panmictic case.
在群体遗传学中，莫兰模型描述了在受到突变影响的单倍体个体群体中双等位基因的中性进化。我们在本文中表明，该模型可以映射到受到外部影响的网络上的影响动力学过程。莫兰所考虑的随机交配情况对应于完全连通网络，并且可以用超几何函数完全求解。其他类型的网络对应于结构化群体，对于这些群体也有近似解。这种处理经典莫兰模型的方法导致了基于空间网格的规则网络与距离隔离机制之间的一种关系。我们讨论了这种联系对异域物种形成以及中性物种形成和生物多样性理论的影响。我们表明，在结构化群体中，个体只能与邻居交配，突变的影响相对于随机交配情况大大增强。如果交配进一步受到个体之间遗传接近性的限制，就会出现相反趋势的平衡：有效突变增强促进多样性增加，而配偶之间的相似性促进多样性减少。足够大的相反趋势的解决通过模式形成导致物种形成。我们推导了一个明确的表达式，表明何时可能发生物种形成，该表达式涉及表征群体的参数。我们还表明，与随机交配情况相比，物种形成的时间大大缩短。
