Leveraging graphical model techniques to study evolution on phylogenetic networks

TL;DR

This paper demonstrates how graphical model techniques, especially belief propagation, can be applied to efficiently compute likelihoods and perform parameter inference on complex phylogenetic networks with reticulations.

Contribution

It reformulates models of trait evolution on phylogenetic networks as graphical models, enabling scalable inference methods like belief propagation.

Findings

Belief propagation can be applied for exact likelihood calculations on phylogenetic networks.

Approximate methods significantly reduce computational costs for complex networks.

Novel results for efficient parameter inference in linear Gaussian models are provided.

Abstract

The evolution of molecular and phenotypic traits is commonly modelled using Markov processes along a phylogeny. This phylogeny can be a tree, or a network if it includes reticulations, representing events such as hybridization or admixture. Computing the likelihood of data observed at the leaves is costly as the size and complexity of the phylogeny grows. Efficient algorithms exist for trees, but cannot be applied to networks. We show that a vast array of models for trait evolution along phylogenetic networks can be reformulated as graphical models, for which efficient belief propagation algorithms exist. We provide a brief review of belief propagation on general graphical models, then focus on linear Gaussian models for continuous traits. We show how belief propagation techniques can be applied for exact or approximate (but more scalable) likelihood and gradient calculations, and prove novel results for efficient parameter inference of some models. We highlight the possible fruitful interactions between graphical models and phylogenetic methods. For example, approximate likelihood approaches have the potential to greatly reduce computational costs for phylogenies with reticulations.