FIXATION OF A DELETERIOUS ALLELE AT ONE OF 2 DUPLICATE LOCI BY MUTATION PRESSURE AND RANDOM DRIFT

The authors consider a diploid population and assume two gene loci with two alleles each, A and a at one locus and B and b at the second locus. Mutation from wild-type alleles A and B to deleterious alleles a and b occurs with mutation rates v(a) and v(b), respectively. The authors assume that alleles are completely recessive and that only the double recessive genotype aabb shows a deleterious effect with relative fitness I - ε. Then, it can be shown that if v(a) > v(b) mutant a becomes fixed in the population by mutation pressure and a mutation-selection balance is ultimately attained with respect to the B/b locus alone. The main aim of this paper is to investigate the situation in which v(a)=v(b) exactly. In this case a neutral equilibrium is attained and either locus can drift to fixation for the mutant allele. Diffusion models are developed to treat the stochastic process involved whereby the deleterious mutant eventually becomes fixed in one of the two duplicated loci by random sampling drift in finite populations. In particular, the equation for the average time until fixation of mutant a or b is derived, and this is solved numerically for some combinations of parameters 4N(e)v and 4N(e)ε, where v is the mutation rate (v(a)=v(b)̄=v) and N(e) is the effective size of the population. Monte Carlo experiments have been performed (using a device termed 'pseudo sampling variable') to supplement the numerical analysis.