A maximum pseudo-likelihood approach for phylogenetic networks

Abstract

BackgroundSeveral phylogenomic analyses have recently demonstrated the need to account simultaneously for incomplete lineage sorting (ILS) and hybridization when inferring a species phylogeny. A maximum likelihood approach was introduced recently for inferring species phylogenies in the presence of both processes, and showed very good results. However, computing the likelihood of a model in this case is computationally infeasible except for very small data sets.ResultsInspired by recent work on the pseudo-likelihood of species trees based on rooted triples, we introduce the pseudo-likelihood of a phylogenetic network, which, when combined with a search heuristic, provides a statistical method for phylogenetic network inference in the presence of ILS. Unlike trees, networks are not always uniquely encoded by a set of rooted triples. Therefore, even when given sufficient data, the method might converge to a network that is equivalent under rooted triples to the true one, but not the true one itself. The method is computationally efficient and has produced very good results on the data sets we analyzed. The method is implemented in PhyloNet, which is publicly available in open source.ConclusionsMaximum pseudo-likelihood allows for inferring species phylogenies in the presence of hybridization and ILS, while scaling to much larger data sets than is currently feasible under full maximum likelihood. The nonuniqueness of phylogenetic networks encoded by a system of rooted triples notwithstanding, the proposed method infers the correct network under certain scenarios, and provides candidates for further exploration under other criteria and/or data in other scenarios.

Fast and accurate statistical inference of phylogenetic networks using large-scale genomic sequence data

“…Our finding is consistent with the study of Yu and Nakhleh [13], and contrasts with the conclusions of Salichos and Rokas. Specifically, the distribution of observed local genealogies better reflects a multi-species network coalescent model [16] as opposed to a basic multi-species coalescent model.…”

“…The substitution model was selected using ProtTest [45]. Following the procedures of Yu and Nakhleh [13], unrooted gene trees were rooted under the MDC criterion [21] using the species tree reported in [39].…”

“…In the performance study of Hejase and Liu [15], the probabilistic network inference methods were found to be the most accurate among state-of-the-art methods, and MPL was among the fastest methods in this class. MPL utilized a pseudo-likelihood-based approximation for increased computational efficiency compared with full likelihood methods [13]. However, the tradeoff netted efficiency that was well short of current phylogenomic dataset sizes [15].…”

“…The yeast dataset in our empirical study was originally published by Salichos and Rokas [39] and re-analyzed by Yu and Nakhleh [13]. Comparing and contrasting the three studies reveals several important areas of strict and majority consensus.…”

“…We re-analyzed genomic sequence data that was originally published by Neafsey et al [46], which is a superset of the data studied by Fontaine et al [51] and Yu and Nakhleh [13]. The two-reticulation species phylogeny inferred by FastNet(MPL) is shown in Figure 3, where reticulations are visualized in a manner similar to [13]. (shown as Figure 1C in [51]) and the MLE-inferred species phylogeny reported by Wen et al [52], both of which were inferred using the 6-taxon Fontaine et al…”