Population Genetics

1. Population Genetics • The study of Mendel’s laws and other genetic principles as they apply to entire populations of organisms • Major theme: the origin, maintenance and significance of genetic variation

2. Paradox of genetic variability • It is to an individual organism's advantage to have the genetic make up best suited to the environment • It is to a population’s advantage to have genetic variability among its members in order to respond to changes in the environment

3. Paradox of genetic variability • Genetic variability is necessary in order for populations to adapt to changing environments • This adaptation is what many refer to as evolution • Evolution is a populational phenomenon; individuals cannot adapt in this sense

4. Kettlewell’s Moths • Studied Biston betularia, the peppered moth, in a heavily industrialized area of England • Two color morphs present: • peppered; PP, Pp • melanic; pp

5. Kettlewell’s Moths • By the time Kettlewell studied the moths in the 1950’s, most of the moths were homozygous recessive • Natural selection: • More of the melanic moths survive; • therefore more of the melanic moths reproduce • therefore more of the recessive alleles are passed on

6. Kettlewell’s Moths • Today, the peppered variety is increasing in frequency. • Anti-pollution laws are reducing soot emissions • Lichen returning; trees lightening • Melanic form easier for birds to spot • P increasing; p decreasing

7. Definitions • Polymorphism • the presence of more than one allele at a locus • generally, for a locus to be considered polymorphic the rare allele must be at a frequency of at least 5%

8. Definitions • Monomorphic loci • loci where all individuals in a population have the same allele • no genetic variation at these loci • populations are said to be “fixed” for these alleles

9. Definitions • Population • a community of individuals of the same type • Mendelian population • a community of interbreeding, sexually reproducing individuals • sometimes called a deme

10. Biological Species Concept • A species is the most inclusive Mendelian population • Biological Species Concept: • A species is a group of actually or potentially interbreeding individuals which are reproductively isolated from other such groups

11. Definitions • Gene pool - all the alleles present in a population • we generally consider only one locus at a time

12. Allele frequencies • We use the frequencies of alleles as a measure of genetic change in a population • Allele frequencies: • the percentage of a certain allele in a population • Freq (A) = # A alleles / Total # of alleles

13. Allele Frequencies... Aa aa aa Aa aa AA AA aa Aa AA Aa aa AA aa Aa Aa Aa 15 Freq (A) = ----------- = 0.44 34

14. Allele Frequencies... • Notice: the frequency of the A allele plus the frequency of the a allele totals 1 • 0.44 + 0.56 = 1 • The allele frequencies must total 1 or 100%

15. Allele Frequencies... • In a two allele system, if we set the frequency of the A allele to sum number called “p” and the frequency of the a allele to “q” then: • p + q = 1 • For a three allele system, we would use p, q, and r: • p + q + r = 1

16. Allele Frequencies... • For example, ABO Blood grouping • p = freq. of A allele • q = freq. of B allele • r = freq. of O allele • p + q + r = 1 • there are no other alleles; these percentages must total 1

17. Allele Frequencies... • In the real world, we cannot see gene pools directly, we use the numbers of each phenotype to calculate allele frequencies • Beta thalassaemia: TT Tt tt normal carrier(slight anemia) anemic 400 75 25 # :

18. TT Tt tt normal carrier anemic 400 75 25 2(400) + 1(75) freq (T) = p = ------------------------- = 0.875 2(400 + 75 + 25)

19. Snails: Brown Mottled White BB BW WW 150 500 350

20. Allele frequencies • In the case of true dominance, we run into problems • it is not possible to distinguish homozygous dominants from heterozygotes; therefore we cannot directly calculate allele frequencies

21. The Hardy-Weinberg Equilibrium • May be used to estimate allele frequencies if direct calculation is not possible • Used to quantify changes in allele frequencies • a way to “measure” evolution, in a way

22. The Hardy-Weinberg Equilibrium • Relates allele frequencies and genotype frequencies • Allows us to move back and forth between allele and genotype frequencies • Allows us to see the effects of various outside forces on allele and genotype frequencies

23. The Hardy-Weinberg Equilibrium • States: In the absence of certain factors, genotype frequencies and allele frequencies remain constant from generation to generation • In an “ideal” population, there will be no genetic change

24. The Hardy-Weinberg Equilibrium • Five forces which may change allele frequencies: • mutation • migration • small population size • non-random mating • selection

25. Five forces changing H/W frequencies: • Mutation • ultimate source of all variation • with each mutation of one allele to another, their relative frequencies will change • very s l o w change

26. Five forces changing H/W frequencies: • Migration • “gene flow” - introduction of alleles from one population to another • may be one way or two way exchange

27. Five forces changing H/W frequencies: • Small population size • leads to random genetic drift • allele frequencies change randomly • most noticeable in populations smaller than around 2,000 individuals

28. Five forces changing H/W frequencies: • Non-random mating • not all matings equally likely to occur • positive assortative mating - like genotypes mate • negative assortative mating - genotypes mate with other genotypes

29. Five forces changing H/W frequencies: • Selection • Natural selection: when one allele confers an advantage in survival • If the presence of a certain allele enables individuals carrying that allele to better exploit the environment, that allele will increase in frequency • remember the peppered moth!

