Lecture 8: Types of Selection September 17, 2012

Reminders uI will be gone Thursday and Friday. No office hours this week. uMonday Review Session  Bring specific questions! uExam next Wednesday  Everything mentioned in lecture and lab fair game uFormulas provided: see sample exam

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

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

Putting it all together 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 Δq =pq[q(ω 22 – ω 12 ) - p(ω 11 - ω 12 )] ω Reduces to: Δq =-pqs[ph + q(1-h)] 1-2pqhs-q 2 s

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

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

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

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 =

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

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 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

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

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

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?

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

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?

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

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

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

Heterozygote Disadvantage (Underdominance) Genotype A1A1A1A1 A1A2A1A2 A2A2A2A2 Fitnessω 11 ω 12 ω 22 Fitness in terms of s and h1 + s s 2 ω A1A1A1A1 A1A2A1A2 A2A2A2A2

Heterozygote Disadvantage (Underdominance) Genotype A1A1A1A1 A1A2A1A2 A2A2A2A2 Fitnessω 11 ω 12 ω 22 Fitness in terms of s and t1 + s11 + t s = 0.1 t = 0.1

Equilibrium under Underdominance uAllele frequency moves away from equilibrium point and to extremes when perturbed uUnstable equilibrium uEquilibrium point is at local minimum for average fitness uPopulation approaches trivial equilibria: fixation of one allele

Where are equilibrium points? ω 11 =1.1ω 12 = 1ω 22 = 1.1

Underdominance Revisited Genotype A1A1A1A1 A1A2A1A2 A2A2A2A2 Fitnessω 11 ω 12 ω 22 Fitness in terms of s 1 and s s s 2 Fitness in terms of s and h11-hs1-s A1A1A1A1 ω s 1 hs s2s2 s A1A2A1A2 A2A2A2A2

Why does “nontrivial” equilibrium occur with underdominance? uWhy doesn’t A 1 allele always go to fixation if A 1 A 1 is most fit genotype? q (pq+p 2 ) pq = Proportion of A 1 alleles in heterozygous state: A1A1A1A1 ω A1A2A1A2 A2A2A2A2

ω A1A1A1A1 A1A2A1A2 A2A2A2A2 What determines the equilibrium point with underdominance? uWhy does equilibrium point of A 1 allele frequency increase when selection coefficient decreases? A1A1A1A1 A1A2A1A2 A2A2A2A2 ω ω 11 =1; ω 12 =0.8; ω 22 =1 ω 11 =0.85; ω 12 =0.8; ω 22 =1

Example: Kuru in Fore Tribespeople uPrion disease in Fore tribesmen uTransmitted by cannibalism of relatives by women/children uCannibalism stopped in 1950’s  Older people exposed to selection, younger are ‘controls’ uIdentified locus that causes susceptibility: Prion Protein Gene, PRNP  MM and VV are susceptible, MV are resistant

Kuru and Heterozygote Advantage uTremendous selective advantage in favor of heterozygotes uBalancing selection maintains polymorphism in human populations Selection coefficient (only females)