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Allele frequencies in multidimensional Wright-Fisher models with a general symmetric mutation structure

1980; Elsevier BV; Volume: 17; Issue: 1 Linguagem: Inglês

10.1016/0040-5809(80)90014-3

1096-0325

Robert Griffiths,

Mathematical and Theoretical Epidemiology and Ecology Models

The diffusion form of a multiple-allele Wright-Fisher model of allele frequencies of types A1,…,AK at a neutral locus where there are general symmetric mutation rates of Mij (=Mji) from Ai → Aj is studied. A convenient recurrence relationship for the moments of linear forms in the allele frequencies is found. A formula is derived for the expected homozygosity in the transient and stationary models, which is applied to general stepwise mutation models where mutation over more than one step is possible. The probability that two randomly chosen genes are j steps apart at time t in the stepwise mutation model is found to have a reasonably simple form if conditioning is on the initial allele frequencies arranged in order of magnitude. Of interest is a new geometric charge state model, mutation over several steps roughly corresponding to independent charge changes. The expected homozygosity and expected distance between two randomly chosen genes is tabulated in this model.