Chapter 7 Genetics of populations

1. Chapter 7 Genetics of populations • Read Chapter 7 of text

2. Chapter 7 Genetics of populations • We saw in chapter 6 that a cross between two individuals heterozygous for a dominant allele produces a 3:1 ratio of individuals expressing the dominant phenotype: to those expressing the recessive phenotype. • For example brachydachtyly (shortening of the digits) displays this pattern of inheritance.

4. Population genetics • In the early 1900’s when Mendel’s work was rediscovered there was confusion about how these simple patterns of inheritance affected populations. • Why, for example, was not 3 of every 4 people a person with brachdactyly? • Why did not dominant alleles replace recessive alleles?

5. Population genetics • The confusion stemmed from confusing what was happening at the level of the individual with what occurs at the population level. • Individual-level thinking enables us to figure out the result of particular crosses.

7. Population genetics • Population level thinking however is needed to figure out how the genetic characteristics of populations change over time. • It enables us to figure out quantitatively what is happening in a population as a result of evolution. Remember, evolution occurs when genotype frequencies change over time.

9. Hardy-Weinberg Model: a null model for population genetics. • Null models provide us with a baseline. They tell us what we expect to be the case if certain forces are not operating. • The Hardy-Weinberg equilibrium tells us what we expect to happen to genotype frequencies when forces such as natural selection are not operating on a population.

10. Hardy-Weinberg Model: a null model for population genetics. • The Hardy-Weinberg model enables us to determine what allele and genotype frequencies we would expect to in a population if all that is happening is alleles are being randomly assigned to gametes and those gametes meet up at random.

11. 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

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

13. Hardy-Weinberg Model • The three conclusions of the H-W 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).

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

15. 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.

16. 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.

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

18. Assumptions of Hardy-Weinberg • 4. Large population size. • Population is large enough that chance plays no role. Eggs and sperm collide at same frequencies as the actual frequencies of p and q. • If assumption was 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.

19. 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.

20. Deriving the H-W model

21. 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.

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

23. 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).

24. Hardy-Weinberg Equilibrium • Then we can calculate expected 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).

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

26. 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.

27. 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.

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

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

30. Hardy Weinberg Equilibrium with more than 2 alleles • If there are 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

31. Conclusions from Hardy-Weinberg Equilibrium • 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. • 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.

32. Conclusions from Hardy-Weinberg Equilibrium • 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.

34. 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 you would expect in the population?

35. 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.

36. 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?

37. 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.

38. 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.

39. 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?

40. 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.

41. 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.

42. Hardy-Weinberg Equilibrium • If we relax the H-W assumption of no selection how does that affect allele frequencies?

43. Strength of selection • To quantify the strength of selection against a recessive allele we can use a parameter (s) called the selection coefficient to describe the reduction in fitness of one phenotype vs the other.

44. Strength of selection • For example pocket mice coat color is affected by a gene with two alleles D and d. D allele is dominant. • DD: dark phenotype • Dd: dark phenotype • Dd: light phenotype • On dark backgrounds light phenotype will be selected against.

47. Strength of selection • The higher the value of s the more strongly natural selection will act.

49. Frequency independent selection • The mouse coat color example is an example of frequency-independent selection. The fitness of a trait is not associated with how common the trait is.

50. Directional selection • The commonest form of frequency- independent selection is directional selection. • Under directional selection one allele is consistently favored over the other allele so selection drives allele frequencies in only one direction towards a higher frequency of the favored allele. • Eventually favored allele may replace other alleles and become fixed.