On the inference of complex phylogenetic networks by Markov Chain Monte-Carlo

Abstract

For various species, high quality sequences and complete genomes are nowadays available for many individuals. This makes data analysis challenging, as methods need not only to be accurate, but also time efficient given the tremendous amount of data to process. In this article, we introduce an efficient method to infer the evolutionary history of individuals under the multispecies coalescent model in networks (MSNC). Phylogenetic networks are an extension of phylogenetic trees that can contain reticulate nodes, which allow to model complex biological events such as horizontal gene transfer, hybridization and introgression. We present a novel way to compute the likelihood of biallelic markers sampled along genomes whose evolution involved such events. This likelihood computation is at the heart of a Bayesian network inference method called SnappNet, as it extends the Snapp method inferring evolutionary trees under the multispecies coalescent model, to networks. SnappNet is available as a package of the well-known beast 2 software. Recently, the MCMC_BiMarkers method, implemented in PhyloNet, also extended Snapp to networks. Both methods take biallelic markers as input, rely on the same model of evolution and sample networks in a Bayesian framework, though using different methods for computing priors. However, SnappNet relies on algorithms that are exponentially more time-efficient on non-trivial networks. Using simulations, we compare performances of SnappNet and MCMC_BiMarkers. We show that both methods enjoy similar abilities to recover simple networks, but SnappNet is more accurate than MCMC_BiMarkers on more complex network scenarios. Also, on complex networks, SnappNet is found to be extremely faster than MCMC_BiMarkers in terms of time required for the likelihood computation. We finally illustrate SnappNet performances on a rice data set. SnappNet infers a scenario that is consistent with previous results and provides additional understanding of rice evolution.

Recent progress on methods for estimating and updating large phylogenies

“…Because of this performance, Solís-Lemus et al [101] argue for the use of likelihood-based phylogenetic network methods for estimating the 'main tree' in the presence of gene flow. Unfortunately, likelihood-based methods for estimating explicit phylogenetic networks are enormously computationally intensive and even the most scalable such methods are limited to a few tens of species [108][109][110][111].…”

Identifiability of local and global features of phylogenetic networks from average distances

“…Remark The proof below uses basic algebra. Condition (5) ensures that (6) can be solved to give non-negative µa and µ b , and (4) ensures that γata > 0 and γ b t b > 0. If ( 4) is an equality, then the 4-point condition is satisfied and d is tree-like.…”

“…Conversely, suppose that a metric d on {a, g, b, h} satisfies ( 4) and (5). Then there exists γ such that…”

“…It is easy to see that they satisfy (4) from Theorem 19 for the circular ordering (a, b, c, d), because their displayed trees only have 2 topologies. Then N 2 (or N 3 ) satisfies condition (5) with d as the taxon of hybrid origin on a parameter subset of positive Lebesgue measure, in which case N 2 (or N 3 ) has the same average distances as N 1 for some choice of parameters on N 1 .…”

“…Inferring phylogenetic networks is hard, however. Computing times are prohibitive with more than a handful of taxa for likelihood-based approaches, such as full likelihood or Bayesian methods in PhyloNet or SnappNet [3][4][5]. Methods based on pairwise distances have the potential to be must faster [6].…”