The Maintenance of Genetic Variation in Natural Populations

1. The Maintenance of Genetic Variation in Natural Populations Professor Hamish G. Spencer Allan Wilson Centre for Molecular Ecology & Evolution National Research Centre for Growth & Development Department of Zoology, University of Otago Dunedin, New Zealand

2. Robert M. May, 1973 Stability and Complexity in Model Ecosystems Princeton University Press

3. Ecological Complexity • Multi-species ecosystems appear robust to small perturbations (stable)

4. May’s Modeling • Mathematical models of species interactions • Analyzed whether or not they were stable • The more species, the less stable!

5. May’s Paradox • Complex real ecosystems appear stable • Complex model ecosystems are unstable

6. Richard C. Lewontin, 1974 The Genetic Basis of Evolutionary Change Columbia University Press “Paradox of Variation”

7. Variation in the Wild • Natural populations are usually variable • Reflects underlying genetic variation • Variation is essential for adaptation by natural selection

8. Heterozygote Homozygote Genetic Variation • Individuals have two copies of each gene • For any gene, a population may have many different alleles

9. Why is Variation Present? • Central problem in genetics • Variation is the fuel for natural selection & should be consumed • Two Main Hypotheses • Neutralism • Selectionism

10. Neutralism • Motoo Kimura • Standing variation is selectively equivalent or “neutral” • Balance between neutral mutation & genetic drift Expected heterozygosity Neutral mutation rate Effective population size

11. Neutralism as a Null Hypothesis • No selection acting on standing variation • Several statistical tests • Many patterns of variation now known to reject neutralism

12. Selectionism • Balancing selection maintains standing variation • Heterozygote advantage • Frequency-dependent selection • Spatially varying selection • Temporally varying selection • Particular alleles matter

13. Natural Selection

14. > Heterozygote Advantage • Fitness: • Constant viability selection on 2 alleles is necessary & sufficient to maintain both alleles • Heterozygotes have more flexibility?

15. Lewontin’s Mathematical Study • Different genotypes have different fitnesses • Fitness set = All the fitnesses of different types in a population • What proportion of possible fitness sets maintains all alleles? • Randomly generated fitness sets

16. Lewontin’s Result • For 2 alleles, 1/3 of fitness sets keep both alleles • For 3 alleles, ~4% >

17. Lewontin’s Result Lewontin et al., 1978, Genetics

18. Lewontin’s Conclusion • The chance that natural selection maintains more than 3 or 4 alleles is vanishingly small • Selection does not maintain genetic variation

19. Parallel with May’s Paradox • Modelling suggests multi-species communities should not exist • Modelling suggests multi-allele variation should not exist

20. Peter J. Taylor

21. Taylor’s Ecological Model • What if new species repeatedly try to invade an existing ecosystem? • Most invaders fail • A few invaders succeed • Complexity that is stable builds up over time

22. R. William Marks

23. Spencer & Marks’ Genetic Model • Evolution works by trial and error • Mutation constantly bombards populations with new alleles • Most new mutants become extinct • A very few survive • But these survivors may lead to variation

24. AjAllele Frequency Before Selection Fitness of AiAj AiAllele Frequency After Selection Mean Fitness Mathematical Model • Equations • Computer simulation For I := 1 To N Do For J := I To N Do

25. Simulation

26. Single Run Result Spencer & Marks, 1988, Genetics

27. 1000 Runs Result Marks & Spencer, 1991, American Naturalist

28. Spencer & Marks’s Conclusions • Evolution (natural selection & mutation) constructs multi-allele systems very easily • Evolution seeks out those vanishingly rare fitness sets that do maintain many alleles

29. Significance • Selection can maintain genetic variation • But the number of alleles is still small (< 20; usually < 10)

30. Solution to the Paradox? • Frequency-dependent selection • Rare types do better • immunity in parasite’s hosts • camouflage in snails

31. The PIM: A General FDS Model • “Pairwise Interaction Model” (PIM) • Schutz et al. (1968) • Fitness of a genotype is the weighted sum of its viabilities in pairwise interactions with other genotypes • AiAj has fitness

32. Meredith Trotter

33. FDS Investigations • Selection alone • Analogous to Lewontin model • Measures “potential” of FDS • Selection with Mutation • Analogous to Spencer & Marks’s model • Measures “constructability” of FDS-maintained polymorphisms

34. Proportion of Runs Keeping All n Alleles Trotter & Spencer, 2007, Genetics

35. FDS; Two PIM Runs Trotter & Spencer, 2008, Genetics

36. FDS; Many PIM Runs • 104 generations: Mean No. Alleles = 7.4 Trotter & Spencer, 2008, Genetics

37. Bastiaan Star

38. Spatially Varying Selection • Two subpopulations = Demes • Each generation • Selection in each deme independently • Migration: Proportion m/2 switch demes each generation

39. Selection Model with Spatial Structure Deme A Deme B Number of Alleles = 3 Generation 0

40. Selection Model with Spatial Structure Deme A Deme B Selection Number of Alleles = 3 Generation 1

41. Selection Model with Spatial Structure Deme A Deme B Migration Number of Alleles = 3 Generation 1

42. Models with Spatial Structure • Selection alone • Analogous to Lewontin model • Measures “potential” of selection in structured populations • Selection with Mutation • Analogous to Spencer & Marks’s model • Measures “constructability” of selective polymorphisms in structured populations

43. Potential of Spatial Structure Star et al., 2007a, Genetics

44. Constructed Polymorphisms Star et al., 2007b, Genetics

45. Conclusion • Both frequency-dependent selection & spatial structure greatly affect ability of natural selection to maintain genetic variation • Potential to maintain variation may be orders of magnitude greater

46. Collaborators Marjorie Asmussen Reed Cartwright Bill Marks Bastiaan Star Rick Stoffels Meredith Trotter Funding Marsden Fund Allan Wilson Centre for Molecular Ecology & Evolution National Research Centre for Growth & Development NZ Ministry of Research, Science & Technology NZ/USA Scientific and Technological Co-operative Science Programme University of Otago Research Committee Acknowledgements