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In genetics the Moran model describes the neutral evolution of a bi-allelicgene in a population of haploid individuals subjected to mutations. We show inthis paper that this model can be mapped into an influence dynamical process onnetworks subjected to external influences. The panmictic case considered byMoran corresponds to fully connected networks and can be completely solved interms of hypergeometric functions. Other types of networks correspond tostructured populations, for which approximate solutions are also available.This new approach to the classic Moran model leads to a relation betweenregular networks based on spatial grids and the mechanism of isolation bydistance. We discuss the consequences of this connection for topopatricspeciation and the theory of neutral speciation and biodiversity. We show thatthe effect of mutations in structured populations, where individuals can mateonly with neighbors, is greatly enhanced with respect to the panmictic case. Ifmating is further constrained by genetic proximity between individuals, abalance of opposing tendencies take place: increasing diversity promoted byenhanced effective mutations versus decreasing diversity promoted by similaritybetween mates. Stabilization occurs with speciation via pattern formation. Wederive an explicit relation involving the parameters characterizing thepopulation that indicates when speciation is possible.

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