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One-locus diploid model

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. Back to the Foré. Genotype MM MV VV juvenile 31 72 37

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One-locus diploid model

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  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.

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