Lab 12. Linkage Disequilibrium
November 28, 2012
Goals1. Estimation of LD in terms of D, D’ and r2.
2. Determine effect of random and non-random mating on LD.
3. Estimate LD from diploid genotype data using EM-algorithm.
LD estimation in two-locus (A&B) and two-allele (1 & 2) model
A1 A1 A2 A2
B1 B2 B1 B2
p1 p1 p2 p2
q1 q2 q1 q2
Gamete Observed gametic frequency
Expected gametic frequency under linkage equilibrium
Allele Allele frequency
A1B1 x11 p1q1 A1 p1=x11+x12A1B2 x12 p1q2 A2 p2= x21+x22A2B1 x21 p2q1 B1 q1= x11+x21A2B2 x22 p2q2 B2 q2= x12+x22
211222111221122122221111 xxxxxqpxqpqpxqpxD
2121 qqpp
Dr
If D > 0, Dmax = min(p1q2, p2q1)
If D < 0, Dmax = min(p1q1, p2q2).
max
'D
DD
Different measures of LD
2121
222
qqpp
NDNr
Allele history
High driftorSelective sweep
Time
LD Broken by recombination
A1 B1
A2 B2
A1 B2
A2 B1
A1 B1
A1 B2
A1 B2
A1 B1
LD Broken by recombination
Closer proximity -> less recombination -> stronger LD
Decay of LD00)1( DeDcD ctt
t
0
ln1
D
D
ct t
Recombination rate for self-fertilizing organisms:
Gamete CountA1B1 138A1B2 88A2B1 78A2B2 152Total 456
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)
a.)Calculate D, D’, and r2, 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 r2 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 r2 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
• When we genotype, we often don’t know the actual haplotypes– Unphased haplotypes
• Can use a maximum likelihood method to obtain haplotype frequencies– Expectation Maximization (EM)
Haplotypes through EM
Haplotypes through EM1. Initialize – Guess the gamete frequencies2. Expectation Step – Find expected frequencies of
known phase genotypes given gamete frequencies3. Maximization Step – Find expected frequencies of all
unphased genotypes given gamete frequenciesa. 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.
5431543
221
54321 !!!!!
!)sfrequencie haplotype|( nnnnn PPPPP
nnnnn
nDataPL
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.
http://en.wikipedia.org/wiki/Melanesia
Han
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