Chapter 6 The ways of change: drift and selection

1. Chapter 6The ways of change: drift and selection

2. Assigned reading • Read Chapter 6 of text

3. Chapter 6 Genetics of populations • Brachydachtyly displays the classic 3:1 pattern of inheritance (for a cross between heterozygotes) that mendel described.

5. Population genetics • In the early 1900’s there was confusion about how such simple patterns of inheritance affected populations. • Why, aren’t 3 of every 4 people brachdactylyous? • Why don’t dominant alleles replace recessive alleles?

6. Population genetics • Problem stems from confusing what happens at the individual level with what occurs at the population level. • Individual-level thinking enables us to figure out the result of particular crosses.

8. Population genetics • Population level thinking is used to figure out how the genetic characteristics of populations change quantitatively over time.

10. Population genetics • Population genetics is the study of the frequency distribution of alleles and genotypes in populations and the causes of allele frequency changes

11. Key Concepts • Diploid individuals carry two alleles at every locus • Homozygous: alleles are the same • Heterozygous: alleles are different

12. Key Concept • Hardy-Weinberg equilibrium model serves as the fundamental null model in population genetics

13. Hardy-Weinberg Model • The Hardy-Weinberg model examines a situation in which there is one gene with two alleles A1 and A2. • There are three possible genotypes A1A1, A2 A2,and A1 A2

14. Hardy-Weinberg Model • Hardy and Weinberg used their model to predict what would happen to allele frequencies and genotype frequencies in a population in the absence of any evolutionary forces acting on the population. • Their model produced three important conclusions

15. Hardy-Weinberg Model • In the absence of evolutionary processes acting on them: • 1. The frequencies of the alleles A1 and A2 do not change over time. • 2. If we know the allele frequencies in a population we can predict the equilibrium genotype frequencies (frequencies of A1A1, A2 A2,and A1 A2).

16. Hardy-Weinberg Model • 3. A gene not initially at H-W equilibrium will reach H-W equilibrium in one generation.

17. Assumptions of Hardy-Weinberg • 1. No selection. • If individuals with certain genotypes survived better than others, allele frequencies would change from one generation to the next.

18. Assumptions of Hardy-Weinberg • 2. No mutation • If new alleles were produced by mutation or alleles mutated at different rates, allele frequencies would change from one generation to the next.

19. Assumptions of Hardy-Weinberg • 3. No migration • Movement of individuals in or out of a population would alter allele and genotype frequencies.

20. Assumptions of Hardy-Weinberg • 4. Large population size. • Population is large enough that chance does not affect allele frequencies. • If assumption is violated and by chance some individuals contributed more alleles than others to next generation allele frequencies might change. This mechanism of allele frequency change is called Genetic Drift.

21. Assumptions of Hardy-Weinberg • 5. Individuals select mates at random. • Individuals do not prefer to mate with individuals of a certain genotype. • If this assumption is violated allele frequencies will not change, but genotype frequencies might.

23. Deriving the H-W model

25. Hardy-Weinberg Equilibrium • Assume two alleles A1 and A2 with known frequencies (e.g. A1 = 0.6, A2 = 0.4.) • Only two alleles in population so their allele frequencies add up to 1.

26. Hardy-Weinberg Equilibrium • Can predict frequencies of genotypes in next generation using allele frequencies. • Possible genotypes: A1A1 , A1A2 and A2A2

27. Hardy-Weinberg Equilibrium • Assume alleles A1 and A2 enter eggs and sperm in proportion to their frequency in population (i.e. 0.6 and 0.4) • Assume sperm and eggs meet at random (one big gene pool).

28. Hardy-Weinberg Equilibrium • Then we can calculate genotype frequencies. • A1A1 : To produce an A1A1 individual, egg and sperm must each contain an A1 allele. • This probability is 0.6 x 0.6 or 0.36 (probability sperm contains A1 times probability egg contains A1).

29. Hardy-Weinberg Equilibrium • Similarly, we can calculate frequency of A2A2. • 0.4 x 04 = 0.16.

30. Hardy-Weinberg Equilibrium • Probability of A1A2 is given by probability sperm contains A1 (0.6) times probability egg contains A2 (0.4). 0.6 x 04 = 0.24.

31. Hardy-Weinberg Equilibrium • But, there’s a second way to produce an A1A2 individual (egg contains A1 and sperm contains A2). Same probability as before: 0.6 x 0.4= 0.24. • Overall probability of A1A2 = 0.24 + 0.24 = 0.48.

32. Hardy-Weinberg Equilibrium • Genotypes in next generation: • A1A1 = 0.36 • A1A2 = 0.48 • A2 A2= 0.16 • Adds up to one.

33. Hardy-Weinberg Equilibrium • General formula for Hardy-Weinberg. • Let p= frequency of allele A1 and q = frequency of allele A2. • p2 + 2pq + q2 = 1.

34. Hardy Weinberg Equilibrium with more than 2 alleles • If three alleles with frequencies P1, P2 and P3 such thatP1 + P2 + P3 = 1 • Then genotype frequencies given by: • P12 + P22 + P32 + 2P1P2 + 2P1 P3 + 2P2P3

35. Conclusions from Hardy-Weinberg Equilibrium • 1. Allele frequencies in a population will not change from one generation to the next just as a result of assortment of alleles and zygote formation.

36. Conclusions from Hardy-Weinberg Equilibrium • 2. If the allele frequencies in a gene pool with two alleles are given by p and q, the genotype frequencies will be given by p2, 2pq, and q2.

37. Conclusions from Hardy-Weinberg Equilibrium • 3. The frequencies of the different genotypes are a function of the frequencies of the underlying alleles. • The closer the allele frequencies are to 0.5, the greater the frequency of heterozygotes.

39. Working with the H-W equation • You need to be able to work with the Hardy-Weinberg equation. • For example, if 9 of 100 individuals in a population suffer from a homozygous recessive disorder can you calculate the frequency of the disease causing allele? Can you calculate how many heterozygotes are in the population?

40. Working with the H-W equation • p2 + 2pq + q2 = 1. The terms in the equation represent the frequencies of individual genotypes. • P and q are allele frequencies. It is vital that you understand this difference.

41. Working with the H-W equation • 9 of 100 (frequency = 0.09) of individuals are homozygotes. What term in the H-W equation is that equal to?

42. Working with the H-W equation • It’s q2. • If q2 = 0.09, what’s q? Get square root of q2, which is 0.3. • If q=0.3 then p=0.7. Now plug p and q into equation to calculate frequencies of other genotypes.

43. Working with the H-W equation • p2 = (0.7)(0.7) = 0.49 • 2pq = 2 (0.3)(0.7) = 0.42 • Number of heterozygotes = 0.42 times population size = (0.42)(100) = 42.

44. Working with the H-W equation: 3 alleles • There are three alleles in a population A1, A2 and A3 whose frequencies respectively are 0.2, 0.2 and 0.6 and there are 100 individuals in the population. • How many A1A2 heterozygotes will there be in the population?

45. Working with the H-W equation: 3 alleles • Just use the formulae P1 + P2 + P3 = 1 and P12 + P22 + P32 + 2P1P2 + 2P1 P3 + 2P2P3 = 1 Then substitute in the appropriate values for the appropriate term 2P1P2 = 2(0.2)(0.2) = 0.08 or 8 people out of 100.

46. Hardy-Weinberg Equilibrium • Hardy Weinberg equilibrium principle identifies the forces that can cause evolution. • If a population is not in H-W equilibrium then one or more of the five assumptions is being violated.