Lab 12. Linkage Disequilibrium November 28, 2012
Goals 1. Es<ma<on of LD in terms of D, D and r 2. 2. Determine effect of random and non- random ma<ng on LD. 3. Es<mate LD from diploid genotype data using EM- algorithm.
LD es<ma<on in two- locus (A&B) and two- allele (1 & 2) model A1 p1 A1 p1 A2 p2 A2 p2 B1 q1 B2 q2 B1 q1 B2 q2 Gamete Observed gametic frequency Expected gametic frequency under linkage equilibrium Allele Allele frequency A1B1 x 11 p 1 q 1 A1 p1=x11+x12 A1B2 x 12 p 1 q 2 A2 p2= x21+x22 A2B1 x 21 p 2 q 1 B1 q1= x11+x21 A2B2 x 22 p 2 q 2 B2 q2= x12+x22 D = x p q = x p q = p q x = p q x = x x x x 11 1 1 22 2 2 1 2 12 1 2 12 11 22 12 21
Different measures of LD If D > 0, D max = min(p 1 q 2, p 2 q 1 ) If D < 0, D max = min(p 1 q 1, p 2 q 2 ). D ' = D D max r = D p p q q 1 2 1 2 2 χ = 2 Nr = p 1 ND p q 2 2 1 q 2
Allele history Time High dri/ or Selec2ve sweep
LD Broken by recombina2on A 1 B 1 A 2 B 2 A 1 B 2 A 2 B 1 A 1 B 1 A 1 B 2 A 1 B 2 A 1 B 1
LD Broken by recombina2on Closer proximity - > less recombina2on - > stronger LD
Decay of LD 0 0 ) 1 ( D e D c D ct t t = = 0 ln 1 D D c t t c effective = c 1! S 2! S " # $ % & ' Recombina<on rate for self- fer<lizing 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 (Pinus taeda), Adams and Joly (1980) sampled 456 gametes at loci phosphoglucose isomerase 2 (PGI2, for simplicity, let this be locus A) and glutamate-oxaloacetate transaminase 1 (GOT1, let this be locus B) and observed the following numbers of gametes.(15 minutes) Gamete Count A1B1 138 A1B2 88 A2B1 78 A2B2 152 Total 456 a.)calculate D, D, and r 2, and test the statistical significance of the gametic disequilibrium between the two loci. b.)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? c.) Repeat the calculations from b) assuming c = 0.5 (i.e., assuming that the two loci are physically unlinked). d.) Discuss the relative importance of rates of recombination and self-fertilization in determining the rate of LD decay
Problem 2. Compare rates of decay of r 2 with physical distance in sequences from the phytochrome B2 (PHYB2) gene in European aspen (Populus tremula) and the phytochrome C (PHYC) gene in Arabidopsis thaliana. a) Show scatter plots with trend lines illustrating the decay of r 2 with physical distance for each gene b) How do the patterns of LD differ between these two species, and why? c) GRADUATE STUDENTS: Provide facts and citations supporting your biological explanation
Haplotypes through EM When we genotype, we o/en don t know the actual haplotypes Unphased haplotypes Can use a maximum likelihood method to obtain haplotype frequencies Expecta2on Maximiza2on (EM)
Haplotypes through EM 1. Ini2alize Guess the gamete frequencies 2. Expecta2on Step Find expected frequencies of known phase genotypes given gamete frequencies 3. Maximiza2on Step Find expected frequencies of all unphased genotypes given gamete frequencies a. Use to make new gamete frequency es2mates L = P( Data haplotype frequencies) = 1! n2! n3! n4! n5! where n= # of unphased genotypes in the samples, n1, n2.n5, are the # of 2mes each unphased genotype was observed in the sample, and P1, P2,., P5 are the expected frequencies of the unphased genotypes in the sample. n n! P n 1 1 P n2 2 P n 3 3 P n 4 4 P n 5 5
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 and population structure. 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. a.) How do you interpret the difference in the number of linked loci in the two populations? b.) GRAD STUDENTS: How many pairs of loci are expected to show significant LD at α=0.05 by chance? c.) GRAD STUDENTS: Provide facts and citations supporting your biological claim.
Han hyp://en.wikipedia.org/wiki/melanesia