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Lecture 8: Types of Selection February 5, 2014

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Last Time uIntroduction to selection uPredicting allele frequency change in response to selection

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Today uDominance and types of selection Why do lethal recessives stick around? uEquilibrium under selection Stable equilibrium: overdominance Unstable equilibrium: underdominance

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Lethal Recessives uFor completely recessive case, h=0 uFor lethality, s=1 ω A1A1A1A1 A1A2A1A2 A2A2A2A A1A1A1A1 A1A2A1A2 A2A2A2A2 A1A1A1A1 A1A2A1A2 A2A2A2A2 A 1 A 1 A 1 A 2 A 2 A 2 Relative Fitness (ω)ω 11 ω 12 ω 22 Relative Fitness (hs)1 1-hs 1-s

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Lethal Recessive For q<1 uh=0; s=1 uω 11 =1; ω 12 =1-hs=1; ω 22 =1-s=0 uΔq more negative at large q uPopulation moves toward maximum fitness uRate of change decreases at low q Δq = -pqs[ph + q(1-h)] 1-2pqhs-q 2 s -pq 2 1-q 2 = -q 2 1+q =

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Retention of Lethal Recessives uAs p approaches 1, rate of change decreases uVery difficult to eliminate A 2, recessive deleterious allele from population Heterozygotes “hidden” from selection (ω 11 =1; ω 12 =1-hs=1) At low frequencies, most A 2 are in heterozygous state: q p 2q 2 2pq = q p q Ratio of A2 alleles in heterozygotes versus homozygotes

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Time to reduce lethal recessives It takes a very large number of generations to reduce lethal recessive frequency once frequency gets low See Hedrick 2011, p. 123 for derivation

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Selection against Recessives uFor completely recessive case, h=0 uFor deleterious recessives, s<1 A 1 A 1 A 1 A 2 A 2 A 2 ωω 11 ω 12 ω 22 s1 1-hs 1-s ω A1A1A1A1 A1A2A1A2 A2A2A2A A1A1A1A1 A1A2A1A2 A2A2A2A2 A1A1A1A1 A1A2A1A2 A2A2A2A2

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Selection Against Recessives uh=0; 0~~
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Modes of Selection on Single Loci uDirectional – One homozygous genotype has the highest fitness Purifying selection AND Darwinian/positive/adaptive selection Depends on your perspective! 0 ≤ h ≤ 1 uOverdominance – Heterozygous genotype has the highest fitness (balancing selection) h 1 uUnderdominance – The heterozygous genotypes has the lowest fitness (diversifying selection) h>1, (1-hs) 0 ω A1A1A1A1 A1A2A1A2 A2A2A2A2 ω A1A1A1A1 A1A2A1A2 A2A2A2A2 ω A1A1A1A1 A1A2A1A2 A2A2A2A2

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Equilibrium uThe point at which allele frequencies become constant through time uTwo types of equilibria Stable Unstable uThe question: stable or unstable? What happens if I move q a little bit away from equilibrium?

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Stable Equilibria railslide.com Perturbations from equilibrium cause variable to move toward equilibrium

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Unstable Equilibria Perturbations from equilibrium cause variable to move away from equilibrium

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Heterozygote Advantage (Overdominance) uNew notation for simplicity (hopefully): Genotype A1A1A1A1 A1A2A1A2 A2A2A2A2 Fitnessω 11 ω 12 ω 22 Fitness in terms of s and h1 – s 1 11 – s 2 ω A1A1A1A1 A1A2A1A2 A2A2A2A2

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Equilibrium under Overdominance uEquilibrium occurs under three conditions: q=0, q=1 (trivial), and s 1 p – s 2 q = 0

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Equilibrium under Overdominance uAllele frequency always approaches same value of q when perturbed away from equilibrium value uStable equilibrium uAllele frequency change moves population toward maximum average fitness

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