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At the allele frequencies in case (d), the dominance deviation is smaller because the frequency of A1A2 individuals in the population is smaller, causing less dominance contribution to the population mean. That ultimately results in a smaller difference between the genotypic value of AXAX measured relative to M and the breeding value of AXAX.

We can also determine the mean dominance deviation in a population where all three genotypes are mating at random. As for the average breeding value, the average dominance deviation of all three genotypes is obtained by multiplying the dominance deviation of each genotype by its corresponding genotype frequency. This gives

Mean dominance deviation of all genotypes

which simplifies to zero since the first and third terms cancel with the middle term. The mean dominance deviation of all three genotypes mating at random is zero. Just as for the mean breeding value, a mean dominance deviation makes intuitive sense because when a large parental population in Hardy-Weinberg expected genotype frequencies mates at random, the mean value of the progeny population should be exactly the same since the progeny genotype frequencies are exactly the same as in the parental population. Thus, the impacts of dominance on the progeny means of each genotype counteract each other to give an overall mean of zero under random mating.

One last illustration will help show the connection between the genotypic values and the genotype frequencies on one hand and the breeding values and dominance deviations on the other. Figure 10.4 shows the least-squares regression line between the genotypic values and the number of A1 alleles in a genotype for a population of 100 individuals (since genotype frequencies equal Hardy-Weinberg expectations, the population contains 25 A1A1, 50 A1A2, and 25 A2A2 individuals). The slope of the regression, line gives the average phenotypic effect of a change in the number of A1 alleles in the genotype. So, for example, changing all A2A2 genotypes to A1A2 genotypes (replacing one A2 allele with an

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