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:
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–
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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
a
mean
e
Trait value
p
Dominance
No dominance
= additive
• 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
Complete dominance
aa
Aa
AA
Overdominance
aa
Aa
AA
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:
2
h
estimates for IQ
Can the environment alter expression of a trait when h2 = 0.5?
French IQ experiment
h2 from Artificial Selection
h2 = 0
h2
=
1/4
h2 = 1
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
2
h
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
Heritabilities in
Drosophila
Note:
life history traits
tend to have low
heritabilities,
presumably
because selection
reduces genetic
variation, but
almost all traits
have some
heritable variation
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
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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.
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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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