Phenotypic variation in human height

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• Phenotypic variation in human height

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Phenotypic variation in Human Swimming speed
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Note the near perfect bell-shaped curve. So, by
the central limit theorem from probability, the
sum of 6 binomially distributed random
variables is already normally distributed.
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Note the recovery of parental phenotypes in the
F5 generation even though all members of F1 were
heterozygotes.
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Effects of environment on phenotype. So, in the
context of our previous discussion, some of this
difference is a result of Ve
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Monkey Flowers

• Several species that are pollinated differently
• Bee pollinated (Shallow, yellow, landing strip)
• Hummingbird pollinated (Tubular, red, nectar)
• Reproductively isolated in the field.
• Easily hybridized in the lab.

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Monkey Flowers

• Note the ancestral condition is a bee pollinated
  flower.
• Are the alleles that cause these differences
  subtle in their effects, or are they obvious in
  their effects?

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QTL Mapping in Monkey Flowers

• Selected 66 possible marker loci.
• Parental genotype was essentially homozygous for
  floral morphology.
• Crossed the 2 species in the lab to produce F1
  hybrids.
• Crossed the F2s to produce 465 individuals.

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• The logic behind QTL mapping

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Notice the bars on the right of each graph these
QTLs explain a considerable amount of the
variation in the phenoptypic variance.
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Likelihood ratios

• General statistical procedure.
• In our case
• Imagine 2 scenarios
• QTL and marker locus that are on different
  chromosomes, or recombine in an unlinked fashion.
• QTL and marker locus that are linked, and
  crossover only 10 of the time.

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Likelihood ratios

• With linkage set at 0.1, the expected gametes
  from an F1 individual that is MP/mp would be
• MP 45
• Mp 5
• mP 5
• mp 45
• So, the probability of getting an MP/MP offspring
  would be (.45)(.45) .2025

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Likelihood ratios

• With linkage set at 0.5 (free recombination), the
  expected gametes from an F1 individual that is
  MP/mp would be
• MP 25
• Mp 25
• mP 25
• mp 25
• And the proportion of MP/MP offspring would be
  (.25)(.25) .0625

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Likelihood ratios

• To get the likelihood ratio, divide the liklehood
  of the linkage scenario by the likelihood of the
  free recombination scenario.
• 0.2025/0.0625 3.24
• So, the double homozygote is 3 times more likely
  under the linkage model than under the free
  recombination model.

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Likelihood ratios

• Next, we need to do this for multiple
  individuals, or across an entire population.
• Here, we take the log of the likelihood ratio to
  produce a LOD score (log of the odds).
• Imagine we have 10 individuals with the following
  genotypes (and their likelihood ratios)
• 3 MMPP 3 x .511
• 4 MmPp 4 x .215
• 1 Mmpp 1 x -.444
• 2 mmpp 2 x .511
• The total sum is then 2.97
• Generally, If this value is 3.0 or larger, we say
  the trait locus and the marker are linked.

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Selection Gradient and Selection Differential

• Selection Differential Difference between mean
  for a particular train among the survivors and
  the mean for the entire population.
• Selection Gradient Selection differential
  divided by the variance of the trait. We can
  show easily that this is really the slope of the
  regression of fitness on the trait.