A branching process with coalescence to model random phylogenetic networks

TL;DR

This paper introduces a new mathematically tractable model of random phylogenetic networks incorporating hybridization, providing formulas for biological quantities and analyzing their asymptotic behavior.

Contribution

It presents a novel model linking hybridization rates to phylogenetic distance and characterizes its limiting behavior as a Brownian continuum random tree.

Findings

Formulas for biological quantities of interest.

Convergence of the network to the Brownian continuum random tree.

Explicit description of the local weak limit.

Abstract

We introduce a biologically natural, mathematically tractable model of random phylogenetic network to describe evolution in the presence of hybridization. One of the features of this model is that the hybridization rate of the lineages correlates negatively with their phylogenetic distance. We give formulas / characterizations for quantities of biological interest that make them straightforward to compute in practice. We show that the appropriately rescaled network, seen as a metric space, converges to the Brownian continuum random tree, and that the uniformly rooted network has a local weak limit, which we describe explicitly.