Practical Speedup of Bayesian Inference of Species Phylogenies by Restricting the Space of Gene Trees

Abstract

Species tree inference from multi-locus data has emerged as a powerful paradigm in the post-genomic era, both in terms of the accuracy of the species tree it produces as well as in terms of elucidating the processes that shaped the evolutionary history. Bayesian methods for species tree inference are desirable in this area as they have been shown to yield accurate estimates, but also to naturally provide measures of confidence in those estimates. However, the heavy computational requirements of Bayesian inference have limited the applicability of such methods to very small data sets. In this paper, we show that the computational efficiency of Bayesian inference under the multispecies coalescent can be improved in practice by restricting the space of the gene trees explored during the random walk, without sacrificing accuracy as measured by various metrics. The idea is to first infer constraints on the trees of the individual loci in the form of unresolved gene trees, and then to restrict the sampler to consider only resolutions of the constrained trees. We demonstrate the improvements gained by such an approach on both simulated and biological data.

Recent progress on methods for estimating and updating large phylogenies

“…by using divide-and-conquer to break a large dataset into subsets or constraining the search space (e.g. [20,58,96,97]). However, Bayesian methods produce distributions from which point estimates can be obtained, and these distributions have significant additional value since they enable uncertainty quantification.…”

“…For example, there are new methods for large-scale ML tree estimation (e.g. Very Fast Tree [113]), new techniques to speed up co-estimation of gene trees and species trees [96,114], and even divide-and-conquer approaches to phylogenetic network estimation [115]. This continued effort to develop methods that are highly accurate and scalable leads us to the optimistic prediction that the next 5–10 years will result in new scalable methods to estimate accurate alignments, trees and even phylogenetic networks, and that these methods will enable biologists to make discoveries on the large and ultra-large phylogenomic datasets that they assemble.…”

<strong></strong> Recent Progress on Methods for Estimating and Updating Large Phylogenies

“…Bayesian methods, such as MrBayes (Ronquist and Huelsenbeck, 2003), are well established in the research community and have been shown to provide highly accurate point estimates of alignments, gene trees, and species trees; however, most Bayesian methods use MCMC (Markov Chain Monte Carlo) and are computationally intensive on large datasets since convergence to the stationary distribution is required for high confidence in an accurate result. Some progress has been made on improving the scalability of these point estimations using Bayesian methods, e.g., by using divide-and-conquer to break a large dataset into subsets or constraining the search space (e.g., Zimmermann et al (2014); Nute and Warnow (2016); Wang et al (2020); Gupta et al (2021)). However, Bayesian methods produce distributions from which point estimates can be obtained, and these distributions have significant additional value since they enable uncertainty quantification.…”

“…This study did not discuss all the recent advances in large-scale alignment and tree estimation, and some of these may provide even better scalability and accuracy. For example, there are new methods for large-scale maximum likelihood tree estimation (e.g., Very Fast Tree (Piñeiro et al, 2020)), new techniques to speed up co-estimation of gene trees and species trees (Wang and Nakhleh, 2018;Wang et al, 2020), and even divide-and-conquer approaches to phylogenetic network estimation (Zhu et al, 2019a). This continued effort to develop methods that are highly accurate and scalable leads us to the optimistic prediction that the next 5 to 10 years will result in new scalable methods to estimate accurate alignments, trees, and even phylogenetic networks, and that these methods will enable biologists to make discoveries on the large and ultra-large phylogenomic datasets that they assemble.…”