lec_5_cond_13

Relative fitness of a 1 allele w 1 p w 11 qw 12 and

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Relative fitness of A 1 allele = W 1 = p W 11 + qW 12 and by the same logic, Relative fitness of A 2 allele = W 2 = p W 22 + q W 12 A 2 p A 1 A 2 Heterozygotes A 2 A 2 Homozygotes q lastly, using the same logic, average fitness of both alleles taken together = W = p W 2 + q W 1 a proportion p of the alleles have fitness W 1 a proportion q of the alleles have fitness W 2 W is the average fitness of both alleles which is the average fitness of the whole population Next we will use the concept of a weighted average to calculate the average fitness of an allele. First consider the A 1 allele The allele occurs in two diploid genotypes: Homozygotes & Heterozygotes With random mating alleles are randomly associated in zygotes since p of the available alleles to pair with are A1 Pool of available alleles to pair with: p A 1 q A 2 Homozygotes Heterozygotes A 1 p q A 1 A 1 A 1 A 2 and q are A2 22
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Model of Natural Selection Big picture Gene pool p = freq(A1) q = freq(A2) Genotype pool P = prop(A1A1) H = prop(A1A2) Q = prop(A2A2) Gen=0 Gene pool p = freq(A1) q = freq(A2) Gen=1 Natural selection on phenotypes produced by the genotypes W1, W2, W where indicates value in the next generation Returning to Δ CCR5 and AIDS How rapidly will the Δ CCR5 allele (= A1 allele) increase due to natural selection? Answer depends on the fitness advantage of the Δ CCR5 allele, i.e., on the value of W 1 but we know that it could be large compared to W 2 Discovery of Δ CCR5 allele is so new that we do not yet know the value of its selective advantage (W 1 ) 23 Δ p = p ’- p = - p p W 1 W = p ( - 1) Δ q = 1 - Δ p note: all p’s in above table are lower case except genotype proportions W 1 W W CCR5/CCR5 = W 22 = W* 22 / W* MAX = 1.4/2 = 0.7 W CCR5/ Δ CCR5 = W 12 = W* 12 / W* MAX = 1.8/2 = 0.9 W Δ CCR5/ Δ CCR5 = W 11 = W* 11 / W* MAX = 2/2 = 1.0 To illustrate the use of our model of natural selection, suppose that we found that: W* Δ CCR5/ Δ CCR5 = Sur.*Fec.*K = 2 offspring/lifetime W* CCR5/ Δ CCR5 = Sur.*Fec.*K = 1.8 offspring/lifetime
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