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 va riability and linkage disequilibrium. We derive the distribution of the wai ting time until a gene conversion event occurs in a sample in terms of the distribution of the length of the transferred segment, zeta. We do not assu me any specific form of the distribution of zeta. Further, given that a gen e conversion event occurs we find the distribution of (sigma, tau), the end points of the transferred segment and derive results on correlations betwe en local trees in positions chi(1) and chi(2). Among other results we show that the correlation between the branch lengths of two local trees in the c oalescent with gene conversion land no recombination) decreases toward a no nzero constant when the distance between chi(1) and chi(2) increases. Final ly, we show that a model including both recombination and gene conversion m ight account for the lack of intralocus associations found in, e.g., Drosop hila melanogaster. (C) 2000 Academic Press.