Population Genetics: Chapter 3

1. Population Genetics: Chapter 3 Epidemiology 217January 16, 2011

2. Outline • Allele Frequency Estimation • Hardy-Weinberg equilibrium (HWE) • HWE Game • Population Substructure

3. Allele Frequency • Diploid, autosomal locus with 2 alleles: A and a • Allele frequency is the fraction: No. of particular allele No. of all alleles in population

4. Allele (Gamete) Frequency • Let p = Freq(A) frequency of the dominant allele • Let q = Freq(a) frequency of the recessive allele Then, p + q =1

5. Genotype Frequency • p2 = frequency of homozygous dominant genotype • q2 = frequency of homozygous recessive genotype • 2pq = frequency of heterozygous genotype Then, p2 +2pq + q2 =1

6. Estimating Allele Frequencies from Genotype Frequencies Genotypes: AA Aa aa Frequency: p2 2pq q2 • Frequency of A allele = p2 + ½ (2pq) • Frequency of a allele = q2 + ½ (2pq)

7. Ex. Calculation: Allele Frequencies Assume N=200 in each of two populations • Pop 1: 90 AA 40 Aa 70 aa (N=200) • Pop 2: 45 AA 130Aa 25 aa (N=200) In Pop 1: • p = 90/200 + ½ (40/200) = 0.45 + 0.10 = 0.55 • q = 70/200 + ½ (40/200) = 0.35 + 0.10 = 0.45 In Pop 2: • p = 45/200 + ½ (130/200) = 0.225 + 0.325 = 0.55 • q = 25/200 + ½ (130/200) = 0.125 + 0.325 = 0.45

8. Take home points • p + q =1 (sum of the allele frequencies = 1) • p2 + 2pq + q2 =1 (sum of the genotype frequencies = 1) • Two populations with markedly different genotype frequencies can have the same allele frequencies

9. Hardy-Weinberg The Hardy–Weinberg principle states that both allele and genotype frequencies in a population remain constant—that is, they are in equilibrium—from generation to generation unless specific disturbing influences are introduced p2 + 2pq + q2 = 1

10. Hardy-Weinberg Assumptions • Allele frequencies do not vary IF: • Large population • Random mating • No in or out migration • No isolated groups within the population • No mutation • No selection (no allele is advantageous)

11. Test of Hardy-Weinberg Equilibrium 1. Calculate observed allele & genotype frequencies 100 GG 30 AG 20 AA Genotype frequencies GG = 100/150 = 0.67 AG =30/150 = 0.20 AA = 20/150 = 0.13 Allele frequencies G alleles = 100*2 + 30 = 230 A alleles =20*2 + 30 = 70 Total alleles = 300 G afq (p) = 230/300 = 0.71 A afq (q) = 1-p = 0.23

12. Test of Hardy-Weinberg Equilibrium 2. Calculate expected genotype frequencies based on HW: p2 + 2pq + q2 = 1 p2 (GG) = 0.77 * 0.77 = 0.59 2pq (AG) = 2 * 0.77 * 0.23 = 0.35 q2 (AA) = 0.23 * 0.23 = 0.05

13. Test of Hardy-Weinberg Equilibrium 3. Compare expected genotype frequencies to observed frequencies Chi-square test = Σ(observed – expected)2/expected = 29.17 with 1 degree of freedom p = 6.6 x 10-8 > Out of H-W

14. HWE can be easily expanded to account for any number of alleles at a locus • 3 allele case (p1, p2, p3) Allele frequencies: p1 + p2 + p3 = 1 Genotype frequencies: p12 + p22 + p32 + 2p1p2 + 2p1p3 + 2p2p3= 1 • 4 allele case (p1, p2, p3, p4) Allele frequencies: p1 + p2 + p3 + p4= 1 Genotype frequencies: p12 + p22 + p32 + p42 + 2p1p2 + 2p1p3 + 2p2p3 + 2p3p4= 1

15. Application of Hardy-Weinberg Equilibrium • For genetic association studies: • Used as QC measure to assess the accuracy of the genotyping method • Expect SNPs to be in HWE among control populations (ethnic-specific) • Violations of HWE could indicate genotyping errors or bias in data

16. HWE Game • Everyone receives ~5 pairs of cards • Two allele model: Red (R allele) & Black (B allele) • Random Mating: Exchange one card from each pair with another person (keep cards face down) • Determine genotype frequency: RR, RB, BB • Determine allele frequency: R, B

17. Population Stratification Population stratification is a form of confounding in genetic studies where a gene under study shows marked variation in allele frequency across subgroups of a population and these subgroups differ in their baseline risk of disease

18. Population Stratification: Confounding Exposure of Interest True Risk Factor Disease Genotype of Interest Ethnicity True Risk Factor Disease Wacholder, JNCI, 2000

19. Population Stratification: Gm3;5,13,14 in admixed sample of Native Americans of the Pima and Papago tribes Study Population: 4,290 Pima and Papago Indians Genetic Variant: Gm 3;5,13, 15 haplotype (Gm system of human immunoglobulin G) Outcome: Type 2 diabetes Question: Is the Gm 3; 5,13, 15 haplotype associated with Type 2 diabetes? Knowler, AJHG, 1998

20. Population Stratification: Gm3;5,13,14 in admixed sample of Native Americans of the Pima and Papago tribes Unadjusted for ethnic background OR = 0.27 (95% 0.18-0.40)

21. Population Stratification: Gm3;5,13,14 in admixed sample of Native Americans of the Pima and Papago tribes Adjusted for ethnic background OR = 0.83 (95% 0.58-1.18)

22. Ancestry Informative Markers • Polymorphisms with known allele frequency differences across ancestral groups • Useful in estimating ancestry in admixed individuals • Example: Duffy locus (codes for blood group) • 100% sub-Saharan Africans vs. other groups • protects P. vivax (malaria)

23. Example AIM: Duffy locus http://www.ncbi.nlm.nih.gov/projects/SNP

24. Population Inbreeding Population inbreeding occurs when there is a preference of mating between close relatives or because of geographic isolation in a population. This will cause deviations in HWE by causing a deficit of heterozygotes.

25. How to quantify the amount of inbreeding in a population? • Inbreeding coefficient, F • The probability that a random individual in the population inherits two copies of the same allele from a common ancestor • F ranges 0 to 1: F is low in random mating populations F close to 1 in self-breeding population (plants)

26. Kinship & Reproduction: Icelandic couples # of children # of children that reproduce # of grandchildren mean lifespan of children Helgason, Science, 2008