A Coalescence Approach to Gene Conversion

In this paper we develop a coalescent model with intralocus gene conversion. Such models are of increasing importance in the analysis of intralocus variability and linkage disequilibrium. We derive the distribution of the waiting time until a gene conversion event occurs in a sample in terms of the distribution of the length of the transferred segment, ζ. We do not assume any specific form of the distribution of ζ. Further, given that a gene conversion event occurs we find the distribution of (σ, τ), the end points of the transferred segment and derive results on correlations between local trees in positions χ1 and χ2. Among other results we show that the correlation between the branch lengths of two local trees in the coalescent with gene conversion (and no recombination) decreases toward a nonzero constant when the distance between χ1 and χ2 increases. Finally, we show that a model including both recombination and gene conversion might account for the lack of intralocus associations found in, e.g., Drosophila melanogaster.