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 continuous and quantitative refer to variation, polygenic refers to the mode of inheritance, ("many genes") Quantitative Variation or Continuous variation

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 # of individuals Z Mean (average) Variance in Phenotype (V P ) (mean squared deviation from mean) (Phenotype)

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

Partitioning Variance Total Phenotypic Variance (V P ) VGVG VEVE V G x E

Fig 8.26 Unspecified source population

Partitioning Variance Total Phenotypic Variance (V P ) VGVG VEVE V G x E V ADD V EPI Genetic Variance can be subdivided: V ADD = phenotypic variation due to the additive effects of alleles V DOM = phenotypic variation due to dominance effects (when the effect of the allele depends on the identity of the other allele at that locus) V EPI = phenotypic variation due to epistatic effects (when the effect of the allele depends on the identity of alleles at different loci) V DOM

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

Additive Genetic Variation V ADD = phenotypic variation due to the additive effects of alleles Consider a gene with 2 alleles, A 1 and A 2 : A 1 A 1 A 2 A 2 ad Additive effects only 1086 W/ dominance10 6 How much does each additional copy of A 1 add to phenotype? Which of these can be passed on to offspring?

Partitioning Variance Total Phenotypic Variance (V P ) VGVG VEVE V G x E Environmental Variance can be subdivided: V EN V = phenotypic variation due to random environmental influences V COM = phenotypic variation due to common family influences V MAT = phenotypic variation due to maternal influences V ENV V COM V MAT

Maternal Environment Effect in Guppy Offspring Size Food stressed mothers produce larger offspring 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: H 2 = V G /V P Narrow-sense heritability: h 2 = V A /V P

Partitioning Variance Total Phenotypic Variance (V P ) VGVG VEVE V G x E V DOM V EPI V ADD V ENV V COM V MAT V G x E heritability (h 2 ) = the proportion of phenotypic variation that is due to the additive effects of alleles [how much of V P is made up by V ADD ] Total Phenotypic Variance (V P ) V ADD

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? VEVE Dominant A2 A2A2 A1A2 A1A1a d ADD only w/ DOM

Why only Additive Genetic Variance? The additive effects of alleles are responsible for the degree of similarity between parents and offspring Additive effectsDominant A2 A1A2 x A1A2 Parents = 8Parents = 10 Offspring =.25(6)+.5(8)+.25(10) = 8Offspring =.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 (H 2 = h 2 B = V G /V P ) –could include dominance and epistatic variation Narrow-sense Heritability (h 2 = V A /V P ) –proportion of phenotypic variance that is due to additive genetic causes

Measuring Heritability Heritability is the slope of the regression between offspring and mid-parent phenotype Mid-parent phenotypic trait value Offspring phenotypic trait value Slope = 0.89 h 2 = 0.89 Can look at other relatives too! Slope (mom,daughter) = ½ h 2 Slope (half-sibs) = ¼ h 2

Meaning of Heritability Evolution by natural selection can only occur in pops A & B h 2 =0 in pop C--> none of the variation is due to V A h 2 is undefined, there is no variation

Notes about h 2 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. Total Phenotypic Variance (V P ) V ADD Total Phenotypic Variance (V P ) V ADD