Lecture 8: Selection (Cont’d) • Basic selection model • Selection and Polymorphism • Balancing selection • Underdominance & Overdominance • Mutation as an evolutionary force Selection against B2 • Adaptive landscape for B1: the variation in average fitness over the range of allele frequencies Genotype: B1B1 B1B2 B1B2 Fitness (Abs): 1.0 0.75 0.5 2 2 w = p w11 + 2pqw12 + q w22 Selection against B2 “adaptive landscape” 1.0 0.8 0.6 All B1 B1, w = 1.0 0.4 All B2 B2, Mean fitness, w 0.2 w = 0.5 0.0 0.2 0.4 0.6 0.8 1.0 Frequency of B1 allele (p) Selection against B2 1.0 0.8 0.6 0.4 Mean fitness 0.2 0.0 0.2 0.4 0.6 0.8 1.0 Frequency of B1 allele (p) Rate of evolution Genotype: B1B1 B1B2 B1B2 Fitness (Abs): 1.0 0.75 0.5 Δp = (p/w)(pw11 + qw12 - w) 0.1 0.09 0.08 0.07 0.06 p 0.05 Δ 0.04 0.03 0.02 0.01 0 0 0.2 0.4 0.6 0.8 1 p Selection: a recessive lethal Genotype: B1B1 B1B2 B2B2 Fitness: 1.0 1.0 0.0 1 1 1+S B2 : a recessive lethal s = selection coefficient = -1.0 – difference in selection of one genotype versus others Selection: a recessive lethal Genotype: B1B1 B1B2 B2B2 Fitness: 1.0 1.0 0.0 1 1 1+S 2 q’ = q w22 + pqw12 / w • Substitution q’ = q / (1+q) Tribolium example w = 1.00 Fig 5.16 11 w12 = 1.00 w22 = 0.00 (s22 = 1.0) Frequency of recessive after 500 generation gens = 0.002 Why does the rate of evolution slow down? Tribolium example w11 = 1.00 Gen Fr(lethal) % in het’s w12 = 1.00 w = 0.00 1 0.500 50.0 22 (s22 = -1.0) 10 0.091 90.9 Frequency of 100 0.010 99.0 recessive after 500 1000 0.001 99.9 gens = 0.002 “masked” from selection Tribolium example 0.5 0.45 • As lethal 0.4 allele 0.35 0.3 p 0.25 becomes Δ 0.2 rare, rate 0.15 0.1 of 0.05 0 evolution 0 0.2 0.4 0.6 0.8 1 slows p Selection and polymorphism • Selection against alleles: leads to “fixation” of favored allele • Polymorphism: A population, locus, or trait with more than one allele or phenotype • How can selection maintain polymorphism? Maintained by selection • Heterozygote advantage Balancing • Frequency-dependent selection Selection • Mutation/selection balance • Variable selection in time • Variable selection in space (+ immigration) Selection on heterozygotes Selection on one homozygote and heterozygote the same: w11 = w12 > w22 leads to fixation Selection on heterozygotes • Heterozygote advantage: overdominance w11 < w12 > w22 • Heterozygote disadvantage: underdominance w11 > w12 < w22 Selection on heterozygotes Allele frequencies: Fr(A) = p Fr(a) = q Genotype: AA Aa aa Frequency (z): p2 2pq q2 Fitness (abs): w11 w12 w22 Fitness (abs): 1+S 1 1+T S, T < 0: Overdominance Box 5.8 S, T > 0: Underdominance Selection on heterozygotes Allele frequencies: Fr(A) = p Fr(a) = q Genotype: AA Aa aa Frequency (z): p2 2pq q2 Fitness (abs): w11 w12 w22 Fitness (abs): 1+S 1 1+T Δp = (p/w)(pw11 + qw12 - w) When will Δp = 0? T ˆp = p = 0, p = 1, or p = ˆp S + T Overdominance Allele frequencies: Fr(A) = p Fr(a) = q Genotype: AA Aa aa Frequency (z): p2 2pq q2 Fitness (abs): w11 w12 w22 Fitness (abs): 1+S 1 1+T S = -0.4 and T = -0.6 -0.6 T ˆp = = 0.6 ˆp = -0.4 + -0.6 S + T Adaptive Landscape: Overdominance 0.8 0.6 0.4 Equilibrium Mean fitness (stable) n ’ 0.2 Pop 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Fig 5.20 Frequency of A allele (p) Stability of equilibrium allele frequency 0.12 0.08 Δp p=Fr(A) 0.04 0.00 0.2 0.4 0.8 -0.04 p = 0.0 p = 0.6 p = 1.0 Fig 5.20 Heterozygote advantage in Drosophila wVV = 0.735 wVL = 1.0 wLL = 0.0 S = -0.265 T = -1.000 T p = ˆ S + T ˆp = 0.791 Heterozygote advantage in Drosophila wVV = 0.735 wVL = 1.0 wLL = 0.0 S = -0.265 T = -1.000 T p = ˆ S + T ˆp = 0.791 Figure 5.18 Adaptive Landscape: Underdominance 1.6 S = 0.4 and T = 0.6 1.5 Equilibrium 1.4 (unstable) Mean fitness n ’ 1.3 Pop 1.2 0.0 0.2 0.4 0.6 0.8 1.0 Fig 5.20 Frequency of A allele (p) • Evolution under selection is slow when recessive alleles reside in heterozygotes – Leads to fixation • Selection favoring heterozygotes (overdominance) can maintain polymorphism (underdominance leads to fixation).