Fast algorithms and heuristics for phylogenomics under ILS and hybridization

A Polynomial-Time Algorithm for Minimizing the Deep Coalescence Cost for Level-1 Species Networks

Phylogenetic analyses commonly assume that the species history can be represented as a tree. However, in the presence of hybridization, the species history is more accurately captured as a network. Despite several advances in modeling phylogenetic networks, there is no known polynomial-time algorithm for parsimoniously reconciling gene trees with species networks while accounting for incomplete lineage sorting. To address this issue, we present a polynomial-time algorithm for the case of level-1 networks, in which no hybrid species is the direct ancestor of another hybrid species. This work enables more efficient reconciliation of gene trees with species networks, which in turn, enables more efficient reconstruction of species networks.

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

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.

Assessing the fit of the multi-species network coalescent to multi-locus data

MOTIVATION

With growing genome-wide molecular datasets from next-generation sequencing, phylogenetic networks can be estimated using a variety of approaches. These phylogenetic networks include events like hybridization, gene flow or horizontal gene transfer explicitly. However, the most accurate network inference methods are computationally heavy. Methods that scale to larger datasets do not calculate a full likelihood, such that traditional likelihood-based tools for model selection are not applicable to decide how many past hybridization events best fit the data. We propose here a goodness-of-fit test to quantify the fit between data observed from genome-wide multi-locus data, and patterns expected under the multi-species coalescent model on a candidate phylogenetic network.

RESULTS

We identified weaknesses in the previously proposed TICR test, and proposed corrections. The performance of our new test was validated by simulations on real-world phylogenetic networks. Our test provides one of the first rigorous tools for model selection, to select the adequate network complexity for the data at hand. The test can also work for identifying poorly inferred areas on a network.

AVAILABILITY AND IMPLEMENTATION

Software for the goodness-of-fit test is available as a Julia package at https://github.com/cecileane/QuartetNetworkGoodnessFit.jl.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Integrated likelihood for phylogenomics under a no-common-mechanism model

Background

Multi-locus species phylogeny inference is based on models of sequence evolution on gene trees as well as models of gene tree evolution within the branches of species phylogenies. Almost all statistical methods for this inference task assume a common mechanism across all loci as captured by a single value of each branch length of the species phylogeny.

Results

In this paper, we pursue a “no common mechanism" (NCM) model, where every gene tree evolves according to its own parameters of the species phylogeny. Based on this model, we derive an analytically integrated likelihood of both species trees and networks given the gene trees of multiple loci under an NCM model. We demonstrate the performance of inference under this integrated likelihood on both simulated and biological data.

Conclusions

The model presented here will afford opportunities for exploring connections among various criteria for estimating species phylogenies from multiple, independent loci. Furthermore, further development of this model could potentially result in more efficient methods for searching the space of species phylogenies by focusing solely on the topology of the phylogeny.

Inference of species phylogenies from bi-allelic markers using pseudo-likelihood

Motivation

Phylogenetic networks represent reticulate evolutionary histories. Statistical methods for their inference under the multispecies coalescent have recently been developed. A particularly powerful approach uses data that consist of bi-allelic markers (e.g. single nucleotide polymorphism data) and allows for exact likelihood computations of phylogenetic networks while numerically integrating over all possible gene trees per marker. While the approach has good accuracy in terms of estimating the network and its parameters, likelihood computations remain a major computational bottleneck and limit the method’s applicability.

Results

In this article, we first demonstrate why likelihood computations of networks take orders of magnitude more time when compared to trees. We then propose an approach for inference of phylogenetic networks based on pseudo-likelihood using bi-allelic markers. We demonstrate the scalability and accuracy of phylogenetic network inference via pseudo-likelihood computations on simulated data. Furthermore, we demonstrate aspects of robustness of the method to violations in the underlying assumptions of the employed statistical model. Finally, we demonstrate the application of the method to biological data. The proposed method allows for analyzing larger datasets in terms of the numbers of taxa and reticulation events. While pseudo-likelihood had been proposed before for data consisting of gene trees, the work here uses sequence data directly, offering several advantages as we discuss.

Availability and implementation

The methods have been implemented in PhyloNet (http://bioinfocs.rice.edu/phylonet).

