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Quantitative Genetics

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.

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Quantitative Genetics

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  1. Quantitative Genetics • Up until now, we have dealt with characters (actually genotypes) controlled by a single locus, with only two alleles: Discrete Variation

  2. Many Traits are Polygenic • continuous and quantitative refer to variation, polygenic refers to the mode of inheritance, ("many genes") Quantitative Variation or Continuous variation

  3. 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

  4. Mean (average) # of individuals Z Characterizing a Quantitative Trait Variance in Phenotype (VP) (mean squared deviation from mean) (Phenotype)

  5. # of individuals Z What Causes Phenotypic Variation Among Individuals Genetics? Environment? Both?

  6. Partitioning Variance Total Phenotypic Variance (VP) VG VE VG x E

  7. Fig 8.26 Unspecified source population

  8. Total Phenotypic Variance (VP) VDOM VEPI VADD VG VE VG x E Partitioning Variance Genetic Variance can be subdivided: 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) VEPI = phenotypic variation due to epistatic effects (when the effect of the allele depends on the identity of alleles at different loci)

  9. Dominance and Epistasis BBEE BBee Bbee BBEe bbee BbEE BbEe bbEE bbEe

  10. Additive Genetic Variation VADD= phenotypic variation due to the additive effects of alleles Consider a gene with 2 alleles, A1 and A2: How much does each additional copy of A1 add to phenotype? Which of these can be passed on to offspring?

  11. Total Phenotypic Variance (VP) VENV VG VE VG x E Partitioning Variance Environmental Variance can be subdivided: VEN V= phenotypic variation due to random environmental influences VCOM = phenotypic variation due to common family influences VCOM VMAT VMAT = phenotypic variation due to maternal influences

  12. Maternal Environment Effect in Guppy Offspring Size Food stressed mothers produce larger offspring Reznick and Yang 1993

  13. 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

  14. Total Phenotypic Variance (VP) VDOM VEPI VENV VCOM VMAT VG x E VADD VG VE VG x E Total Phenotypic Variance (VP) VADD Partitioning Variance 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]

  15. Dominant A2 Additive effects Why only Additive Genetic Variance? The additive effects of alleles are responsible for the degree of similarity between parents and offspring 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 A2A2 A1A2 A1A1 a d ADD only 10 8 6 2 0 w/ DOM 10 10 6 2 2

  16. Dominant A2 Additive effects Why only Additive Genetic Variance? The additive effects of alleles are responsible for the degree of similarity between parents and offspring A1A2 x A1A2 Parents = 8 Parents = 10 Offspring = .25(6)+.5(8)+.25(10) = 8 Offspring = .25(6)+.5(10)+.25(10) = 9 Dominance causes offspring phenotype to deviate from parental phenotype!

  17. 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

  18. Slope = 0.89 Offspring phenotypic trait value Mid-parent phenotypic trait value Measuring Heritability Heritability is the slope of the regression between offspring and mid-parent phenotype h2= 0.89 Can look at other relatives too! Slope(mom,daughter) = ½ h2 Slope(half-sibs) = ¼ h2

  19. 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

  20. Total Phenotypic Variance (VP) VADD Notes about h2 • Heritability is NOT THE PROBABILITY A TRAIT IS INHERITED OR THE PROBABILITY A TRAIT HAS A GENETIC BASIS • Estimates of heritability are specific to the population in which they are measured. • 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) • high heritability doesn't mean environment doesn't matter or, vice versa, low heritability doesn't mean genes aren't important. Total Phenotypic Variance (VP) VADD

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