Inbreeding depression and the maintenance of deleterious genes by mutation: model of aDrosophilachromosome

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Abstract
Inbreeding experiments in Drosophila, particularly those carried out using the ‘balancer equilibration’ technique, have revealed high levels of inbreeding depression. It has been estimated that non-lethal chromosomes have a fitness of 20% or less in homozygous condition compared to chromosome heterozygotes. Deleterious recessive genes are, in principle, capable of explaining such inbreeding depression. In this paper we have asked quantitatively whether the observed high levels are consistent with what is known about numbers of loci and mutation rates. We find that accepted mutation rates are easily high enough, provided that the deleterious genes are fully recessive. Partial dominance, even to the extent of 10% or less, reverses this conclusion. These calculations have been made assuming the multiplicative model. However the arguments are potentially sensitive to certain types of selective interactions, and a model which proposes quadratic gene interaction allows for higher levels of partial dominance. We also test the effect of taking into account a further constraint. Crow and Mukai have argued from estimates of the persistence of new deleterious mutations affecting viability that heterozygotes have a reduction in fitness of around 1–2% per locus, similar to the estimate for lethal genes. Application of this additional constraint would markedly reduce the range of permissible selection coefficients. However we argue that the selective disadvantages in heterozygotes of most mutations affecting fitness are unlikely to be as high as estimated for mutations affecting viability.