Topological linkage disequilibrium calculated from coalescent genealogies

We revisit the classical, and introduce a novel, concept of two-locus linkage disequilibrium (LD). In contrast to defining haplotypes as allele combinations at two marker loci, we concentrate on the clustering of a sample of chromosomes induced by their coalescent genealogy. The root of a binary coalescent tree defines two clusters of chromosomes, each one of them containing the left and right descendants of the root. At two different loci this assignment may be different as a result of recombination. We show that the proportion 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 it is, on average, larger than classical LD for any given distance between loci. Furthermore, tLD has a smaller coefficient of variation, which should provide an advantage, compared to the use of classical LD, for any kind of mapping purposes. We conclude with a practical application to the LCT region in human populations.