Goals • Estimation of LD in terms of D, D’ and r2. • Determine effect of random and non-random mating on LD. • Estimate LD from diploid genotype data using EM-algorithm.
LD estimation in two-locus (A&B) and two-allele (1 & 2) model p2 p2 p1 A2 A2 p1 A1 A1 q2 q1 q2 B2 B2 B1 B1 q1
Different measures of LD If D > 0, Dmax = min(p1q2, p2q1) If D < 0, Dmax = min(p1q1, p2q2).
Allele history Time High drift or Selective sweep
LD Broken by recombination A1 B1 A1 B2 A2 B1 A2 B2 A1 B1 A1 B2 A1 B2 A1 B1
LD Broken by recombination Closer proximity -> less recombination -> stronger LD
Decay of LD Recombination rate for self-fertilizing organisms:
Problem 1.In most conifers, gamete frequencies and the linkage phase of diploid genotypes can be determined directly because seeds contain relatively large amounts of haploid nutritional tissue (called endosperm or megagametophyte), which originates from the maternal gamete. As part of a study of the linkage relationship among allozyme loci in loblolly pine (Pinustaeda), Adams and Joly (1980) sampled 456 gametes at loci phosphoglucoseisomerase 2 (PGI2, for simplicity, let this be locus A) and glutamate-oxaloacetatetransaminase 1 (GOT1, let this be locus B) and observed the following numbers of gametes. • Calculate D, D’, andr2, and test the statistical significance of the gametic disequilibrium between the two loci. • Because the linkage phase of each mother tree was known, Adams and Joly were able to estimate that the recombination rate between the two loci is c = 0.044. • i) What is the expected value of D in the next generation (i.e., in the offspring of the seeds that were included in the study)? • ii) How many generations of random mating will it take for D to decay below 0.005? • iii) What is the expected value of D in the next generation if: • S = 0.1? • S = 0.5? • S = 0.9? • Repeat the calculations from b) assuming c = 0.5 (i.e., assuming that the two loci are physically unlinked). • Discuss the relative importance of rates of recombination and self-fertilization in determining the rate of decay of LD.
Problem 2. Compare rates of decay of r2 with physical distance in sequences from the phytochrome B2 (PHYB2) gene in European aspen (Populustremula) and the phytochrome C (PHYC) gene in Arabidopsis thaliana. • Show scatter plots with trend lines illustrating the decay of r2 with physical distance for each gene. • How do the patterns of LD differ between these two species, and why? (BIOLOGICAL EXPLANATION) • GRADUATE STUDENTS ONLY: Provide facts and citations supporting your biological explanation.
Haplotypes through EM • When we genotype, we often don’t know the actual haplotypes • Unphasedhaplotypes • Can use a maximum likelihood method to obtain haplotype frequencies • Expectation Maximization (EM)
Haplotypes through EM • Initialize – Guess the gamete frequencies • Expectation Step – Find expected frequencies of known phase genotypes given gamete frequencies • Maximization Step – Find expected frequencies of all unphased genotypes given gamete frequencies • Use to make new gamete frequency estimates where n= # of unphased genotypes in the samples, n1, n2….n5, are the # of times each unphased genotype was observed in the sample, and P1, P2, …., P5 are the expected frequencies of the unphased genotypes in the sample.
Problem 3. File human_LD.arp contains data for humans from two populations (Han and Melanesian) genotyped for the same loci you have analyzed for departures from Hardy-Weinberg Equilibrium. The Han sample includes individuals from a broad geographic area in China, whereas the Melanesian sample only includes individuals from the Bougainville Island. Use Arlequin to test for significant linkage disequilibrium among the 10 loci in each of these populations. • How do you interpret the difference in the number of linked loci in the two populations? (STATISTICAL AND BIOLOGICAL INTERPRETIONS) • GRADUATE STUDENTS ONLY: How many pairs of loci are expected to show significant LD at α = 0.05 by chance (i.e., if there is no gametic disequilibrium among them in the population)? • GRADUATE STUDENTS ONLY: Provide facts and citations supporting your biological interpretation of the results.