Coalescent models of gene conversion with and without selection

We investigate the probabilities of identity-by-descent at three loci in order to find a signature which differentiates between the two types of crossing over events: recombination and gene conversion. We use a Markov chain to model coalescence, recombination, gene conversion and mutation in a sample of size two. Using numerical analysis, we calculate the total probability of identity-by-descent at the three loci, and partition these probabilities based on a partial ordering of coalescent events at the three loci. We use these results to compute the probabilities of four different patterns of conditional identity and non-identity at the three loci under recombination and gene conversion. Although recombination and gene conversion do make different predictions, the differences are not likely to be useful in distinguishing between them using three locus patterns between pairs of DNA sequences. This implies that measures of genetic identity in larger samples will be needed to distinguish between gene conversion and recombination. The effect of recombination on Linkage Disequilibrium (LD) between two neutral loci located near a third locus that has undergone a selective sweep has two predictions: two loci on the same side of a selected locus might show substantial LD, whereas the expected LD for two loci on opposite sides of a selected locus is zero. Here, we extend McVean's model to include gene conversion. We show that one of the conclusions is strongly affected by gene conversion: when gene conversion is present, there may be substantial LD between two loci on opposite sides of a selective sweep. We also explore the ability of gene conversion to rescue ancestral variation during a strong selective sweep. During a selective sweep, gene conversion can, in principle, rescue short sections from ancestral haplotypes that lack the beneficial mutation from extinction by placing them on haplotypes that carry the beneficial mutation. To study this effect, we incorporate gene conversion into the standard sweep model. We use the model to derive the pairwise differences between n sampled lineages after a selective sweep.