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.

BackgroundPhylogenomic analyses involving whole-genome or multi-locus data often entail dealing with incongruent gene trees. In this paper, we consider two causes of such incongruence, namely, incomplete lineage sorting (ILS) and hybridization, and consider both parsimony and probabilistic criteria for dealing with them.ResultsUnder the assumption of ILS, computing the probability of a gene tree given a species tree is a very hard problem. We present a heuristic for speeding up the computation, and demonstrate how it scales up computations to data sizes that are not feasible to analyze using current techniques, while achieving very good accuracy. Further, under the assumption of both ILS and hybridization, computing the probability of a gene tree and parsimoniously reconciling it with a phylogenetic network are both very hard problems. We present two exact algorithms for these two problems that speed up existing techniques significantly and enable analyses of much larger data sets than is currently feasible.ConclusionOur heuristics and algorithms enable phylogenomic analyses of larger (in terms of numbers of taxa) data sets than is currently feasible. Further, our methods account for ILS and hybridization, thus allowing analyses of reticulate evolutionary histories.

Abstract. One of the criteria for inferring a species tree from a collection of gene trees, when gene tree incongruence is assumed to be due to incomplete lineage sorting (ILS), is minimize deep coalescence, or MDC. Exact algorithms for inferring the species tree from rooted, binary trees under MDC were recently introduced. Nevertheless, in phylogenetic analyses of biological data sets, estimated gene trees may differ from true gene trees, be incompletely resolved, and not necessarily rooted. In this paper, we propose new MDC formulations for the cases where the gene trees are unrooted/binary, rooted/non-binary, and unrooted/nonbinary. Further, we prove structural theorems that allow us to extend the algorithms for the rooted/binary gene tree case to these cases in a straightforward manner. Finally, we study the performance of these methods in coalescent-based computer simulations.

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