Average dominance for polygenes: drawbacks of regression estimates.

T HE dominance of genes controlling fitness components and other quantitative characters is important for theoretical predictions concerning the maintenance of genetic variability (see e.&, CABALLERO and KEIGHTLEY 1994). Consider, for instance, mutation selection balance at a diallelic autosomal locus with mutation rate p to the deleterious allele and fitnesses 1, 1-sh, and 1-s, with s > 0 and 0 < h < 1. Assuming that p Q sh, the equilibrium mean fitness is approximately 1-2 p, independent of h, but the additive (and total) genetic variance for fitness is approximately 2 p sh (MUKAI et al. 1974), which is directly proportional to h. Moreover, if these genotypes have pleiotropic effects on a quantitative trait, with average effects a, d , and-a, the additive variance for the trait contributed by this locus depends on the deviation d of the heterozygote from the average of the two homo-zygotes, i.e., on the coefficient of dominance for the effects on the trait (FALCONER and MACKAY 1996, Chapter 8). In Drosophila, estimates of the average dominance for newly arising spontaneous mutations (e.g., MUKAI and YAMAZAIU 1968), Pelement insertion mutations HUGHES 1995) have been obtained by regressing the heterozygous effect of the chromosome or line on the sum of the two homozygous effects of the two parental lines (or the homozygous effect of the insertion line only for Pelements). Estimates of also feature prominently in an estimation method for genomic mutation rates for fitness traits based on the performance of selfed and outbred progeny in populations assumed to be at mutation-selection balance (CHARLESWORTH et al. 1990; JOHNSTON and SCHOEN 1995). These and other methods for estimating average degrees of dominance are discussed by LYNCH and WAL~H (1997, Chapters 10 and 20).spectively. In their analysis of viability polygenes segregating on chromosomes sampled from nature, MUKAI et al. (1972) and MUKAI and YAMAGUCHI (1974) showed that the regression coefficient of the heterozy-gous effect on the sum of the two homozygous effects is equal to a weighted average of the coefficient of dominance over loci (E) , CpiqisS [hi + qi (1-2hi) I Cpiqi$hi E = w 9 (1) where the summation is over loci, and the right hand side approximation assumes small values of qi. The reliability of estimates from the regression coefficient depends on two assumptions: (l) that the homozygous effects are known precisely and (2) that the dominance of alleles are uncorrelated with their homozygous …