1. Population genetics and Hardy-Weinberg equilibrium

2. Mendelian-Darwinian Synthesis- Population Genetics Although Mendel’s and Darwin’s work were published within 5 years of each other, a synthesis of their ideas was not truly met until 1930’s Recognition that the relative abundance of traits in a population is tied to the relative abundance of alleles that influence them Under what circumstances will the relative abundance of alleles change within a population (i.e. the population evolves)?

3. Population genetics integrates Darwin’s evolution by natural selection with Mendelian genetics Evolution is change in allele frequency across generations Population genetics begins with a model of what happens to allele and genotype frequencies in an idealized population

4. A Suppose that in a population there are two alleles, A and A at a locus of interest. There are three possible genotypes. Homozygous, AHeterozygous Homozygous, A

5. A A AA A A AAAAAAAAAAA A A A A A A A A A A A A

6. If gametes join at random… a will meet with a half the time, and with a the other half the time. A A A Similarly, a will join with the two egg types at a 50:50 ratio. A

7. A A A A A A A A A A A A AAAAAAA A AAAA Half of all eggs have A and half have A Half of all sperm have A and half have A

8. A AA A A A A A Zygotes

9. A AA A A A A A Homozygous, A freq. = 0.25 = p 2 Heterozygous freq = 0.5 = 2pq p = freq. of the A allele = 0.5 q = freq. of the A allele = 0.5 Homozygous, A freq. = 0.25 = q 2

10. p 2 + 2pq + q 2 = 1 Regardless of allele frequencies - no matter what the values of p and q - genotype frequencies will go to, and remain at… Hardy-Weinberg equilibrium equation

13. How are different alleles inherited? - Law of Segregation each diploid individual carries 2 non-blending copies of each gene each gamete (sperm/egg) receives only one of these genes each gene is segregated randomly – there is no way of knowing which copy of the gene a specific gamete will receive different forms (alleles) of the gene are thus also segregated randomly amongst the gametes

14. How are allele frequencies and genotypes related in a population? For a simple 2 allele (A 1 and A 2 ) locus, possible genotypes are A 1 A 1, A 1 A 2 and A 2 A 2 If we know the relative frequencies of A 1 and A 2, we can predict the relative frequencies of each genotype

15. In a hypothetical 2 allele closed population frequency of A 1 in gene pool = p frequency of A 2 in gene pool = q Since there are only 2 alleles in the population: p + q = 1

16. Sperm A 1 A 2 A 1 Eggs A 2 A1A1A1A1 A1A2A1A2 A1A2A1A2 A2A2A2A2

17. Sperm A 1 A 2 A 1 Eggs A 2 A1A1A1A1 A1A2A1A2 A1A2A1A2 A2A2A2A2

18. Sperm A 1 A 2 A 1 Eggs A 2 A1A1A1A1 A1A2A1A2 A1A2A1A2 A2A2A2A2

19. Genotypic Outcome Probabilities A 1 A 1 Homozygotes = p x p = p 2 A 1 A 2 Heterozygotes = (p x q) + (p x q) = 2pq A 2 A 2 Homozygotes = q x q = q 2 p 2 + 2pq + q 2 = 1

20. Yule’s Numerical Example: The Simplest Case If the frequency of each of 2 alleles in the population is exactly equal, the frequency of each allele = 0.5 i.e. A 1 = 0.5, A 2 = 0.5 Since any 2 gametes in a randomly mixed “gene lottery” will have an equal chance of being picked, the probability of a sperm having the A 1 allele = 0.5

22. Conclusion 1: allele frequencies in a population will not change, generation after generation Conclusion 2: if allele frequencies are given by p & q, the genotype frequencies are p 2, 2pq, q 2

23. 5 Assumptions for H-W Principle 1) no selection 2) no mutation 3) no migration to or from population 4) no random events that cause some individuals to pass on more of their genes than others 5) random mating

25. So what is the value of this null model with entirely unrealistic assumptions? 1) We can quantify what will happen if there is selection on an allele 2) Likewise if there are mutations 3) etc.

26. 5 Assumptions for H-W Principle 1) no selection 2) no mutation 3) no migration to or from population 4) no random events that cause some individuals to pass on more of their genes than others 5) random mating

28. When individuals with some genotypes survive at higher rates than individuals with other genotypes, allele frequencies can change from one generation to the next. ie. natural selection causes evolution Violation of no-selection assumption violates Conclusion 1: allele frequencies in a population will not change, generation after generation

30. Persistent selection can cause substantial changes in allele frequencies over time

32. 5 Assumptions for H-W Principle 1) no selection 2) no mutation 3) no migration to or from population 4) no random events that cause some individuals to pass on more of their genes than others 5) random mating

34. Mutation can cause appreciable changes in allele frequencies over very long periods of time

35. Mutation is a weak force of evolution Nonetheless it provides the raw material upon which natural selection acts Mutation - selection balance

36. 5 Assumptions for H-W Principle 1) no selection 2) no mutation 3) no migration to or from population 4) no random events that cause some individuals to pass on more of their genes than others 5) random mating

37. Migration is a potent force in evolution

39. Migration is most important in preventing populations from diverging Violation of no-migration assumption violates Conclusion 2: if allele frequencies are given by p & q, the genotype frequencies are p 2, 2pq, q 2

40. 5 Assumptions for H-W Principle 1) no selection 2) no mutation 3) no migration to or from population 4) no random events that cause some individuals to pass on more of their genes than others 5) random mating

41. In populations of finite size, chance events - in the form of sampling error in drawing gametes from the gene pool - can cause evolution Selection is differential reproductive success that happens for a reason; genetic drift is differential reproductive success that just happens Genetic drift is most important in small populations

42. Generation Average heterozygosity Frequency of allele A 1 Popln = 4 Popln = 400 Popln = 40

43. As alleles drift to fixation or loss, the frequency of heterozygotes in the population declines

45. Violation of no-drift assumption violates both Conclusion 1: allele frequencies in a population will not change, generation after generation Conclusion 2: if allele frequencies are given by p & q, the genotype frequencies are p 2, 2pq, q 2

46. 5 Assumptions for H-W Principle 1) no selection 2) no mutation 3) no migration to or from population 4) no random events that cause some individuals to pass on more of their genes than others 5) random mating

47. Coral releasing gametes into the water

49. Violation of random mating assumption violates Conclusion 2: if allele frequencies are given by p & q, the genotype frequencies are p 2, 2pq, q 2

50. Inbreeding: decreases the frequency of heterozygotes and increases the frequency homozygotes.

51. Inbreeding can lead to “Inbreeding Depression” Most mutations are deleterious when homozygous, but not when heterozygous Close relatives are likely to have inherited the same deleterious mutations from their ancestors, and carry them in the heterozygous state. When close relatives mate, they produce homozygotes for the mutation.

52. PPPp pp PPPp PPPpPPPp Inbreeding increases the chance that deleterious homozygotes are produced

53. Assortative Mating by Height in Humans 155 160 165 170 175 180 185 190 195 200 135140145150155160165170175180 Mother's Height Father's Height  = 0.49

54. How do you know if a population is in H-W? Look at observed genotype frequencies in the population… From these, calculate allele frequencies.. From allele frequencies, calculate the genotype frequencies predicted by H-W… Compare observed genotype frequencies to predicted

55. Wild flower population

56. AA, n = 44 Aa, n = 46 aa, n = 10