and response to selection calculated for Fig. 9.10, the realized heritability is then h2 = 1.0/2.5 = 0.40 (9.16)

This tells us that 40% of the variance in trait values in the parental population was caused by additive genetic variation based on the definition of heritability.

Why was there a response to selection? Why did increase in value compared to ||? The phenotypic value in the selected group of parents was greater than the rest of the parental population partly due to the alleles that they possessed in their multi-locus genotypes for this trait. When they bred, these alleles were passed down to their offspring. Selection changed the frequency of alleles that confer larger trait values because allele frequencies in the P1 individuals above the selection threshold were different than in the P1 population as a whole. Alleles that contributed to larger trait values became more frequent in the progeny population than they were initially in the parental population. Therefore, the mean phenotypic value in the progeny population increased relative to the mean phenotypic value of the parental population.

But why is the progeny mean phenotypic value (p') not equal to the mean value of the selected parents (ps)? Parents in the selected group had phenotypic values above the truncation point partly due to causes other than the effects of the alleles in their multilocus genotypes for the trait. Part of the phenotypic variance in the parental generation (Vp) was caused by factors that do not contribute to the resemblance of parents and offspring. The genotypic values of the selected parents were due to the combination of alleles in their genotypes. Such genotype effects cause dominance variance (VD) and interaction variance (Vj) in quantitative trait values. However, these components of the genotypic variance are not inherited and do not contribute to resemblance between parents and offspring on average. In addition, some of the phenotypic variance in the parental population could have been caused by environmental variance (VE) that would also not contribute to resemblance between the selected parents and the offspring. In the example of Fig. 9.10, 60% (or 1 - P2) of the variation in the P1 phenotypic values was caused by the combination of non-additive genetic variation (VD + Vj) and environmental variation (VE). This 60% is the percentage of the selection differential that did not produce a response to selection.

Estimating heritability by parent-offspring regression

Another method used to estimate the heritability based on the resemblance between parents and their offspring is parent-offspring regression. Parent-offspring regressions predict VA without actually carrying out a response-to-selection experiment. This method to estimate heritability is therefore applicable to populations where selection experiments cannot be carried out. Estimation of heritability by parent-offspring regression can even be carried out in natural populations if a reliable method to identify the parents of offspring, such as paternity analysis, is available. This method takes advantage of the fact that the phenotypes of offspring resemble the phenotypes of their parents to the extent that phenotypic values are caused by shared alleles. Neither dominance nor epistasis components of the geno-typic variance are inherited by progeny so they do not cause progeny to resemble their parents. This phenomenon was explained in the first section of the chapter and illustrated in Table 9.3. Now we will revisit the resemblance between parents and offspring in greater depth.

By comparing the phenotypes of parents and their offspring, it is possible to determine the degree of phenotypic resemblance. The necessary data come from the measures of phenotypic values for pairs of parents as well as the phenotypic values of all progeny produced by each pair of parents. Figure 9.11

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