A monoecious and diploid Moran model of random mating

• A diploid monoecious Moran model is proposed for random mating with possible selfing.
• The Moran model is compared with a diploid and monoecious Wright–Fisher model.
• Diffusion approximations are derived on two time scales.
• Genotype frequencies oscillate as an Ornstein–Uhlenbeck process on the local time scale.
• Fixation index fIS oscillates as an Ornstein–Uhlenbeck process around a fixed point.

An exact Markov chain is developed for a Moran model of random mating for monoecious diploid individuals with a given probability of self-fertilization. The model captures the dynamics of genetic variation at a biallelic locus. We compare the model with the corresponding diploid Wright–Fisher (WF) model. We also develop a novel diffusion approximation of both models, where the genotype frequency distribution dynamics is described by two partial differential equations, on different time scales. The first equation captures the more slowly varying allele frequencies, and it is the same for the Moran and WF models. The other equation captures departures of the fraction of heterozygous genotypes from a large population equilibrium curve that equals Hardy–Weinberg proportions in the absence of selfing. It is the distribution of a continuous time Ornstein–Uhlenbeck process for the Moran model and a discrete time autoregressive process for the WF model. One application of our results is to capture dynamics of the degree of non-random mating of both models, in terms of the fixation index fIS. Although fIS has a stable fixed point that only depends on the degree of selfing, the normally distributed oscillations around this fixed point are stochastically larger for the Moran than for the WF model.