A Duality Identity between a Model of Bacterial Recombination and the Wright–Fisher Diffusion

Abstract

In this article, we establish, using a duality argument, an identity stating that the Laplace transform of the length of a contiguous bacterial recombination region equals the probability of choosing a given allele in a stationary population evolving according to the one-dimensional Wright–Fisher diffusion model. Beyond giving us an improved inferential strategy for parameter estimation in bacterial recombination, the matching of the selection and recombination parameters in the identity also suggests the existence of an intriguing formal relationship between gene conversion and the ancestral selection graph.