A simulation approach for change-points on phylogenetic trees

TL;DR

This paper introduces a Bayesian inference method for detecting change-points in evolutionary model parameters across phylogenetic trees, using a novel approximation and a particle MCMC algorithm to improve computational efficiency.

Contribution

It proposes a new computational approach combining the time machine approximation with a particle marginal Metropolis-Hastings algorithm for change-point detection in phylogenetics.

Findings

The method effectively detects change-points in simulated data.

It outperforms ABC-based methods in empirical tests.

The approach is applicable to real biological data.

Abstract

We observe $n$ sequences at each of $m$ sites, and assume that they have evolved from an ancestral sequence that forms the root of a binary tree of known topology and branch lengths, but the sequence states at internal nodes are unknown. The topology of the tree and branch lengths are the same for all sites, but the parameters of the evolutionary model can vary over sites. We assume a piecewise constant model for these parameters, with an unknown number of change-points and hence a trans-dimensional parameter space over which we seek to perform Bayesian inference. We propose two novel ideas to deal with the computational challenges of such inference. Firstly, we approximate the model based on the time machine principle: the top nodes of the binary tree (near the root) are replaced by an approximation of the true distribution; as more nodes are removed from the top of the tree, the cost of computing the likelihood is reduced linearly in $n$. The approach introduces a bias, which we investigate empirically. Secondly, we develop a particle marginal Metropolis-Hastings (PMMH) algorithm, that employs a sequential Monte Carlo (SMC) sampler and can use the first idea. Our time-machine PMMH algorithm copes well with one of the bottle-necks of standard computational algorithms: the trans-dimensional nature of the posterior distribution. The algorithm is implemented on simulated and real data examples, and we empirically demonstrate its potential to outperform competing methods based on approximate Bayesian computation (ABC) techniques.