Joint Linkage and Linkage Disequilibrium Mapping Key Reference Li, Q., and R. L. Wu, 2009 A...
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Transcript of Joint Linkage and Linkage Disequilibrium Mapping Key Reference Li, Q., and R. L. Wu, 2009 A...
Joint Linkage and Linkage Disequilibrium Mapping
Key ReferenceLi, Q., and R. L. Wu, 2009 A multilocus model for constructing a linkage disequilibrium map in human populations. Statistical Applications in Genetics and Molecular Biology 8 (1): Article 18.
Genetic Designs for Mapping• Controlled crosses – Backcross, F2, full-sib family, …
(linkage)• Unrelated (random) individuals from a natural
population (linkage disequilibrium)• Cases and controls from a natural population• Unrelated (random) families from a natural population
(linkage and LD)• Related (non-random) families from a natural
population (linkage, LD and identical-by-descent)
Family designs are increasingly used for genetic studies because of much information contained.
Natural Population• Consider two SNPs 1 (with two allele A and a)
and 2 (with two alleles B and b)• The two SNPs are linked with recom. frac. r • The two SNPs form four haplotypes, AB, Ab, aB,
and ab• Prob(A) = p, Prob(B) = q, linkage disequilibrium
= D. We have haplotype frequencies as
Segregation of double heterozygote
• Overall haplotype frequencies produced by this parent are calculated as 1/2ω1 for AB or ab and 1/2ω2 for Ab or aB
A Joint Probability
• Mother genotypes (Mm)
• Father genotypes (Mf )
• Offspring genotypes (Mo)
P(Mm,Mf,Mo) = P(Mm,Mf)P(Mo|Mm.Mf)
= P(Mm)P(Mf)P(Mo|Mm,Mf)
EM algorithm for r
• E step - calculate the probability with which a considered haplotype produced by a double heterozygote parent is the recombinant type using
E step (cont’d)
• Calculate the probability with which a double heterozygote offspring carries recombinant haplotypes by
Hypothesis tests
Linkage and Linkage disequilibriumH0: r = 0 and D = 0H1: At least one equality does not hold
LR = -2(log L0 – log L1)
Critical threshold x2 (df=2)