## Igfv

-| Genotypic value of A1A1 relative to M

Genotypic value Genotype

-| Breeding value of A1A1 Dominance deviation

Midpoint = 0

1.155 Genotypic value of A,A, relative to M 1.26 Breeding value of A1A1 -0.105 Dominance deviation

Figure 10.3 Illustration of dominance deviation for the IGF1 gene in dogs. The dominance deviation is the difference between the genotypic value (measured relative to the population mean, M) and the breeding value. The dominance deviation is a consequence of the heterozygote genotypic value not falling at the midpoint. Panels (a) and (b) correspond to cases (c) and (d), respectively, in Tables 10.3, 10.5, and 10.7.

Interact box 10.1 Average effects, breeding values, and dominance deviations

Average effects, breeding values, and dominance deviations across all allele frequencies can be interactively graphed using an Excel spreadsheet. Parameter values of a and d can be set in the model. Use a = 10.5 as in the IGF1 example. Then set d to 0.0 and 5.25 view the graphs in each instance.

Another way to understand the breeding values is to determine the total breeding value in a population where all three genotypes are mating at random. Let the population of parents have Hardy-Weinberg expected genotype frequencies of p2, 2pq, and q2. To find the average breeding value of all three genotypes in the parental population, multiply the breeding value of each genotype by its corresponding genotype frequency. This gives

Mean breeding value of all genotypes

This equation can be simplified by factoring 2pq from each term and expanding (q - p)a in the middle term to give

Mean breeding value of all genotypes

The conclusion is that the mean breeding value of all three genotypes mating at random is zero. This result makes intuitive sense because when a large parental population composed of genotypes in Hardy-Weinberg expected 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. It is only when genotypes mate more or less often than expected by random mating that the progeny population mean value differs from the parental population mean value. Note that with natural or artificial selection, mating is by definition non-random and some genotypes mate more frequently than others. It is the over- or under-representation of parental genotypes in mating that causes the mean value of progeny to differ from the mean value of their parents.

### Dominance deviation

With the breeding value established, we can now focus on the dominance deviation that makes up the second portion of the total mean genotypic value in G = A + D (equation 10.25). While the breeding value measures the mean value of alleles passed to progeny by a given genotype, these same progeny also possess genotypes. Due to dominance, genotypes may not completely reflect the combinations of the alleles that make them up. For example, with complete dominance of the A1 allele, an A1A2 genotype masks the fact that it has one A2 allele since its phenotype is indistinguishable from that of an A1A1 genotype. When there is no dominance, the average value of progeny is a perfect representation of the parental genotypic value. However, dominance changes the average value of progeny and can make the breeding value different than the parental geno-typic values. The difference between the genotypic value and the breeding value caused by dominance is called the dominance deviation.

Dominance deviation The difference between the genotypic value and the breeding value where the genotypic value is measured relative to the mean value of the population.

Expressions for the dominance deviations are obtained by taking the difference between the genotypic value and the breeding value for each genotype. We have already obtained all of the expressions needed for the dominance deviation. We do, however, need to obtain one new equation. Since breeding values are expressed relative to the population mean, we have to start by also expressing genotypic values relative to the population mean rather than relative to the midpoint. For the A1A1 genotype, the difference between the genotypic value and the population mean in equation 10.4 is a - (a(p - q) + 2pqd) (10.39)

which simplifies to

as the genotypic value of A1A1 relative to the population mean.

 Table 10.6 Expressions for genotypic values relative to the population mean, breeding values and dominance deviations. Genotypic values can be expressed relative to the population mean by subtracting the population mean (M = a(p - q) + 2pqd) from a genotypic value measured relative to the midpoint. The dominance deviation is the difference between the genotypic value expressed relative to the population mean (M) and the breeding value.
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