lec_5_cond_13

Irst consider the a 1 allele the allele occurs in two

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±irst 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 Ftness 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* / W* MAX = 2/2 = 1.0 To illustrate the use of our model of natural selection, suppose that we found that: Next, let p = proportion of Δ CCR5 W* Δ CCR5/ Δ CCR5 = Sur.*±ec.*K = 2 offspring/lifetime W* CCR5/ Δ CCR5 = Sur.*±ec.*K = 1.8 offspring/lifetime W* CCR5/ CCR5 = Sur.*±ec.*K = 1.4 offspring/lifetime 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 is on phenotypes produced by the genotypes W 1, W2, W Gene Pool Gen=0 Selection Gen= 1 W 1 freq (A 2 ) = q W 2 qW 2 W W 1 Gene Pool W total ʼ = W W = 1 Gene Pool q ʼ = qW 2 W p W 1 = 1- p ʼ p ʼ = p W 1 freq (A 1 ) = p (Total) = p +q = 1 Next, let p = proportion of ! CCR5
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W = p (W 1 ) + q (W 2 ) = .1 (.91) + .9 (.72) = 0.739 W 2 = q (W 22 ) + p (W 12 ) = .9 (.7) + .1 (.9) = 0.72 W 1 = p (W 11 ) + q (W 12 ) = .1 (1) + .9 (.9) = 0.91 Because humans have such a long generation time, substantial evolutionary adaptation to the HIV/AIDS will take at least about 2500 years (a hundred generations) But eventually it would occur Let, Δ CCR5 = A1 CCR5 = A2 p = 0.1 q = 0.9 (rounding 9.1% to 10%) Then, to make math easier p ’ = p in next generation = p W 1 W = 0.1 .91 .739 = .123 = p ’ - p = .123 - .1 = 0.023
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irst consider the A 1 allele The allele occurs in two...

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