lec_5_cond_13

# Feck 18 offspringlifetime w ccr5 ccr5 surfeck 14

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Sur.*Fec.*K = 1.8 offspring/lifetime W* CCR5/ CCR5 = Sur.*Fec.*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 , W 2 , 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 So the change is SUBSTANTIAL but SLOW Δ p = Change in p If evolution is so slow, then how did Δ CCR5 rise to a frequency of 9% in Northern Europe? Recent evidence indicates that another virus also uses the CCR5 receptor to enter cells the virus that causes smallpox, so 100’s of years of past adaptation to smallpox may have lead to the high frequency of Δ CCR5 in N. Europeans. We do not yet know for certain, but Very Important to do study questions from this lecture material p = 0.1 p ’ = .123 24 0.05 0.15 0.25 0.1 0.2 0.3 Generation 0 1 2 3 4 5 W is the average fitness of an allele in the gene pool and it also is the average fitness of an individual in the population = average population fitness Frequency of Δ CCR5 ( p ) 4 years with 2-week life cycle But only 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 W CCR5/CCR5 = W 22 = W* 22 / W* MAX = 1.4/2 = 0.7 0.1 0.5 1.0 100 0 (2500 years)
population one individual W = individual fitness = Darwinian fitness average W for all A 1 A 1 average W for all A 2 A 2 average W for all A 1 A 2 W * 11 W * 12 W * 22 divide by largest W * ij W 11 W 12 W 22 relative
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