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already taken to represent environmental variance). In Chapter 10, the Mendelian basis of quantitative traits is used to derive quantitative expectations for VG and its components. For now, let's continue to develop an intuitive understanding of the causes of total phenotypic variation in addition to VG and VE.
Components ofgenotypic variation (VG)
Thus far, we have distinguished between the genetic and environmental causes of phenotypic variation. In quantitative genetics, a primary goal is to explain the hereditary causes of phenotypic variation. To fully understand the genetic contribution to total phenotypic variation it is necessary to recognize that VG is itself made up of three separate causal components. The components of the total genotypic variation are
where VA is additive genetic variation, VD is dominance genetic variation, and VT is interaction or epistasis genetic variation.
The additive genetic variance is the genotypic variance caused by the cumulative phenotypic effects of alleles when they are assembled into genotypes. Additive simply means that the phenotypic effect of each allele can be added together to determine the phenotypic value of any genotype. When alleles have additive effects, then the specific pairing of alleles in a genotype, be it a homozygote or a heterozygote, has no impact on the way alleles combine to produce a phenotype. In other words, additivity describes the situation when each allele has the same effect on the phenotypic value regardless of the context where it is found. Figure 9.2 shows an illustration of additive genetic variation in a quantitative trait. Each a or b allele in a genotype contributes V4 unit of pigment in the phenotype whereas each A or B allele in a genotype contributes 2V4 units of pigment in the phenotype. The phenotype of any genotype can be determined simply by adding together the phenotypic effects of the two alleles.
When gene action is additive, the amount of additive genetic variance (VA) in a population depends on allele frequencies. There is more additive genetic variance in phenotype when alleles are at intermediate allele frequencies than when they are near fixation and loss. This is because intermediate allele frequencies result in all possible genotypes (assuming random mating) being represented in the population, which in turn produces a wide range of phenotypes.
Figure 9.2 shows the wide range of phenotypes found in a population where genetic variation is additive and all alleles are at a frequency of V2.
To see how genetic variation causes phenotypic variation when allelic effects are strictly additive, compare Figs 9.2 and 9.4. In both figures, phenotypes for each genotype are determined by adding together the phenotypic effects of the alleles in a genotype (each a or b contributes V4 unit of pigment and each A or B contributes 2V4 units of pigment). However, the allele frequencies in Fig. 9.4 are closer to fixation and loss so there is a much less even genotype frequency distribution in the population. The change in allele frequencies leads to two very common genotypes and three genotypes that are very rare. This reduction in genetic variation causes a reduction in phenotypic variation. With allele frequencies nearer fixation and loss, the frequency distribution of phenotypes is now narrower and clumped around values at the upper end of the range.
Additive genetic variance (V^) The proportion of the total genotypic variance (VG) caused by the sum of phenotypic effects of alleles when they are assembled into genotypes.
In addition to the additive effects of alleles, quantitative trait variation is also caused by the effect of genotypes. Dominance and epistasis are properties of genotypes that can be thought of in two conceptually distinct ways (see Wade 1992; Cheverud & Routman 1995; Phillips 1998). In a physiological or functional sense, dominance and epistasis describe the way phenotypes map to genotypes. Both are forms of genetic interaction. With dominance, the phenotype depends on the combination of alleles within a locus that compose a genotype (allele interactions). With epistasis, the phenotype depends on the combination of genotypes at two or more loci (genotype interactions). Two diallelic loci can produce eight distinct ways by which genotypic values are determined by combinations of twolocus genotypes. These eight genetic effects are illustrated in Table 9.2. In general, there are a total of 3n  1 distinct genetic effects for n diallelic loci (Cockerham 1954; see also Goodnight 2000).
At the same time, both dominance and epistasis have a populationlevel meaning that is statistical. Both dominance and epistasis can be thought of as the "leftover" part of genotypic variance in the population
Table 9.2 The eight uncorrelated (or orthogonal) types of genetic effects that can occur between two diallelic loci. Four of the eight types of genetic effects are interactions that give rise to V.. The genotypic values assume all allele frequencies are 1/2. Table after Goodnight (2000).
Genetic effect Genotypic value
Table 9.2 The eight uncorrelated (or orthogonal) types of genetic effects that can occur between two diallelic loci. Four of the eight types of genetic effects are interactions that give rise to V.. The genotypic values assume all allele frequencies are 1/2. Table after Goodnight (2000).
Genetic effect Genotypic value
Genotypes and 

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