One-locus diploid model

1. One-locus diploid model Goals: Predict the outcome of selection: when will it result in fixation, when in polymorphism Understand the effect of dominance on the rate of evolution

2. Back to the Foré • Genotype MM MV VV • juvenile 31 72 37 • adult 4 23 3 If selection continues to act in the same way, what will be the outcome?

3. One-locus diploid model • Selection acts in the diploid phase • random mating, • no migration, and • no mutation • large population

4. Model conditions • :allele frequencies • initial genotype frequencies • After selection? p[t] q[t] p[t] q[t]

5. Genotype frequencies after selection f’(AA) f’(Aa) f’(aa)

6. Allele frequencies after selection f’(AA) = f’(A) = 100% f’(Aa) = 50% f’(a) = 50% f’(aa) = 100%

7. One-locus diploid model p(t+1) = p(t)2WAA + p(t)q(t)Waa p(t)2WAA + 2p(t)q(t)WAa + q(t)2Waa

8. One-locus diploid model Forms of selection • Directional Selection: Favoring allele A Favoring allele a • Heterozygote advantage • Heterozygote disadvantage • (Which forms of selection were present in the haploid selection model?)

9. Directional selection

10. Directional selection: terms WAA = 1 WAa = 1 + hs Waa = 1 + s s: h:

11. Dominance

12. Waa 1 + s WAA 1 WAa 1 + s/2 Dominance Imagine two alleles fighting over the phenotype (in this case, fitness(: where does the heterozygote end up?

13. Waa 1 + s WAA 1 WAa= Dominance Imagine two alleles fighting over the phenotype (in this case, fitness(: where does the heterozygote end up?

14. Waa 1 + s WAA 1 WAa 1 + hs Dominance Imagine two alleles fighting over the phenotype (in this case, fitness(: where does the heterozygote end up?

15. Waa 1 + s WAA 1 WAa 1 + hs Dominance Imagine two alleles fighting over the phenotype (in this case, fitness(: where does the heterozygote end up?

16. Waa 1 + s WAA= 1 WAa Dominance Imagine two alleles fighting over the phenotype (in this case, fitness(: where does the heterozygote end up?

17. Dominance example • Sickle cell anemia: • HH = healthy red blood cells • Hh = sickle cell trait • hh = sickle cell anemia • Describe the dominance of H for: • blood oxygen capacity? • malaria resistance?

18. Dominance and selection p(t+1) = p(t)2WAA + p(t)q(t)WAa p(t)2WAA + 2p(t)q(t)WAa + q(t)2Waa If A is dominant and rare: If A is dominant and common:

19. Selection against a common allele If WAA < WAa < Waa, selection favors the a allele

20. Heterozygote advantage WAa = 1; Waa = 0.9; WAA= 0.8 WAa > Waa; WAa > WAA

21. Heterozygote disadvantage Heterozygote disadvantage WAa = 0.9; Waa = 1.0; WAA= 0.95 WAa < Waa; WAa < WAA

22. Equilibria What are the equilibria?

23. Behaviour at polymorphic equilibrium

24. One-locus diploid model Examples: Sickle-cell anemia

25. One-locus diploid model Examples: Sickle-cell anemia For the Nigerian population studied: WHH = 0.88 WHh = 1 Whh = 0.14 What is the expected equilibrium frequency of the non-mutant allele (H)?

26. Readings and questions • References: • Mead, S., M. P. H. Stumpf, et al. 2003. Balancing selection at the prion protein gene consistent with prehistoric kurulike epidemics. Science 300: 640-643. • Reading:Freeman and Herron, chapter 6 (chapter 5) • Questions: • What are the relative fitnesses for the three Foré genotypes? (Use the juvenile data to estimate genotype frequencies prior to selection). What is the expected outcome of selection? Explain. • Imagine that a population experienced malaria but lacked the sickle-cell allele. Using the Nigerian fitness data, sketch the evolution of the population if a new sickle cell mutation arose in the population. • You have identified a locus that influences survival in sparrows. The relative fitnesses for each genotype are: WAA = 1.0; WAa = 0.9; Waa = 0.6. Describe the relationship between the two alleles in terms of dominance.