Because of selective interference among loci, and because partial selfing creates identity disequilibrium (positive associations between homozygous genotypes at different loci, even in the absence of linkage; Haldane 1949; Weir and Cockerham 1973), it is difficult to analyze an exact model of the maintenance of high inbreeding depression by recessive lethal mutations. To investigate the relative importance of selective interference and identity disequilibrium in determining the threshold selfing rate for purging recessive lethals, we develop two simplified deterministic models.
Denoting the mean viability of selfed zygotes caused by embryonic lethals as [Mathematical Expression Omitted] and that of outcrossed zygotes as [Mathematical Expression Omitted], the component of inbreeding depression caused by embryonic lethal mutations is defined as
An unrealistic feature of this model is that for completely recessive lethal mutations under low selfing rates, the mean number of lethals per plant becomes infinite.
We derive a version of Kondrashov's model for the case of homozygous lethal mutations, such that wild-type homozygotes, mutant heterozygotes, and mutant homozygotes at each locus have viabilities of 1, 1 - h, and 0 respectively.
Time scales for approaching equilibrium varied from infinity for completely recessive lethal mutations with selfing rates below the threshold, to a few hundred generations for slightly dominant lethals under random mating, and several generations under complete selfing.
Thus, when 2n[square root of [Mu]] [greater than] 10 selective interference among loci creates a threshold selfing rate necessary for purging recessive lethal mutations.
Slight dominance of lethal mutations substantially reduces the equilibrium load in comparison to that for full recessivity, as seen in figures 2 and 3.
Regardless of the average dominance of lethal mutations, for selfing rates below the threshold, nearly all selfed zygotes are lethal.
- Solid lines in figure 2 show that in the Kondrashov model the mean number of lethals per plant blows up for completely recessive lethal mutations, not only under random mating, but also in any situation where the inbreeding depression is very high and the secondary selfing rate is very low.
Figure 5 demonstrates that for completely recessive lethal mutations the mean number of lethal alleles maintained at low selfing rates increases sharply as the number of loci is increased, confirming that the blow up of the mean number of completely recessive lethals per plant in the Kondrashov model is caused by the assumption of an infinite number of loci.