We consider the diffusion approximation of the multivariate Wright-Fisher model with mutation. Analytically tractable formulae for the first- and second-order moments of the model are derived, and the moments are subsequently used to better understand key population genetics parameters and modelling frameworks
 

In particular we investigate the behaviour of the expected homozygosity (the probability that two randomly sampled genes are identical) in the transient and stationary phases, and how appropriate the Balding-Nichols model is for modelling allele frequency changes at different evolutionary time scales.

We find that the Balding-Nichols model is adequate for the pure drift model (no mutation), but the model is not sufficiently flexible for more general mutation structures. We suggest a new hierarchical Beta approximation for the Wright-Fisher model with a mutation model on the nucleotide level that distinguishes between transitions and transversions.