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Heritability – “the fraction of the total variation in a trait that is due to variation in genes.” (Freeman and Herron, 2007) Typically, this variation is considered as the phenotypic variation. Vp – the total variance in the phenotypic trait of a population. VP = VG + VE VG = Genetic variation VE = Environmental variation Broad Sense Heritability h2 or H2 ℎ2 ℎ2 = 𝑉𝐺 𝑉𝑃 𝑉𝐺 = 𝑉𝐺 + 𝑉𝐸 The problem? VG represents all of the genetic variation as a single value. Real genetic variation is complicated. V𝐺 = V𝐴 + V𝐷 + V𝐼 VA = additive genetic variance VD = dominance genetic variance VI = variance due to epistatic interactions Additive Variation –VA V𝐺 = V𝐴 + V𝐷 + V𝐼 • Important because it is why relatives resemble each other. • Alleles act independently. • The phenotype of an organism is the sum of the effect of each allele, hence additive. • Additive alleles are not affected by the presence of other alleles. • The effect of additive alleles allow biologists to follow evolution in a predictable way. Additive Variation –VA V𝐺 = V𝐴 + V𝐷 + V𝐼 A1 = 0.5, A2 = 0.5 Note: The best fit line (far right) explains all of the genetic variation. VG = VA. Dominance Variation –VD V𝐺 = V𝐴 + V𝐷 + V𝐼 • The addition of alleles is not additive. • Dominance is one type of variation where alleles interact (between sister alleles on other chromosome). • The effect of an allele depends upon what it is paired with. • Because of this dependence, the outcome of dominance variation is not entirely predictable - it is context dependent. • This context disappears every generation because of meiosis. The pairing of an allele with a sister allele on another chromosome in forming a zygote is unpredictable. • Because of this , the effects of dominance variation change every generation, and are not predictable. Dominance Variation –VD V𝐺 = V𝐴 + V𝐷 + V𝐼 A1 = 0.5, A2 = 0.5 Note: Adding a second copy of A2 does not change the phenotype. The Dominance Variation (VD) does not explain all of the Genetic Variation (VG). VG = VA + VD Epistatic Effects –VI V𝐺 = V𝐴 + V𝐷 + V𝐼 • The effect of an allele at a locus is dependent the presence of an allele at another locus. • The phenotype is dependent upon the allele at one locus interacting with an allele at another locus. Not a predictable outcome. • Allele X may affect the phenotype one way in the presence of allele A, and affect the phenotype another way in the presence of allele B. • Because of this dependence, the outcome of epistasis is not entirely predictable - it is context dependent. • This context disappears every generation because of meiosis. When chromosomes independently assort and recombine, the pairings of alleles change. • Because of this , the effects of epistasis change every generation, and are not predictable. Narrow-Sense Heritability h2 or H2 ℎ2 = 𝑉𝐴 𝑉𝑃 𝑉 𝐴 2 ℎ = 𝑉𝐺 + 𝑉𝐸 𝑉 𝐴 2 ℎ = 𝑉𝐴 + 𝑉𝐷 + 𝑉𝐼 + 𝑉𝐸 In determining heritability, only narrow-sense heritability is used, because only the variation due to additive effects permits predictions due to selection.