1. Evolutionary operator: p`= p 2 +pq; q` = q 2 +pq. For lethal alleles: p`= p 2 +pq; q` = q 2 +pq. Allele frequenses A-p, a - q For Thalassemia evolutionary operator or

2. Evolutionary operator with selection - mean fitness Selection in case Thalassemia: W AA =0.89; W Aa =1; W aa =0.2 Selection recessive lethal gene: W AA =1; W Aa =1; Waa=0

3. - mean fitness W AA, W Aa, W aa –individual fitnesses Why mean?

4. Equilibria points p=0, q=1 - population contains a allele only and on the zygote level the population consist of the homozygotes aa; p=1,q=0 - population contains A allele only and on the zygote level the population consist of the homozygotes A A.

5. Equation for equilibria points

6. Condition of the polymorphic state

7. Superdominance, when a heterozygote is fitter than both homozygotes Superrecessivity, when a heterozygote is les fit than either homozygotes In intermediate cases: W AA  W aa  W Aa (if W AA < W Aa ) or W Aa  W aa  W AA (if W Aa < W AA ) The population has no polymorphic equilibria Heterozygote equilibrium states: p>0, q>0

8. Lethal allele Let W aa =0 If W Aa > max(W AA,W aa ) =W AA Equilibrium point is polymorphic Previous conditions: W AA =W Aa =1, W aa =0 Condition not so realistic

9. Selection against a recessive allele.

10. Selection in case Thalassemia W AA =0.89, W Aa =1, W aa =0.2 If W Aa > max(W AA,W aa ) =W AA Equilibrium point is polymorphic Good condition. Note, that can be W AA <1

11. Dominant selection(also selection against a recessive allele) Two different phenotypes {AA, Aa}, {aa} W AA =W Aa =1, W aa =1-s W AA =W Aa =1-s, W aa =1 No polymorphic equilibria point

12. Haploid selection

13. Equilibria points and trajectories

14. Selection against a recessive allele. Trajectories.

15. Example. Selection against recessive lethal gene

16. Fisher’s Fundamental Theorem of Natural Selection Mean fitness increase along the trajectory

17. Lethal allele

18. max

19. Selection against a recessive allele.

21. Mean fitness in case Thalassemia W AA =0.89, W Aa =1, W aa =0.2

22. W AA =0.50, W Aa =1, W aa =0.2

23. Mean fitness calculation and dynamics

24. Convergence to equilibria In intermediate cases: W aa  W Aa  W AA (or W AA  W Aa  W aa ) The population has no polymorphic equilibria

25. Convergence to equilibria Superdominance (overdominance), when a heterozygote is fitter than both homozygotes Superrecessivity (underdominance), when a heterozygote is les fit than either homozygotes

26. Blood groups A,B,O –alleles allel enzyme A O B dominance A A AA, AO, = A B B BB, BO, = B O - AB = AB OO = O

28. A O B dominance A A AA, AO, = A B B BB, BO, = B O - AB = AB OO = O

29. Evolutionary operator

30. Simulation

31. One-locus multiallele autosomal systems

32. Fishers Fundamental Theorem of Natural Selection Mean fitness increase along the trajectory