Quantitative Genetics

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Quantitative Genetics

• Genetics of Complex Phenotypes

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Simple Trait Color of Snapdragons
Intermediate dominance additive gene action
Discrete distribution
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More complex trait color of wheat kernels
three additive genes
aabbcc AABBCC
AaBbCC
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Genetic effects on Quantitative Traits
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Complex trait Genetic and non-genetic effects
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Mean and Variance of a Distribution
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Phenotypic Mean and Variance of a Quantitative
Trait
of individuals
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Phenotypic Mean and Variance of a Quantitative
Trait
of individuals
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Question

• If two populations have different phenotypic
  means, is the difference due to heredity or due
  to the environment?
• How could you tell?

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Is variation genetic or non-genetic?

• Raise individuals from populations with different
  means in the same environment common garden
  experiment.
• Raise individuals with same genotype under
  different environmental conditions.

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Genetic and non-genetic effects on quantitative
traits Quantified as genetic and non-genetic
variance in the trait
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Types of Variance

• Phenotypic variance
• Genetic variance

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Phenotypic Variance
Mean 68 in
Var 9.5 in2
Phenotypic Genetic Environmental Variance
Variance Variance VP
VG VE
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Phenotypic Genetic Environmental Variance
Variance Variance VP
VG VE
Genetic variance Additive variance Dominance
Variance VG VA
VD
VP VA VD VE
What do we mean by Additive Genetic Variance
and Dominance Genetic Variance
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Additive and Dominance Effects (Ignore environ.
effects for now)
Body length, in cm.
If an A1A2B1B2 mouse mates w/ an A2A2B1B2 mouse,
what is the mean size of the parents?
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A1A2B1B2 X A2A2B1B2 7
8 mean What is the mean size of the
offspring? All these offspring types are equally
likely A1A2B1B1 6 A2A2B1B1
7 A1A2B1B2 7 A2A2B1B2 8 A1A2B2B1
7 A2A2B2B1 8 A1A2B2B2 7 A2A2B2B2
8 mean
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A1A2B1B2 X A2A2B1B2 7
8 mean What is the mean size of the
offspring? All the offspring types are equally
likely A1A2B1B1 6 A2A2B1B1
7 A1A2B1B2 7 A2A2B1B2 8 A1A2B2B1
7 A2A2B2B1 8 A1A2B2B2 7 A2A2B2B2
8 mean variance How much
of the offspring variation is due to genetic, and
how much to non-genetic variation? How much
variation is due to additive effects and how much
to dominance effects?
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Genotypic values
Genotype DD Dd
dd Phenotype 5 4 1 Genotypic a
d 0 -a
value a d
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VA2pqad(q-p)2VD(2pqd)2
Single locus
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Ways to Measure VA and VD

• Straightforward to estimate ratio of VA to VP
  this is the heritability
• h2VA/VP
• The degree to which offspring resemble their
  parents is determined by the narrow-sense
  heritability, h2

VP VA VD VE
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Measuring Genetic Variance

• Mseasures of resemblance among other kinds of
  relatives can also be used to measure genetic
  variance and heritability.
• Parents and offspring--share only additive
  variation. Correlation between parent and
  offspring 1/2(VA/VP)
• Half Sibs--share only additive variation.
  Correlation among half sibs 1/4(VA/VP)
• Full Sibs--share additive and dominance effects
  b/c some full sibs will have the same genotype.
  Correlation among full sibs 1/2(VA/VP) 1/4
  (VD/VP)

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h2 1

• h2 can be measured as the linear relationship
  between parental phenotypes values and offspring
  phenotypes.

VA/VP 1
h2 0
VA/VP 0
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It is simple to measure VP. So once you know h2
and VP, can easily calculate VA. However, there
are some assumptions being made here.
h2 0.8
VA/VP 0.8