Markov jump processes in modeling coalescent with recombination

TL;DR

This paper proves that two main classes of recombination simulation models in population genetics share identical statistical properties, unifying their theoretical understanding and aiding future inference methods.

Contribution

It provides the first rigorous proof that back-in-time and spatially moving models have the same probability distribution on ancestral recombination graphs.

Findings

Both classes of models share the same probability distribution.

The study offers a unified interpretation of simulation algorithms.

Facilitates statistical inference on recombination.

Abstract

Genetic recombination is one of the most important mechanisms that can generate and maintain diversity, and recombination information plays an important role in population genetic studies. However, the phenomenon of recombination is extremely complex, and hence simulation methods are indispensable in the statistical inference of recombination. So far there are mainly two classes of simulation models practically in wide use: back-in-time models and spatially moving models. However, the statistical properties shared by the two classes of simulation models have not yet been theoretically studied. Based on our joint research with CAS-MPG Partner Institute for Computational Biology and with Beijing Jiaotong University, in this paper we provide for the first time a rigorous argument that the statistical properties of the two classes of simulation models are identical. That is, they share the same probability distribution on the space of ancestral recombination graphs (ARGs). As a consequence, our study provides a unified interpretation for the algorithms of simulating coalescent with recombination, and will facilitate the study of statistical inference on recombination.