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1 2 3 4 5 6 7 8 Phenotypic value (units of pigment)

Figure 9.2 The phenotypic distribution for a trait determined by two Mendelian loci. This hypothetical phenotype might be something like flower color, ranging between nearly white and deep blue. The genotypes are those expected in a large number of progeny from a cross between two doubly heterozygous (AaBb) parents. Alternatively, the genotype frequencies are those expected in a large number of progeny from a parental population with Hardy-Weinberg genotype frequencies where mating is random and all allele frequencies are V2. Each a or b allele in a genotype causes V4 unit of pigment in the phenotype whereas each A or B allele in a genotype causes 2V4 units of pigment in the phenotype. As the number of loci contributing to the trait increases, the expected frequency of any individual genotype decreases and the phenotypic distribution will become smoother. For this phenotypic distribution the mean = 5, the variance = 4, and the coefficient of variation (CV) = 40.

a normal distribution with symmetry about a single central mode. This hypothetical two locus pigment trait has five classes between 10 and 90% pigment that are evenly spaced as expected for a quantitative trait. One assumption in Fig. 9.2 is that the population of individuals is large. This ensures there is not a lot of chance sampling variation that would cause an observed distribution of phenotypes to differ greatly from its expected frequencies (e.g. due to chance no individuals with 10% pigment phenotypes are observed). This assumption is implicit in all of the expectations in quantitative genetics.

As the number of loci determining a trait increases, the phenotypic differences between adjacent genotype classes also decreases, resulting in a phenotypic distribution that is smoother. For a phenotype where there is codominance (also known as semi-dominance) and allele frequencies are all 1/2, the expected frequencies of each class of phenotypic values can be found by taking the expected frequencies of the three geno-

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