Inferring Phylogenetic Networks Using PhyloNet

PhyloNet was released in 2008 as a software package for representing and analyzing phylogenetic networks. At the time of its release, the main functionalities in PhyloNet consisted of measures for comparing network topologies and a single heuristic for reconciling gene trees with a species tree. Since then, PhyloNet has grown significantly. The software package now includes a wide array of methods for inferring phylogenetic networks from data sets of unlinked loci while accounting for both reticulation (e.g., hybridization) and incomplete lineage sorting. In particular, PhyloNet now allows for maximum parsimony, maximum likelihood, and Bayesian inference of phylogenetic networks from gene tree estimates. Furthermore, Bayesian inference directly from sequence data (sequence alignments or biallelic markers) is implemented. Maximum parsimony is based on an extension of the "minimizing deep coalescences" criterion to phylogenetic networks, whereas maximum likelihood and Bayesian inference are based on the multispecies network coalescent. All methods allow for multiple individuals per species. As computing the likelihood of a phylogenetic network is computationally hard, PhyloNet allows for evaluation and inference of networks using a pseudolikelihood measure. PhyloNet summarizes the results of the various analyzes and generates phylogenetic networks in the extended Newick format that is readily viewable by existing visualization software.

Microbial sequence typing in the genomic era

Next-generation sequencing (NGS), also known as high-throughput sequencing, is changing the field of microbial genomics research. NGS allows for a more comprehensive analysis of the diversity, structure and composition of microbial genes and genomes compared to the traditional automated Sanger capillary sequencing at a lower cost. NGS strategies have expanded the versatility of standard and widely used typing approaches based on nucleotide variation in several hundred DNA sequences and a few gene fragments (MLST, MLVA, rMLST and cgMLST). NGS can now accommodate variation in thousands or millions of sequences from selected amplicons to full genomes (WGS, NGMLST and HiMLST). To extract signals from high-dimensional NGS data and make valid statistical inferences, novel analytic and statistical techniques are needed. In this review, we describe standard and new approaches for microbial sequence typing at gene and genome levels and guidelines for subsequent analysis, including methods and computational frameworks. We also present several applications of these approaches to some disciplines, namely genotyping, phylogenetics and molecular epidemiology.

Improved Maximum Parsimony Models for Phylogenetic Networks

Phylogenetic networks are well suited to represent evolutionary histories comprising reticulate evolution. Several methods aiming at reconstructing explicit phylogenetic networks have been developed in the last two decades. In this article, we propose a new definition of maximum parsimony for phylogenetic networks that permits to model biological scenarios that cannot be modeled by the definitions currently present in the literature (namely, the "hardwired" and "softwired" parsimony). Building on this new definition, we provide several algorithmic results that lay the foundations for new parsimony-based methods for phylogenetic network reconstruction.

Bayesian inference of phylogenetic networks from bi-allelic genetic markers

Phylogenetic networks are rooted, directed, acyclic graphs that model reticulate evolutionary histories. Recently, statistical methods were devised for inferring such networks from either gene tree estimates or the sequence alignments of multiple unlinked loci. Bi-allelic markers, most notably single nucleotide polymorphisms (SNPs) and amplified fragment length polymorphisms (AFLPs), provide a powerful source of genome-wide data. In a recent paper, a method called SNAPP was introduced for statistical inference of species trees from unlinked bi-allelic markers. The generative process assumed by the method combined both a model of evolution for the bi-allelic markers, as well as the multispecies coalescent. A novel component of the method was a polynomial-time algorithm for exact computation of the likelihood of a fixed species tree via integration over all possible gene trees for a given marker. Here we report on a method for Bayesian inference of phylogenetic networks from bi-allelic markers. Our method significantly extends the algorithm for exact computation of phylogenetic network likelihood via integration over all possible gene trees. Unlike the case of species trees, the algorithm is no longer polynomial-time on all instances of phylogenetic networks. Furthermore, the method utilizes a reversible-jump MCMC technique to sample the posterior of phylogenetic networks given bi-allelic marker data. Our method has a very good performance in terms of accuracy and robustness as we demonstrate on simulated data, as well as a data set of multiple New Zealand species of the plant genus Ourisia (Plantaginaceae). We implemented the method in the publicly available, open-source PhyloNet software package.

