Chapter 10 review

• Genotypic values can be expressed on an arbitrary scale with +a and -a representing the values of the homozygotes with respect to a midpoint between +a and -a of zero. The value of the heterozygote is represented by d.

• The mean phenotypic value of a population with Hardy-Weinberg expected genotype frequencies is M = a(p — q) + 2pqd where p is the frequency of the allele that increases value and q is the frequency of the allele that decreases value.

• The average effect of an allele is the difference between the mean value of that subset of genotypes that contain a given allele and the mean value of the entire population. Because alleles are inherited and genotypes are not, the average effect describes the mean value of those progeny that inherit a certain allele from one parent and the other allele sampled at random from the population.

• The genotypic mean is the sum of the breeding value and the dominance deviation.

• The breeding value of an individual is the mean value of the progeny produced by a given genotype assuming random mating. The breeding value is the sum of the average effects of the alleles in an individual's genotype.

• The dominance deviation is the difference between the genotypic value of a given genotype and the breeding value. When there is dominance (d ^ 0), those progeny that are heterozygotes will have a value that is not the sum of the two alleles in their genotype.

• Since the mean breeding value of all genotypes is zero in a population under random mating, the mean value of a population should not change from one generation to the next under the many assumptions of Hardy-Weinberg.

• The variance in genotypic values around the population mean under random mating, commonly called the total genetic variance VG, is the sum of the squared breeding values and the squared dominance deviations or VG = VA + VD.

• The resemblance in genotypic value between relatives caused by VA and VD can be related to the probability of identity by descent. The expected covariance in genotypic values is a function of the probability that individuals share an allele that is identical by descent plus the probability that individuals share a genotype identical by descent. This covariance in genotypic values forms the basis of the parent-offspring method to estimate heritability.

Further reading

For more details on the Mendelian basis of interaction variance (Vj) as well as numerous perspectives on the role of epistasis in the evolutionary change of phenotypes, see chapters in:

Wolf JB, Brodie ED III, and Wade MJ (eds) 2000. Epistasis and the Evolutionary Process. Oxford University Press, Oxford.

Problem box answers

Problem box 10.1 answer

The entire range of genotypic values is 2a = 30 - 9 = 21. Therefore, a = 10.5 kg. The midpoint is then either 30 - 10.5 = 19.5 or 9 + 10.5 = 19.5. The genotypic value of the heterozygote relative to the midpoint is d = 24.75 - 19.5 = 5.25. The degree of dominance is 5.25/10.5 = 0.50 or 50%.

Problem box 10.2 answer

Case (a):

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