Download Population Genetics HWE as an orgy

11/3/2012
Population Genetics
Hardy-Weinberg
• G.H. Hardy
• Wilhelm Weinberg
• Published independently in early 20th
century
• Hardy-Weinberg equilibrium model
– Serves as a null model
– Model for diploid organisms
– Allele frequencies are constant if
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No selection
No mutation
Random mating
No movement into (immigration) or out of
(emigration) the population
• Population infinite
HWE as an orgy
Relative Allele Frequencies
• Frequencies are simply the number of
occurrences
• Relative frequencies are the proportions of
occurrences
• Must sum to 1.0
– If 100 individuals, what is the relative frequency of
A1 and A2 if 14 individuals are homozygous A1 A1,
63 are heterozygous and 23 are homozygous A2 A2
– A1 =
A2 =
1
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Mind your p’s and q’s
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Example of HWE
p = f[A1] = f[A1]+ f[A1]/2
q= f[A2] = f[A2]+ f[A2]/2
p+q=1
p2 + 2pq + q2 = 1
HWE predictions p and q is constant
HWE Example: Takata et al. 2002
• f[A1]= p=0.755, q=0.245
• Expected values
– f[A1A1] = p? = ?
– f[A1A2] = ?pq = ?
– f[A2A2] = q? = ?
• Observed
– f[A1A1] = 0.59
– f[A1A2] = 0.33
– f[A2A2] = 0.08
HWE with natural selection
• Selection coefficient (s)
• Fitness (w)
– Scaled to 1
– Fitness of most fittest = 1
– Other alleles, w = 1- s
• How well does expected = observed?
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HWE with natural selection
• Simulations
– deterministic
– http://darwin.eeb.uconn.edu/simulations/selectio
n.html
• Possible outcomes
– Fixation
• 1 or 0
– Balanced polymorphism
What we learned
• In terms of fixation, polymorphisms and rates
describe:
• Frequency of A1 in dominant/recessive model
– Selection against dominant:
– Selection against recessive:
• Frequency of A1 in codominance model
• Frequency of A1 in overdominance model
– Starting p = 0.5, 0.1, 0.9
• Frequency of A1 in underdominance model
– Starting p = 0.5, 0.1, 0.9
Frequency dependent selection
• Just showed frequency-independent selection
– Values are constant
• Frequency-dependent selection
– Positive: increasing fitness with increasing frequency
– Negative: the rarer the allele the higher the fitness
Mutation and HWE
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Mutations
Mutation Rates
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Mutations in a 2 allele system
Mutations and HWE
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p’ = p(1-µ) + qν, where p’ is frequency of p at t+1 and
p* 
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
 
Where p* is the frequency of A1 at equilibrium
Try changing values of mu and nu
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One more term for phylogenetics
• Autapomorphy
• Plesiomorphy
• Symplesiomorphy
Coalescent Theory
• Gene Trees vs.
Phylogenetic Trees
– Phylogenetic trees show
the relationships among
taxa
– Gene trees show the
relationship among
different forms of the
gene
• Genetic Drift
• http://darwin.eeb.uconn.edu/simulations/drif
t.html
Coalescent Theory
• Figure 8.14
• 8.14A . Gene copes i, ii,
and iii coalesce at the
red dot
• 8.14B. All gene copies
coalesce at the green
dot
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Coalescent Theory
• Time to coalesce is 2N
for a randomly chosen
pair of gene copies
• Time to coalesce is 4N
for a larger set of gene
copies
Coalescent Theory and You!
• Mitochondrial DNA show
coalesce 200,000 years ago
• Y chromosome has genes that
coalesce at 35,000 years ago
• Human-Neanderthal: 400,000
years ago
Natural section and molecular
evolution
• If a gene mutation does not affect fitness (i.e., is
neutral) then the frequency of the mutation is
equivalent to the mutation rate
• If a mutation is beneficial (i.e., increases fitness)
then it should increase in frequency
– Positive selection
• If a mutation is deleterious (i.e., decreases fitness)
then it should be less frequent
– Purifying selection
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Pleiotropy and selection
Read chapters 11 and 12
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