Quantitative Genetics

• Theoretical justification

• Estimation of heritability– Family studies– Response to selection– Inbred strain comparisons

• Quantitative trait loci (QTL)

• Genetic correlations

Most traits follow a normal distribution

When multiple genes affect a trait, expect a continuous distribution

But, the environment also contributes variation

Isogenic line of Drosophila

Quantitative genetics• Partitions genetic and environmental effects• Assumptions

– Each locus contributes additively to the trait– Environmental effects are independent

• Definitions: – p = phenotypic value– g = genotypic value– a = additive genetic value (breeding value)– e = environmental effect– d = dominance deviation

• p = g + e and g = a + d, so p = a + d + e

mean p

a Trait valuee

Dominance

• Exists whenever the phenotype of a heterozygote is not the average of the parental values

• Attribute of a genotype, not an allele• May be scale dependent• Only relationships which can share

genotypes can share dominance, e.g. full-sibs, twins

aa Aa AA

Phe

noty

pe

aa Aa AA

Phe

noty

pe

No dominance = additive

Complete dominance

aa Aa AA

Phe

noty

pe

Overdominance

Heritability

• Vp = Vg + Ve

= Va + Vd + Ve

• heritability = h2 = Va/Vp, i.e the fraction of phenotypic variation due to additive genetic effects, i.e. those which can be passed from parent to offspring

• applies only to population measured

• determines the rate of evolution

Galton’s parent-offspring regression

Note: median offspring values regress toward the parental median

h2 = heritability = slope of the regression of midoffspring on midparent

The regression estimate of heritability

h2 from family resemblance• Offspring and mid-parent: b = Va/Vp = h2

– b is a regression slope

• Offspring and one parent: b = Va/2Vp = h2/2

• Full-sibs (r = 1/2): t ≥ Vg/2Vp = h2/2

• Identical (MZ) twins: t ≥ Vg/Vp = h2

• Half-sibs (r = 1/4): t = Va/4Vp = h2/4– t is a correlation coefficient

• Therefore: resemblance (b or t) = rh2 where r = degree of relatedness

Example: h2 estimates for IQ

Can the environment alter expression of a trait when h2 = 0.5?

French IQ experiment

h2 from Artificial Selection

h2 = 1h2 = 0 h2 = 1/4

Response to selection

R = h2S is the breeder’s equation where

R = the change in means across a generation

h2 = heritability

S = the change in means within a generation due to selection

Response to selection = trait evolution

S

R

Selection for nest building behavior

h2 from inbred strains

• Inbreeding leads to genetic uniformity

• Ve = variation within an inbred strain or among the F1 progeny

• Vp = variation among F2 progeny

• h2 “broad sense” = (VF2 - VF1)/VF2

Avoidance learning by inbred strains

Note: life history traits tend to have low heritabilities, presumably because selection reduces genetic variation, but almost all traits have some heritable variation

Heritabilities in Drosophila

QTL analysis

•Much current work aims to locate and estimate the effect of quantitative trait loci (QTLs)•Use F2 or backcross individuals•Genotype each individual at multiple genetic markers•Construct linkage map•Measure association between markers and trait

Correlated response to selection

Troy Bartlett

Genetic correlations• Multiple potential causes

– Physical linkage (proximity of two loci)– Pleiotropy– Selection for allelic combinations– Nonrandom mating

• Persistance– Pleiotropy decays only by mutation– Linkage decays with random mating due to

recombination

• Can alter response to selection– Negative genetic correlation will cause one trait to

become reduced when another is increased– Expect such neg. correlations for life history traits

Sample problem

• A population of sunfish has an average swimming speed of 80 cm/s, individuals having a mean of 110 cm/s survived a flood to be parents of the next generation; their offspring had a mean speed of 90 cm/s. Calculate the realized heritability for swimming speed.

• Selection differential (S) = mean after selection - mean before selection

• selection response (R) = mean of offspring generation - mean of previous generation

• heritability = response / selection, i.e. h2 = R/S

• So: S = 110 - 80 = 30

• R = 90-80 = 10

• and h2 = 10 / 30 = 0.33