Unusual behaviour of linkage disequilibrium in two-locus gene conversion models

The amount of linkage of disequilibrium maintained in a two-locus infinite population model by gene conversion and recombination is examined. Intrachromosomal conversion (conversion between different loci on the same chromosome) generates positive linkage disequilibrium. Specifically, [formula omitted] = p(1 − p) [1 − r/(γ + r − γr)], where p is the frequency of allele A at both loci, r is the recombination rate between loci and γ is the per-gamete conversion rate. Somewhat unexpectedly, interchromosomal conversion (conversion between loci on different chromosomes) also generates positive disequilibrium, albeit very small. More interestingly, the behaviour of this disequilibrium as a function of recombination is unusual. If β is the interchromosomal conversion rate between a pair of loci, then [formula omitted] = p(1 − p) [rβ/(β+r − βr)]. [formula omitted] increases with increasing recombination, being zero for the case of complete linkage (r = 0), and maximized at r = 1/2. This unusual behaviour can be accounted for by the generation of excess coupling gametes when an interchromosomal conversion event is followed by recombination.