Hybridization plays an important role in the evolution of certain groups of organisms, adaptation to their environments, and diversification of their genomes. The evolutionary histories of such groups are reticulate, and methods for reconstructing them are still in their infancy and have limited applicability. We present a maximum likelihood method for inferring reticulate evolutionary histories while accounting simultaneously for incomplete lineage sorting. Additionally, we propose methods for assessing confidence in the amount of reticulation and the topology of the inferred evolutionary history. Our method obtains accurate estimates of reticulate evolutionary histories on simulated datasets. Furthermore, our method provides support for a hypothesis of a reticulate evolutionary history inferred from a set of house mouse (Mus musculus) genomes. As evidence of hybridization in eukaryotic groups accumulates, it is essential to have methods that infer reticulate evolutionary histories. The work we present here allows for such inference and provides a significant step toward putting phylogenetic networks on par with phylogenetic trees as a model of capturing evolutionary relationships. reticulate evolution | incomplete lineage sorting | phylogenetic networks | maximum likelihood P hylogenetic trees have long been a mainstay of biology, providing an interpretive model of the evolution of molecules and characters and a backdrop against which comparative genomics and phenomics are conducted. Nevertheless, some evolutionary events, most notably horizontal gene transfer in prokaryotes and hybridization in eukaryotes, necessitate going beyond trees (1). These events result in reticulate evolutionary histories, which are best modeled by phylogenetic networks (2). The topology of a phylogenetic network is given by a rooted, directed, acyclic graph (rDAG) that is leaf-labeled by a set of taxa ( Fig. 1; more details are provided in Model and SI Appendix). Reticulation events result in genomic regions with local genealogies that are incongruent with the speciation pattern. Several methods and heuristics use this incongruence as a signal for inferring reticulation events and reconstructing phylogenetic networks from local genealogies. These methods, which are surveyed elsewhere (2-4), assume that reticulation events are the sole cause of all incongruence among the gene trees and seek phylogenetic networks to explain all of the incongruence. A serious limitation of these methods is that they would grossly overestimate the amount of reticulation in a dataset when other causes of incongruence are at play. Indeed, several recent studies (5-9) have shown that detecting hybridization in practice can be complicated by the presence of incomplete lineage sorting (ILS) (Fig. 1).Recently, a set of methods was devised to analyze data where reticulation and ILS might both be simultaneously at play (10-15). However, these methods are all applicable to simple scenarios of species evolution and mostly assume a known hypothesis about the topol...

Background: Phylogenies, i.e., the evolutionary histories of groups of taxa, play a major role in representing the interrelationships among biological entities. Many software tools for reconstructing and evaluating such phylogenies have been proposed, almost all of which assume the underlying evolutionary history to be a tree. While trees give a satisfactory first-order approximation for many families of organisms, other families exhibit evolutionary mechanisms that cannot be represented by trees. Processes such as horizontal gene transfer (HGT), hybrid speciation, and interspecific recombination, collectively referred to as reticulate evolutionary events, result in networks, rather than trees, of relationships. Various software tools have been recently developed to analyze reticulate evolutionary relationships, which include SplitsTree4, LatTrans, EEEP, HorizStory, and T-REX.

Gene tree topologies have proven a powerful data source for various tasks, including species tree inference and species delimitation. Consequently, methods for computing probabilities of gene trees within species trees have been developed and widely used in probabilistic inference frameworks. All these methods assume an underlying multispecies coalescent model. However, when reticulate evolutionary events such as hybridization occur, these methods are inadequate, as they do not account for such events. Methods that account for both hybridization and deep coalescence in computing the probability of a gene tree topology currently exist for very limited cases. However, no such methods exist for general cases, owing primarily to the fact that it is currently unknown how to compute the probability of a gene tree topology within the branches of a phylogenetic network. Here we present a novel method for computing the probability of gene tree topologies on phylogenetic networks and demonstrate its application to the inference of hybridization in the presence of incomplete lineage sorting. We reanalyze a Saccharomyces species data set for which multiple analyses had converged on a species tree candidate. Using our method, though, we show that an evolutionary hypothesis involving hybridization in this group has better support than one of strict divergence. A similar reanalysis on a group of three Drosophila species shows that the data is consistent with hybridization. Further, using extensive simulation studies, we demonstrate the power of gene tree topologies at obtaining accurate estimates of branch lengths and hybridization probabilities of a given phylogenetic network. Finally, we discuss identifiability issues with detecting hybridization, particularly in cases that involve extinction or incomplete sampling of taxa.

Single-cell sequencing enables the inference of tumor phylogenies that provide insights on intra-tumor heterogeneity and evolutionary trajectories. Recently introduced methods perform this task under the infinite-sites assumption, violations of which, due to chromosomal deletions and loss of heterozygosity, necessitate the development of inference methods that utilize finite-sites models. We propose a statistical inference method for tumor phylogenies from noisy single-cell sequencing data under a finite-sites model. The performance of our method on synthetic and experimental data sets from two colorectal cancer patients to trace evolutionary lineages in primary and metastatic tumors suggests that employing a finite-sites model leads to improved inference of tumor phylogenies.Electronic supplementary materialThe online version of this article (doi:10.1186/s13059-017-1311-2) contains supplementary material, which is available to authorized users.

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.

Phylogenetic networks model the evolutionary history of sets of organisms when events such as hybrid speciation and horizontal gene transfer occur. In spite of their widely acknowledged importance in evolutionary biology, phylogenetic networks have so far been studied mostly for specific data sets. We present a general definition of phylogenetic networks in terms of directed acyclic graphs (DAGs) and a set of conditions. Further, we distinguish between model networks and reconstructible ones and characterize the effect of extinction and taxon sampling on the reconstructibility of the network. Simulation studies are a standard technique for assessing the performance of phylogenetic methods. A main step in such studies entails quantifying the topological error between the model and inferred phylogenies. While many measures of tree topological accuracy have been proposed, none exist for phylogenetic networks. Previously, we proposed the first such measure, which applied only to a restricted class of networks. In this paper, we extend that measure to apply to all networks, and prove that it is a metric on the space of phylogenetic networks. Our results allow for the systematic study of existing network methods, and for the design of new accurate ones.

Phylogenomics has largely succeeded in its aim of accurately inferring species trees, even when there are high levels of discordance among individual gene trees. These resolved species trees can be used to ask many questions about trait evolution, including the direction of change and number of times traits have evolved. However, the mapping of traits onto trees generally uses only a single representation of the species tree, ignoring variation in the gene trees used to construct it. Recognizing that genes underlie traits, these results imply that many traits follow topologies that are discordant with the species topology. As a consequence, standard methods for character mapping will incorrectly infer the number of times a trait has evolved. This phenomenon, dubbed "hemiplasy," poses many problems in analyses of character evolution. Here we outline these problems, explaining where and when they are likely to occur. We offer several ways in which the possible presence of hemiplasy can be diagnosed, and discuss multiple approaches to dealing with the problems presented by underlying gene tree discordance when carrying out character mapping. Finally, we discuss the implications of hemiplasy for general phylogenetic inference, including the possible drawbacks of the widespread push for "resolved" species trees.

Current variant callers are not suitable for single-cell DNA sequencing (SCS) as they do not account for allelic dropout, false-positive errors, and coverage non-uniformity. We developed Monovar, a novel statistical method for detecting and genotyping single nucleotide variants in SCS data. Evaluation based on an isogenic fibroblast cell line and three different human tumor datasets showed substantial improvement of Monovar over standard algorithms for identifying driver mutations and delineating clonal substructure.