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Quantitative Genetics • Up until now, we have dealt with characters (actually genotypes) controlled by a single locus, with only two alleles: Discrete Variation Many Traits are Polygenic Quantitative Variation or Continuous variation • continuous and quantitative refer to variation, polygenic refers to the mode of inheritance, ("many genes") Studying Quantitative Traits • It would be impossibly difficult to use the same approach as population genetics to consider inheritance at many many loci, especially if the number of loci is unknown • We need to look at DISTRIBUTIONS of characters rather than frequencies of alleles Characterizing a Quantitative Trait Mean (average) z # of individuals Variance in Phenotype (VP) (mean squared deviation from mean) zi z N Z (Phenotype) 2 What Causes Phenotypic Variation Among Individuals # of individuals Genetics? Environment? Both? Z VP VG VE VG x E Partitioning Variance VP VG VE VG x E Total Phenotypic Variance (VP) VG VE VG x E Fig 8.26 Unspecified source population Partitioning Variance Total Phenotypic Variance (VP) VG VE VG x E Genetic Variance can be subdivided: VADD VDOM VEPI VEPI = phenotypic variation due to epistatic effects (when the effect of the allele depends on the identity of alleles at different loci) VADD= phenotypic variation due to the additive effects of alleles VDOM = phenotypic variation due to dominance effects (when the effect of the allele depends on the identity of the other allele at that locus) Dominance and Epistasis BBEE BBee Bbee bbee BBEe BbEE BbEe bbEE bbEe Additive Genetic Variation VADD= phenotypic variation due to the additive effects of alleles Consider a gene with 2 alleles, A1 and A2: A1 A1 A1 A2 A2 A2 Additive effects only 10 8 6 W/ dominance 10 10 6 a d How much does each additional copy of A1 add to phenotype? Which of these can be passed on to offspring? Partitioning Variance Total Phenotypic Variance (VP) VG VE VG x E Environmental Variance can be subdivided: VENV VCOM VMAT VEN V= phenotypic variation due to random environmental influences VCOM = phenotypic variation due to common family influences VMAT = phenotypic variation due to maternal influences Maternal Environment Effect in Guppy Offspring Size Food stressed mothers produce larger offspring Offspring Size (mg) 1.4 1.3 1.2 1.1 1 0.9 Low High Maternal Food Level Reznick and Yang 1993 Breaking the Stick of Variation • By breaking the stick of variation, we can determine how much of the phenotypic variation is due to each component. • Selection acts on phenotypic variation, but can only cause evolution if the variation is heritable • Broad-sense heritability: H2 = VG/VP • Narrow-sense heritability: h2 = VA/VP Partitioning Variance Total Phenotypic Variance (VP) VG VADD VDOM VEPI VE VG x E VENV VCOM VMAT VG x E heritability (h2) = the proportion of phenotypic variation that is due to the additive effects of alleles [how much of VP is made up by VADD] VADD Total Phenotypic Variance (VP) Why only Additive Genetic Variance? The additive effects of alleles are responsible for the degree of similarity between parents and offspring Additive effects a = the effect of substituting an A1 or A2 allele Why is there spread around the phenotypic values of 6, 8, and 10 for each genotype? VE Dominant A2 A2A2 A1A2 A1A1 a ADD only 10 8 6 2 w/ DOM 10 10 6 2 d 0 2 Why only Additive Genetic Variance? The additive effects of alleles are responsible for the degree of similarity between parents and offspring Additive effects Dominant A2 A1A2 x A1A2 Parents = 8 Offspring = .25(6)+.5(8)+.25(10) = 8 Parents = 10 Offspring = .25(6)+.5(10)+.25(10) = 9 Dominance causes offspring phenotype to deviate from parental phenotype! So, What is Heritability? Heritability describes the proportion of variation in trait that can respond to selection Broad-sense Heritability (H2 = h2B = VG/VP) – could include dominance and epistatic variation Narrow-sense Heritability (h2= VA/VP) – proportion of phenotypic variance that is due to additive genetic causes Measuring Heritability Offspring phenotypic trait value Heritability is the slope of the regression between offspring and mid-parent phenotype slope = covariance between parent & offspring variance of parents h2= 0.89 Slope = 0.89 Can look at other relatives too! Mid-parent phenotypic trait value Slope(mom,daughter) = ½ h2 Slope(half-sibs) = ¼ h2 Meaning of Heritability • Evolution by natural selection can only occur in pops A &B • h2=0 in pop C--> none of the variation is due to VA • h2 is undefined, there is no variation Notes about h2 1) Heritability is NOT THE PROBABILITY A TRAIT IS INHERITED OR THE PROBABILITY A TRAIT HAS A GENETIC BASIS 2) Estimates of heritability are specific to the population in which they are measured. 3) heritabilities are statements about variance, not means (e.g., the number of eyes in humans has a 0 heritability, but this doesn't mean that eye number is not under genetic control) 4) high heritability doesn't mean environment doesn't matter or, vice versa, low heritability doesn't mean genes aren't important. VADD VADD Total Phenotypic Variance (VP) Total Phenotypic Variance (VP)