30. Five forces changing H/W frequencies: • Any one of these forces (alone or in combination) may change allele & genotype frequencies • some are more efficient than others • In the absence of these factors, there will be NO CHANGE in frequencies = equilibrium

31. Hardy - Weinberg Equilibrium • Equilibrium means there is no change in allele frequencies • Equilibrium DOES NOT mean there are equal numbers of each allele • equilibrium is possible if p = q = 0.5 • equilibrium is possible at any other values of p and q also

32. Relationship between allele and genotype frequencies p = freq (A) q = freq (B) Since gametes are haploid, the allele frequencies are equal to the frequencies of the gametes carrying each allele. If the frequency of an allele is p, the frequency of gametes carrying that allele will also be p

33. Relationship between allele and genotype frequencies If mating is random, we can construct a Punnett square: eggs A B p q A B AA AB p q p2 pq sperm AB BB pq q2

34. Relationship between allele and genotype frequencies A B p q AA AB A B p q p2 pq AB BB pq q2 genotypes: AA AB BB frequencies: p2 2pq q2

35. genotypes: AA AB BB frequencies: p2 2pq q2 Are there any other possible genotypes with these two alleles? No! Therefore: p2 + 2pq + q2 = 1

36. Three or more alleles: • freq (A) = p; freq (B) = q; freq (C) = r • p + q + r = 1 • genotype frequencies: AA AB AC BB BC CC p2 2pq 2pr q2 2qr r2 p2 + 2pq + 2pr + q2 + 2qr + r2 = 1

37. Relationship between allele/genotype frequencies and equilibrium p = q = .5 A B p q A p2 pq B pq q2 p q

38. Relationship between allele/genotype frequencies and equilibrium p = .70 q = .30 A B A B p q p2 pq pq q2 p q

39. Using the Hardy-Weinberg Equations • To test for equilibrium • used when numbers of each genotype is known • To estimate allele and genotype frequencies • used in cases of true dominance • must assume equilibrium • (really, really cheating)

40. Testing for equilibrium genotypes: AA AB BB numbers: 100 100 100 Is this population in equilibrium? i.e. do the genotype frequencies = p2, 2pq, and q2? 200 + 100 p = --------------- = 0.5 600 q = 0.5

41. Testing for equilibrium genotypes: AA AB BB numbers: 100 100 100 exp. freqs: (.5)2 2(.5)(.5) (.5)2 0.25 0.50 0.25 exp. #’s: 0.25(300) 0.50(300) 0.25(300) 75 150 75 So, do the observed #’s match the expected #’s?

42. genotypes: AA AB BB obs. #’s: 100 100 100 exp. #’s: 75 150 75 (100 - 75)2 (100 - 150)2 (100 - 75)2 c2 = ------------- + -------------- + ------------ 75 150 75 = 33.27 d.f. = # classes - 1 - # independent variables calculated from data = 3 - 1 - 1 = 1 p < 0.01

43. Testing for equilibrium • If a population is not in equilibrium, one or more of those five factors is at work • it is generally not possible to tell which one • Once all five conditions are met, it will take only one generation to return to equilibrium

44. Testing for equilibrium Congenital adrenal hyperplasia neonatal death if untreated; treatment w/ cortisones leads to normal lifespan, health and fertility. Carriers detectable w/ RFLP analysis. Frequency of HH: ~1/20,000 in general U.S. population. 1/500 in Yupik Eskimos. HH Hh hh 1520 464 16

45. Estimating allele/genotype frequencies • If there is true dominance, we cannot distinguish homozygous dominants from heterozygotes • therefore, we cannot calculate allele frequencies • therefore, we cannot test for equilibrium • We must ASSUME equilibrium and estimate p and q • (generally not a valid assumption)

46. Estimating allele/genotype frequencies Tay-Sachs Disease: autosomal recessive, lack of hexosaminidase A --> build-up of gangliosides TT Tttt 8777 1223 assume q2 = 1223/10000 q = 0.35 p = 0.65

47. Estimating allele/genotype frequencies So, how many of the normal individuals are expected to be carriers? expected frequency: 2pq = 2(0.65)(0.35) = 0.455 expected #’s: 0.455 (10000) = 4550