Lecture 8: Types of Selection

Lecture 8: Types of Selection September 17, 2012

Reminders • I will be gone Thursday and Friday. No office hours this week. • Monday Review Session • Bring specific questions! • Exam next Wednesday • Everything mentioned in lecture and lab fair game • Formulas provided: see sample exam

Last Time • Introduction to selection • Predicting allele frequency change in response to selection

Today • Dominance and types of selection • Why do lethal recessives stick around? • Equilibrium under selection • Stable equilibrium: overdominance • Unstable equilibrium: underdominance

Putting it all together ω Reduces to: Δq =pq[q(ω22 – ω12) - p(ω11- ω12)] Δq =-pqs[ph + q(1-h)] 1-2pqhs-q2s A1A1 A1A2 A2A2 Relative Fitness (ω) ω11ω12ω22 Relative Fitness (hs) 1 1-hs 1-s

ω ω ω Modes of Selection on Single Loci • Directional – One homozygous genotype has the highest fitness • Purifying selection AND Darwinian/positive/adaptive selection • Depends on your perspective! • 0 ≤ h ≤ 1 A1A1 A1A1 A1A1 A1A2 A1A2 A1A2 A2A2 A2A2 A2A2 • Overdominance – Heterozygous genotype has the highest fitness (balancing selection) • h<0, 1-hs > 1 • Underdominance– The heterozygous genotypes has the lowest fitness (diversifying selection) • h>1, (1-hs) < (1 – s) < 1 for s > 0

Directional Selection Δq =-pqs[ph + q(1-h)] 1-2pqhs-q2s 0 ≤ h ≤ 1 q Δq Time 0.5 1 0 q h=0.5, s=0.1

Lethal Recessives A1A1 A1A2 A2A2 A1A1 A1A2 A2A2 Relative Fitness (ω) ω11ω12ω22 Relative Fitness (hs) 1 1-hs 1-s • For completely recessive case, h=0 • For lethality, s=1 1 0.8 0.6 ω 0.4 0.2 0 A1A1 A1A2 A2A2 A1A1 A1A2 A2A2

Lethal Recessive -pq2 -q2 = = 1-q2 1+q Δq = -pqs[ph + q(1-h)] 1-2pqhs-q2s For q<1 • h=0; s=1 • ω11=1; ω12=1-hs=1; ω22=1-s=0 • Δq more negative at large q • Population moves toward maximum fitness • Rate of change decreases at low q

Retention of Lethal Recessives q = 0.5 1 2pq p p 0.1 9 q q 2q2 0.01 99 • As p approaches 1, rate of change decreases • Very difficult to eliminate A2, recessive deleterious allele from population • Heterozygotes “hidden” from selection (ω11=1; ω12=1-hs=1) • At low frequencies, most A2are in heterozygous state: Ratio of A2 alleles in heterozygotes versus homozygotes

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

Selection against Recessives A1A1 A1A2 A2A2 A1A1 A1A2 A2A2 ωω11ω12ω22 s 1 1-hs 1-s • For completely recessive case, h=0 • For deleterious recessives, s<1 1 0.8 0.6 ω 0.4 0.2 0 A1A1 A1A2 A2A2 A1A1 A1A2 A2A2

Selection Against Recessives -pq2s -q2s(1-q) = = 1-q2s 1-q2s s=0.2 s=0.2 s=0.2 s=0.4 s=1 s=0.4 Δq = -pqs[ph + q(1-h)] 1-2pqhs-q2s • h=0; 0<s<1 • Maximum rate of change at intermediate allele frequencies • Location of maximum depends on s: q=2/3 for small s • Where is maximum rate of change in q for lethal recessive? • What is final value of q? • What is final average fitness of population? Lethal recessive, continues off chart

ω ω ω Modes of Selection on Single Loci • Directional – One homozygous genotype has the highest fitness • Purifying selection AND Darwinian/positive/adaptive selection • Depends on your perspective! • 0 ≤ h ≤ 1 A1A1 A1A1 A1A1 A1A2 A1A2 A1A2 A2A2 A2A2 A2A2 • Overdominance – Heterozygous genotype has the highest fitness (balancing selection) h<0, 1-hs > 1 • Underdominance– The heterozygous genotypes has the lowest fitness (diversifying selection) h>1, (1-hs) < (1 – s) < 1 for s > 0

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

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

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

Does selection always cause average fitness to approach 1?

Under what conditions do we reach an equilibrium while polymorphisms still exist in the population?

ω Heterozygote Advantage (Overdominance) • New notation for simplicity (hopefully): A1A1 A1A2 A2A2

Equilibrium under Overdominance • Equilibrium occurs under three conditions: q=0, q=1 (trivial), and s1p – s2q = 0

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

ω Heterozygote Disadvantage (Underdominance) A1A1 A1A2 A2A2

Heterozygote Disadvantage (Underdominance) s = 0.1 t = 0.1

Equilibrium under Underdominance • Allele frequency moves away from equilibrium point and to extremes when perturbed • Unstable equilibrium • Equilibrium point is at local minimum for average fitness • Population approaches trivial equilibria: fixation of one allele

Where are equilibrium points? ω11 =1.1 ω12 = 1 ω22 = 1.1

Underdominance Revisited s s1 hs s2 ω A1A1 A1A2 A2A2

Proportion of A1 alleles in heterozygous state: pq q = (pq+p2) Why does “nontrivial” equilibrium occur with underdominance? • Why doesn’t A1 allele always go to fixation if A1A1 is most fit genotype? ω A1A1 A1A2 A2A2

ω11=1; ω12=0.8;ω22=1 ω ω11=0.85; ω12=0.8;ω22=1 A1A1 A1A2 A2A2 ω A1A1 A1A2 A2A2 What determines the equilibrium point with underdominance? • Why does equilibrium point of A1 allele frequency increase when selection coefficient decreases?

Example: Kuru in Fore Tribespeople • Prion disease in Fore tribesmen • Transmitted by cannibalism of relatives by women/children • Cannibalism stopped in 1950’s • Older people exposed to selection, younger are ‘controls’ • Identified locus that causes susceptibility: Prion Protein Gene, PRNP • MM and VV are susceptible, MV are resistant http://learn.genetics.utah.edu/features/prions/kuru.cfm

Kuru and Heterozygote Advantage 0.403 0.373 0.2985 Selection coefficient (only females) • Tremendous selective advantage in favor of heterozygotes • Balancing selection maintains polymorphism in human populations

Lecture 8: Types of Selection