The availability of genomic data has revolutionized the study of evolutionary histories and phylogeny inference. Inferring evolutionary histories from genomic data requires, in most cases, accounting for the fact that different genomic regions could have evolutionary histories that differ from each other as well as from that of the species from which the genomes were sampled. In this paper, we introduce a method for inferring evolutionary histories while accounting for two processes that could give rise to such differences across the genomes, namely incomplete lineage sorting and hybridization. We introduce a novel algorithm for computing the likelihood of phylogenetic networks from bi-allelic genetic markers and use it in a Bayesian inference method. Analyses of synthetic and empirical data sets show a very good performance of the method in terms of the estimates it obtains.

Multilocus inference of species trees and DNA barcoding

The unprecedented amount of data resulting from next-generation sequencing has opened a new era in phylogenetic estimation. Although large datasets should, in theory, increase phylogenetic resolution, massive, multilocus datasets have uncovered a great deal of phylogenetic incongruence among different genomic regions, due both to stochastic error and to the action of different evolutionary process such as incomplete lineage sorting, gene duplication and loss and horizontal gene transfer. This incongruence violates one of the fundamental assumptions of the DNA barcoding approach, which assumes that gene history and species history are identical. In this review, we explain some of the most important challenges we will have to face to reconstruct the history of species, and the advantages and disadvantages of different strategies for the phylogenetic analysis of multilocus data. In particular, we describe the evolutionary events that can generate species tree—gene tree discordance, compare the most popular methods for species tree reconstruction, highlight the challenges we need to face when using them and discuss their potential utility in barcoding. Current barcoding methods sacrifice a great amount of statistical power by only considering one locus, and a transition to multilocus barcodes would not only improve current barcoding methods, but also facilitate an eventual transition to species-tree-based barcoding strategies, which could better accommodate scenarios where the barcode gap is too small or inexistent.

This article is part of the themed issue ‘From DNA barcodes to biomes’.

Phylogenomics reveals a complex evolutionary history of lobed-leaf white oaks in western North America

Species within the genus Quercus (oak) hybridize in complex patterns that have yet to be fully explored with phylogenomic data. Analyses to date have recovered reasonable divergent patterns, suggesting that the impact of introgression may not always be obvious in inferred oak phylogenies. We explore this phenomenon using RADseq data for 136 samples representing 54 oak species by conducting phylogenetic analyses designed to distinguish signals of lineage diversification and hybridization, focusing on the lobed-leaf species Quercus gambelii, Q. lobata, and Q. garryana in the context of a broad sampling of allied white oaks (Quercus section Quercus), and particularly the midwestern Q. macrocarpa. We demonstrate that historical introgressive hybridization between once sympatric species affects phylogeny estimation. Historical range expansion during periods of favorable climate likely explains our observations; analyses support genetic exchange between ancestral populations of Q. gambelii and Q. macrocarpa. We conclude that the genomic consequences of introgression caused the attraction of distant lineages in phylogenetic tree space, and that introgressive and divergent signals can be disentangled to produce a robust estimate of the phylogenetic history of the species.

Chromosomal Speciation in the Genomics Era: Disentangling Phylogenetic Evolution of Rock-wallabies

The association of chromosome rearrangements (CRs) with speciation is well established, and there is a long history of theory and evidence relating to "chromosomal speciation." Genomic sequencing has the potential to provide new insights into how reorganization of genome structure promotes divergence, and in model systems has demonstrated reduced gene flow in rearranged segments. However, there are limits to what we can understand from a small number of model systems, which each only tell us about one episode of chromosomal speciation. Progressing from patterns of association between chromosome (and genic) change, to understanding processes of speciation requires both comparative studies across diverse systems and integration of genome-scale sequence comparisons with other lines of evidence. Here, we showcase a promising example of chromosomal speciation in a non-model organism, the endemic Australian marsupial genus Petrogale. We present initial phylogenetic results from exon-capture that resolve a history of divergence associated with extensive and repeated CRs. Yet it remains challenging to disentangle gene tree heterogeneity caused by recent divergence and gene flow in this and other such recent radiations. We outline a way forward for better integration of comparative genomic sequence data with evidence from molecular cytogenetics, and analyses of shifts in the recombination landscape and potential disruption of meiotic segregation and epigenetic programming. In all likelihood, CRs impact multiple cellular processes and these effects need to be considered together, along with effects of genic divergence. Understanding the effects of CRs together with genic divergence will require development of more integrative theory and inference methods. Together, new data and analysis tools will combine to shed light on long standing questions of how chromosome and genic divergence promote speciation.

