Quantitative inheritance

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Quantitative inheritance
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• Quantitative traits
• Continuos variation (normal distributions)
• Often characterized as being affected by many
  genes expression of which is modified by the
  environment
• Qualitative traits
• Often single gene Mendelian traits
• Segregate into discrete classes

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Distribution of Quantitative trait(s)
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Mean Variance covariance
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Genetic and environmental componentsJohannsen -
1903
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Phenotypic values

• Phenotype P G E
• Phenotypic value is the performance of a
  particular genotype in the environment in which
  it is grown.
• Phenotypic variance s2p s2g s2e s2gxe
  
• The phenotypic variance we observe is due to
  variance among genotypes and environments as well
  due to genotype x environment interactions.
• Requires gt1 genotype and gt1 environment

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Partitioning genetic and environmental effects
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• Source of variation?
• Is the phenotypic variation we observe due to
  differences among genotypes or environments?
• What is the magnitude of experimental error?
• Experimental Design
• Evaluate an array of genotypes over an array of
  environments.
• Use a genotypic structure that can be replicated
• e.g. Clone, or S1, FS or HS families

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Experimental design
Environment 2
Environment 1
In each rep in each environment, evaluate the
array of genotypes
Rep 1
Rep 1
Rep 2
Rep 2
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ANOVA

• Variance sum of squared deviations from the
  mean
• Source Variance
• Environments s2error rs2gxe rgs2environ
• Genotypes s2error rs2gxe rls2genotypes
• GxE s2error rs2gxe
• error s2error

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Components of genetic variance
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• Genotype s2G s2A s2D
• The genotypic value has components due to
• A - the breeding value
• D - the dominance deviation .

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Average effect of allelic substitution
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• The objective of selection is the increase the
  frequency of favorable alleles in populations, by
  substituting favorable alleles for unfavorable
  ones
• How do we measure the transmission of Value?
• We cannot use genotypic values, as meiosis
  results in genes, not genotypes, being
  transmitted from parent to offspring.

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a Average effect of allelic substitution.
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• The effectiveness of gene substitution in
  changing the population mean is related to the
  average effect of allelic substitution a
• Breeding value
• The sum of average effects over all loci S a
• Additive genetic variance 2pqa2
• The variance among individuals in their breeding
  value

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a Average effect
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• We want an expression that can be used to show
  how quantitative traits are transmitted from
  parent to offspring
• The average effect (a) of a gene is the mean
  deviation from the population mean of individuals
  which received that gene from one parent, and the
  other gene at random.

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a Average effect
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• Parent Bb
• B b Difference
• B (p) a d a - d
• b (q) d -a a d
• Therefore a p(a-d) q(ad)
• a a (q - p)d

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Effect of gene frequency on a
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• BB10, Bb10 bb0 a5, d5
• a a (q - p)d
• q .8 5 ( .8-.2)5 8
• q .6 5 ( .6-.4)5 6
• q .5 5 ( .5-.5)5 5
• q .4 5 ( .4-.6)5 4
• q .2 5 ( .2-.8)5 2
• q 0 5 ( 0- 1)5 0

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Additive Genetic Variance
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• s2A 2pqa2
• Fisher (1918 ) showed how total genetic variance
  could be partitioned in to components due to
• Additive genetic variance - variance in breeding
  values
• Dominance genetic variance - dominance deviations
• Epistatic genetic variance - interaction among
  loci

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Additive Genetic Variance
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• s2A 2pqa2
• The original definition of additive genetic
  variance was given by fisher as the variance due
  to linear regression of value (a, d, -a) on
  genotypic frequencies
• It is that portion of the genetic variance that
  is transmitted from parent to offspring

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Additive genetic variance
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Changes in s2Awith changes in gene frequency
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Additive Genetic variance with Dominance
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