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MIT6_047f08_lec13_note13

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MIT OpenCourseWare http://ocw.mit.edu 6.047 / 6.878 Computational Biology: Genomes, Networks, Evolution Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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Fall 2008 6.047/6.878 Lecture 13 Population Genomics II : Pardis Sabeti 1 Introduction In this lecture we will discuss linkage disequilibrium and allele correlations, as well as applications of linkage and association studies. 2 Linkage/Haplotypes Recall Mendel’s Law of Independent Assortment, which states that allele pairs from different loci separate independently during the formation of gametes. For example if we have a population of individuals such that at a given locus we find 80% A and 20% G, while at a second locus of interest we find 50% C and 50% T, then independent assortment would imply that the corresponding haplotype frequencies at this double loci in the next generation should be (80% * 50%) = 40% AC, (20% * 50%) = 20% GC, and similarly, 40% AT, 10% GT. However in real life the separation is not always independent, since the two loci may be linked, by being close together on the same chromosome. For example for the allele frequencies at the two loci given above we might get actual haplotype frequencies of 30% AC, 20% BC, 50% AT, and 0% GT. This occurs due to ”linkage disequilibrium”, which is the disequilibrium of the allele frequencies which occur when the loci are close enough that link- age occurs (eventually, recombination occurs and the frequencies settle into equilibrium). Linkage disequilibrium such as in this example, where there are only two alleles observed at each of two loci of interest, is often measured by a quantity, D, which is defined as follows: D = | ObsP ( A 1 B 1 ) ObsP ( A 2 B 2 ) ObsP ( A 1 B 2 ) ObsP ( A 2 B 1 ) | where ObsP ( A i B j ) denotes the fraction of observed haplotypes at the A and B loci consisting of allele A i at locus A and allele B j at locus B. (Note: in our example, A 1 = A , A 2 = G , B 1 = C , and B 2 = T .) In general, A 1 , B 1 denote 1
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the ”major alleles” and A 2 , B 2 the ”minor alleles” at the two loci. Note that if there is no linkage disequilibrium, i.e., the allele pairs separate independently, then ObsP ( A i B j ) is simply the product of the allele frequencies, P ( A i ) and P ( B j ). It follows that in this case, D = | P ( A 1 ) P ( B 1 ) P ( A 2 ) P ( B 2 ) P ( A 1 ) P ( B 2 ) P ( A 2 ) P ( B 1 ) | = 0 . For the observed haplotype frequencies given above, we instead get D = | 0 . 3 0 0 . 5 0 . 2 | = 0 . 1 . It is useful to compare to D to Dmax , the maximum possible value of D given the allele frequencies you have. One can show that Dmax is equal to the smaller of the expected haplotype frequencies ExpP ( A 1 B 2 ) and ExpP ( A 2 B 1 ) when there is no linkage (see Appendix). In particular, it is convenient to define D D = Dmax which in this case equals 0.1/0.1 = 1, indicating the maximum possible link- age disequilibrium, or ”complete skew”. ( D varies between 0 when totally unlinked, to 1 when totally linked.) Three other examples of linkage disequilibrium are given in the slides for this lecture– two with complete skew (D’=1) in each case where only two ga-
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