The Moran model as a dynamical process on networks and its implications for neutral speciation

TL;DR

This paper maps the Moran model of neutral evolution onto network influence processes, revealing how structured populations and spatial constraints influence genetic diversity and speciation.

Contribution

It introduces a novel network-based framework for the Moran model, linking population structure to neutral speciation mechanisms.

Findings

Structured populations enhance mutation effects compared to panmictic populations.

Spatial constraints can lead to stabilization and pattern formation, promoting speciation.

Explicit conditions for when speciation occurs based on population parameters.

Abstract

In genetics the Moran model describes the neutral evolution of a bi-allelic 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 new 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 take place: increasing diversity promoted by enhanced effective mutations versus decreasing diversity promoted by similarity between mates. Stabilization occurs with speciation via pattern formation. We derive an explicit relation involving the parameters characterizing the population that indicates when speciation is possible.