joint linkage and linkage disequilibrium mapping key reference li, q., and r. l. wu, 2009 a...
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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)
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