Exploring phylogenetic hypotheses via Gibbs sampling on evolutionary networks

Background

Phylogenetic networks are leaf-labeled graphs used to model and display complex evolutionary relationships that do not fit a single tree. There are two classes of phylogenetic networks: Data-display networks and evolutionary networks. While data-display networks are very commonly used to explore data, they are not amenable to incorporating probabilistic models of gene and genome evolution. Evolutionary networks, on the other hand, can accommodate such probabilistic models, but they are not commonly used for exploration.

Results

In this work, we show how to turn evolutionary networks into a tool for statistical exploration of phylogenetic hypotheses via a novel application of Gibbs sampling. We demonstrate the utility of our work on two recently available genomic data sets, one from a group of mosquitos and the other from a group of modern birds. We demonstrate that our method allows the use of evolutionary networks not only for explicit modeling of reticulate evolutionary histories, but also for exploring conflicting treelike hypotheses. We further demonstrate the performance of the method on simulated data sets, where the true evolutionary histories are known.

Conclusion

We introduce an approach to explore phylogenetic hypotheses over evolutionary phylogenetic networks using Gibbs sampling. The hypotheses could involve reticulate and non-reticulate evolutionary processes simultaneously as we illustrate on mosquito and modern bird genomic data sets.

A scalability study of phylogenetic network inference methods using empirical datasets and simulations involving a single reticulation

BACKGROUND

Branching events in phylogenetic trees reflect bifurcating and/or multifurcating speciation and splitting events. In the presence of gene flow, a phylogeny cannot be described by a tree but is instead a directed acyclic graph known as a phylogenetic network. Both phylogenetic trees and networks are typically reconstructed using computational analysis of multi-locus sequence data. The advent of high-throughput sequencing technologies has brought about two main scalability challenges: (1) dataset size in terms of the number of taxa and (2) the evolutionary divergence of the taxa in a study. The impact of both dimensions of scale on phylogenetic tree inference has been well characterized by recent studies; in contrast, the scalability limits of phylogenetic network inference methods are largely unknown.

RESULTS

In this study, we quantify the performance of state-of-the-art phylogenetic network inference methods on large-scale datasets using empirical data sampled from natural mouse populations and a range of simulations using model phylogenies with a single reticulation. We find that, as in the case of phylogenetic tree inference, the performance of leading network inference methods is negatively impacted by both dimensions of dataset scale. In general, we found that topological accuracy degrades as the number of taxa increases; a similar effect was observed with increased sequence mutation rate. The most accurate methods were probabilistic inference methods which maximize either likelihood under coalescent-based models or pseudo-likelihood approximations to the model likelihood. The improved accuracy obtained with probabilistic inference methods comes at a computational cost in terms of runtime and main memory usage, which become prohibitive as dataset size grows past twenty-five taxa. None of the probabilistic methods completed analyses of datasets with 30 taxa or more after many weeks of CPU runtime.

CONCLUSIONS

We conclude that the state of the art of phylogenetic network inference lags well behind the scope of current phylogenomic studies. New algorithmic development is critically needed to address this methodological gap.

Bayesian Inference of Reticulate Phylogenies under the Multispecies Network Coalescent

The multispecies coalescent (MSC) is a statistical framework that models how gene genealogies grow within the branches of a species tree. The field of computational phylogenetics has witnessed an explosion in the development of methods for species tree inference under MSC, owing mainly to the accumulating evidence of incomplete lineage sorting in phylogenomic analyses. However, the evolutionary history of a set of genomes, or species, could be reticulate due to the occurrence of evolutionary processes such as hybridization or horizontal gene transfer. We report on a novel method for Bayesian inference of genome and species phylogenies under the multispecies network coalescent (MSNC). This framework models gene evolution within the branches of a phylogenetic network, thus incorporating reticulate evolutionary processes, such as hybridization, in addition to incomplete lineage sorting. As phylogenetic networks with different numbers of reticulation events correspond to points of different dimensions in the space of models, we devise a reversible-jump Markov chain Monte Carlo (RJMCMC) technique for sampling the posterior distribution of phylogenetic networks under MSNC. We implemented the methods in the publicly available, open-source software package PhyloNet and studied their performance on simulated and biological data. The work extends the reach of Bayesian inference to phylogenetic networks and enables new evolutionary analyses that account for reticulation.

