Genetics of Complex Traits: Quantitative Genetics

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Genetics of Complex TraitsQuantitative Genetics
Extra Credit Question Given in Email
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Genetic Variation
Discrete Variation (presence/absence of tail)

• Continuous Variation (height)

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Height Weight Athletic ability Risk of heart
disease Risk of diabetes Risk of cancer

• Polygenic
• Environmental influences
• Have continuous (not discrete) distributions

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Quantitative Traits

• Polygenic
• Environmental influences
• Have continuous (not discrete) distributions
• Can be measured on a quantitative scale

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Intermediate dominance additive gene action
Partial dominance
Discrete distribution
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Red
Pink
Lt Red
Lt Red
Lt Red
Pink
Pink
Lt Pink
Pink
Lt Pink
Pink
Lt Red
Lt Pink
white
Lt Pink
Pink
1 Red 4 Lt Red 6 Pink 4 Lt Pink 1 white
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Two additive genes discrete phenotypic
distribution
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Color of wheat kernels three additive genes
aabbcc AABBCC
AaBbCC
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Several additive genes
Plus environmental noise
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Additive Genes

• Additive genes Phenotypes Genotypes
• (n) (2n1) (3n)
• 3
  3
• 5
  9
• 7
  27
• 5 11
  243
• 21
  59,049
• 20 41
  3,486,784,401

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Frequency Distribution of Height of the Band
mean68 inches
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Properties of distributions
n160
Mean 68 inches
Variance
9.5 in2
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Types of Variance

• Phenotypic variance total variance of the
  population, includes variation from genes and
  from the environment
• Genetic variance the variance that is due to
  variation among individuals in the alleles that
  they have, excludes environmentally-caused
  variation

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Phenotypic Variance
Mean 68 in
Var 9.5 in2
Phenotypic variance Genetic variance Environ.
variance VP
VG VE
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Phenotypic variance Genetic variance Environ.
variance VP
VG VE
Genetic variance Additive variance Dominance
Variance VG VA
VD
VP VA VD VE
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Additive and Dominance Effects (No Environmental
Effects)
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Mean 18.5 cm
Var 1.333 cm2
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Var 1.333 cm2
VP VA VD VE
1.333
1.0
0.333
0
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Heritability
VP VA VD VE
1.0
Broad-sense heritability H2 VG/VP
0.75
Narrow-sense heritability h2 VA/VP
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Uses of heritability

• The degree to which offspring resemble their
  parents is determined by the narrow-sense
  heritability h2
• The efficacy of natural and artificial selection
  is also determined by h2

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h2 1
VA/VP 1
h2 0
VA/VP 0
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Efficacy of artificial selection size of
Labradors
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Breeders Question

• Q A horse breeder wants to win the Kentucky
  Derby. If she breeds her mare to a really fast
  stallion, how likely is it that the colt will be
  faster than all the other three-year-olds when it
  runs in the Derby?

A It depends on the heritability of running
speed!
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Breeders Equation

• R h2 S
• S Selection differential
• difference between selected parents and the
  population as a whole (within a generation)
• R response to selection
• difference between selected offspring and the
  unselected population (across generations)

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Breeders Equation

• R h2 S
• A dog breeder chooses his largest dogs to breed
  together. The average height of the breed is 60
  cm (at the shoulder), and the dogs he chooses to
  breed average 70 cm tall.
• He knows from previous work that the heritability
  of height is 0.5.
• How big can he expect the offspring to be?

0.5 10cm 5cm
R h2 S
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Breeders Equation

• R h2 S 0.5 10 cm 5 cm
• If the response to selection is 5 cm, he can
  expect his puppies to grow to be
• 60 cm 5 cm 65 cm tall

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Exactly the same equation can be used to
understand natural selection!
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Efficacy of natural selectionDarwins finches
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If large bills are favored in drought years, what
effect will an El Nino year have on the
population?
h2 0.8
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R h2 S

• Birds that survive the drought have bills that
  are 2 mm deeper (on average) than the population
  mean.
• Q What will happen to the average bill depth in
  the next generation?