Covariances of Relatives Stemming from a Population Undergoing Mixed Self and Random Mating

Abstract

We consider covariances of all parent and first-generation relatives from outcrossing or self-fertilization in a parent population that is in equilibrium with respect to these processes. The results, which are for any number of alleles and loci with additive and dominance effects, are phrased in terms of six quadratic genetic components whose coefficients are given by descent measures for equilibrium populations. Because of the variation in the inbreeding coefficients for this system of mating, the expressions include joint contributions of loci to the variances and covariances of relatives. By inclusion of the full complement of relatives, all quadratic components can be estimated. The findings of Ghai (1982, Biometrics 38, 87-92) for compound functions of the covariances with two alleles at a single locus are analyzed in terms of the more general model.

An experimental method for evaluating the contribution of deleterious mutations to quantitative trait variation

“…The ' homozygous dominance effect ' is the dominance deviation associated with a particular allele when that allele is in homozygous form. As shown by Cockerham & Weir (1984), the values for these quantities at a single diallelic locus are…”

“…(Here, I use the term directional dominance instead of the more familiar ' inbreeding depression ' because the latter is often formally defined as a ratio.) Under the model outlined above, the directional dominance associated with a single locus is k2pqd (Cockerham & Weir, 1984). The overall value for B is the sum of this quantity across all quantitative trait loci.…”

“…With inbreeding, the mean phenotype is MjFB, where F is the mean inbreeding coefficient (Jacquard, 1974 ;Cockerham & Weir, 1984). The genetic variance with inbreeding depends on V a , V d and several additional quantities (Harris, 1964 ;Jacquard, 1974 ;Cockerham & Weir, 1984 ;Cornelius, 1988 ;de Boer & Hoeschele, 1993).…”

“…In fact, C ad may be negative when recessive alleles occur at high frequencies (greater than 0n5). All these quantities can be estimated from phenotypic comparisons among relatives if inbred individuals are included in the pedigree (Cockerham & Weir, 1984 ;Cornelius, 1988 ; The ratio of C ad or V hd to the additive genetic variance given the frequency of a partially recessive allele. In this case, the heterozygous effect of the allele is 20 % of its homozygous effect (h l 0n2; d lk0n6a).…”

“…The first is simplicity : the cumulative change in the directional dominance can be measured simply by generating inbred progeny from the base population (or a non-selected control population) and from the selected population. The difference in mean values of inbred and outbred individuals provides an estimate of B (Cockerham & Weir, 1984). Secondly, sampling errors in estimates of C ad and V a , which are caused by genetic drift in this type of experiment, should be positively correlated when quantitative trait variation is caused primarily by rare recessive alleles.…”