Trees have long formed in biology the basic structure with which to represent and understand evolutionary relationships. Mathematical models, computational methods, and software tools for inferring phylogenetic trees and studying their mathematical properties are currently the norm in biology. The availability of genomic data from closely related species, as well as from multiple individuals within species, have brought the two fields of phylogenetics and population genetics closer than ever. In particular, the last two decades have witnessed a great flourish in the development and implementation of phylogenetic methods based on the multispecies coalescent model to capture the intricate relationship between gene and genome evolution. However, when reticulation processes such as hybridization occur, the phylogenetic history is best represented by a network. In this work, we demonstrate how the multispecies coalescent model can be adapted to reticulate evolutionary histories and report on a Bayesian method for inference of such histories under this extended model. As networks subsume trees, the model and method provide a principled and unified statistical framework for inferring treelike and non-treelike evolutionary relationships.

Reticulate evolutionary history and extensive introgression in mosquito species revealed by phylogenetic network analysis

The role of hybridization and subsequent introgression has been demonstrated in an increasing number of species. Recently, Fontaine et al. (Science, 347, 2015, 1258524) conducted a phylogenomic analysis of six members of the Anopheles gambiae species complex. Their analysis revealed a reticulate evolutionary history and pointed to extensive introgression on all four autosomal arms. The study further highlighted the complex evolutionary signals that the co-occurrence of incomplete lineage sorting (ILS) and introgression can give rise to in phylogenomic analyses. While tree-based methodologies were used in the study, phylogenetic networks provide a more natural model to capture reticulate evolutionary histories. In this work, we reanalyse the Anopheles data using a recently devised framework that combines the multispecies coalescent with phylogenetic networks. This framework allows us to capture ILS and introgression simultaneously, and forms the basis for statistical methods for inferring reticulate evolutionary histories. The new analysis reveals a phylogenetic network with multiple hybridization events, some of which differ from those reported in the original study. To elucidate the extent and patterns of introgression across the genome, we devise a new method that quantifies the use of reticulation branches in the phylogenetic network by each genomic region. Applying the method to the mosquito data set reveals the evolutionary history of all the chromosomes. This study highlights the utility of 'network thinking' and the new insights it can uncover, in particular in phylogenomic analyses of large data sets with extensive gene tree incongruence.

A maximum pseudo-likelihood approach for phylogenetic networks

Background

Several 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.

Results

Inspired 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.

Conclusions

Maximum 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.

Maximum likelihood inference of reticulate evolutionary histories

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.

The inference of gene trees with species trees

This article reviews the various models that have been used to describe the relationships between gene trees and species trees. Molecular phylogeny has focused mainly on improving models for the reconstruction of gene trees based on sequence alignments. Yet, most phylogeneticists seek to reveal the history of species. Although the histories of genes and species are tightly linked, they are seldom identical, because genes duplicate, are lost or horizontally transferred, and because alleles can coexist in populations for periods that may span several speciation events. Building models describing the relationship between gene and species trees can thus improve the reconstruction of gene trees when a species tree is known, and vice versa. Several approaches have been proposed to solve the problem in one direction or the other, but in general neither gene trees nor species trees are known. Only a few studies have attempted to jointly infer gene trees and species trees. These models account for gene duplication and loss, transfer or incomplete lineage sorting. Some of them consider several types of events together, but none exists currently that considers the full repertoire of processes that generate gene trees along the species tree. Simulations as well as empirical studies on genomic data show that combining gene tree-species tree models with models of sequence evolution improves gene tree reconstruction. In turn, these better gene trees provide a more reliable basis for studying genome evolution or reconstructing ancestral chromosomes and ancestral gene sequences. We predict that gene tree-species tree methods that can deal with genomic data sets will be instrumental to advancing our understanding of genomic evolution.