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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
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