chapter 3: deviations from the hardy- weinberg equilibrium systematic deviations selection,...
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Chapter 3: Deviations from the Hardy-
Weinberg equilibrium
• Systematic deviations
Selection, migration and mutation
• Random genetic drift
Small effective population size
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Deviations from the Hardy-Weinberg law
Systematic deviations:
• Migration
• Selection
• Mutation
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Deviations from theHardy-Weinberg law
Selection
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Deviations from the Hardy-Weinberg law
Migration
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Deviations from theHardy-Weinberg law
Mutation
Small population size, random changes
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Mutation:
The selection coefficient has the symbol s
The mutation frequency has the symbol Selection mutations equilibrium occurs when:
q2 s = for the recessive genes
pq s = p s = for the dominant genes
Deviations from theHardy-Weinberg law
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Genetic load
• Selection can cause the death of some individuals or make them unable to reproduce
• This cost is called a genetic load
Belgian Blue cattle
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Selection against the recessive
Genotype EE Ee ee Total
Frequency p2 2pq q2 1,00Fitness 1 1 1-s Proportion p2 2pq q2 (1-s) 1-sq2
after selection
Fitness is constant (1-s). That is the opposite of selection, s
Genetic load = sq2
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Selection against the recessive:Example
Example: q =0,25 and s=1:
Genotype EE Ee ee Total
Frekvens 0.5625 0.375 0.0625 1.00Fitness 1 1 0 Proportion 0.5625 0.375 0 0.9375after selection
q’ = (2pq/2 + q2 (1-s))/(1-sq2) = (0.375/2 + 0)/ 0.9375 = 0.20
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Selection against the recessive:Several generations
Formula for the calculating of gene frequency in the following generation
q’ = (2pq/2 + q2 (1-s))/(1-sq2)
q
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Selection against the recessive:Formula for s=1
Expansion to n generations for s=1:
qn = q0/(1+n q0)
n can be isolated
n = 1/qn - 1/q0
Example: Gene frequency changes from 0.01 to 0.005
n = 1/0.005 - 1/0.01 = 200 - 100 = 100 generations
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Bedlington-terrier, example
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Genotype EE Ee ee Total
Frekvens p2 2pq q2 1,00Fitness 1-s1 1 1-s2 Proportion p2 (1-s1) 2pq q2 (1-s2) 1-p2s1 - q2s2
after selection
Genetic load = p2s1 + q2s2
Selection for heterozygotes
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Selection for heterozygotes: Equilibrium frequency
After selection the gene frequency is calculated by use of the gene counting method:
q' = (q2 (1-s2) + pq)/(1-p2s1 - q2s2)
And equilibrium occurs at:
q = pq(ps1- qs2)/(1-p2s1 - q2s2) = 0
for: ps1- qs2 = 0
q= s1 / (s1 + s2)
which is the equilibrium frequency
^
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Selection for heterozygotes: Fitness-graph
Relative fitness by over dominance
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In the population 5% is born with sickle cell anaemia.
q2 = 0.05 q = 0.22 s2 = 1
Equilibrium occurs at:
p= s2 / (s1 + s2) = 1 - qWhich solved gives:
s1 = (s2 /(1 - q)) - s2 = 0.285
^
Sickle cell anaemia in malaria areas
Selection for heterozygotes: Example
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Selection against heterozygotes
The gene couting method gives:
q' = (q2 (1-s2) + pq)/(1-p2s1 - q2s2)
Equilibrium occurs at:
q = pq(ps1- qs2)/(1-p2s1 - q2s2) = 0
forq = s1 / (s1 + s2)
The equilibrium is unstable
^
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Small populations
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Binominal variance on p or q:
2 = (pq)/(2N),
2N is equal to the number of genes, drawn
from the population to form the new generation
Small populations: Variance on the gene frequency
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Small populations, continued
The standard deviation of the gene frequency
Number of genes
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Effective population size (Ne)
The number of sires and dams for the new generation has
significance for Ne
Ne the harmonic mean of the two sexes
4/Ne = 1/Nmales + 1/Nfemales
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• 10 males and 10 females
4/Ne = 1/10 + 1/10 which gives Ne = 20
• 1 male and 10 females 4/Ne = 1/1 + 1/10 which gives Ne = 3.7
• 100 males and 100000 females 4/Ne = 1/100 + 0 which gives Ne = 400
Effective population size (Ne): Examples
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Increase in the degree of inbreeding
(F)The increase in inbreeding per generation is dependent on the effective population size (Ne)
F = 1/(2Ne)
In a population with Ne = 20, the increase in each generation is delta F = 2.5 %.
The inbreeding coefficient F is defined in the next chapter.