Topological linkage disequilibrium calculated from coalescent genealogies

We revisit the classical concept of two-locus linkage disequilibrium (LD) and introduce a novel way of looking at haplotypes. In contrast to defining haplotypes as allele combinations at two marker loci, we concentrate on the clustering of sampled chromosomes induced by their coalescent genealogy. The root of a binary coalescent trees defines two clusters of chromosomes. At two different loci this assignment may be different as a result of recombination. We show that the amount of shared chromosomes among clusters at two different loci, measured by the squared correlation, constitutes a natural measure of LD. We call this topological LD (tLD) since it is induced by the topology of the coalescent tree. We find that its rate of decay decreases more slowly with distance between loci than that of conventional LD. Furthermore, tLD has a smaller coefficient of variation, which should render it more accurate for any kind of mapping purposes than conventional LD. We conclude with a practical application to the LCT region in human populations.