Advances in Computational Methods for Phylogenetic Networks in the Presence of Hybridization

Polyphest: fast polyploid phylogeny estimation

MOTIVATION

Despite the widespread occurrence of polyploids across the Tree of Life, especially in the plant kingdom, very few computational methods have been developed to handle the specific complexities introduced by polyploids in phylogeny estimation. Furthermore, methods that are designed to account for polyploidy often disregard incomplete lineage sorting (ILS), a major source of heterogeneous gene histories, or are computationally very demanding. Therefore, there is a great need for efficient and robust methods to accurately reconstruct polyploid phylogenies.

RESULTS

We introduce Polyphest (POLYploid PHylogeny ESTimation), a new method for efficiently and accurately inferring species phylogenies in the presence of both polyploidy and ILS. Polyphest bypasses the need for extensive network space searches by first generating a multilabeled tree based on gene trees, which is then converted into a (uniquely labeled) species phylogeny. We compare the performance of Polyphest to that of two polyploid phylogeny estimation methods, one of which does not account for ILS, namely PADRE, and another that accounts for ILS, namely MPAllopp. Polyphest is more accurate than PADRE and achieves comparable accuracy to MPAllopp, while being significantly faster. We also demonstrate the application of Polyphest to empirical data from the hexaploid bread wheat and confirm the allopolyploid origin of bread wheat along with the closest relatives for each of its subgenomes.

AVAILABILITY AND IMPLEMENTATION

Polyphest is available at https://github.com/NakhlehLab/Polyphest.

Computing the Bounds of the Number of Reticulations in a Tree-Child Network That Displays a Set of Trees

Phylogenetic network is an evolutionary model that uses a rooted directed acyclic graph (instead of a tree) to model an evolutionary history of species in which reticulate events (e.g., hybrid speciation or horizontal gene transfer) occurred. Tree-child network is a kind of phylogenetic network with structural constraints. Existing approaches for tree-child network reconstruction can be slow for large data. In this study, we present several computational approaches for bounding from below the number of reticulations in a tree-child network that displays a given set of rooted binary phylogenetic trees. In addition, we also present some theoretical results on bounding from above the number of reticulations. Through simulation, we demonstrate that the new lower bounds on the reticulation number for tree-child networks can practically be computed for large tree data. The bounds can provide estimates of reticulation for relatively large data.

Anomalous networks under the multispecies coalescent: theory and prevalence

Reticulations in a phylogenetic network represent processes such as gene flow, admixture, recombination and hybrid speciation. Extending definitions from the tree setting, an anomalous network is one in which some unrooted tree topology displayed in the network appears in gene trees with a lower frequency than a tree not displayed in the network. We investigate anomalous networks under the Network Multispecies Coalescent Model with possible correlated inheritance at reticulations. Focusing on subsets of 4 taxa, we describe a new algorithm to calculate quartet concordance factors on networks of any level, faster than previous algorithms because of its focus on 4 taxa. We then study topological properties required for a 4-taxon network to be anomalous, uncovering the key role of [Formula: see text]-cycles: cycles of 3 edges parent to a sister group of 2 taxa. Under the model of common inheritance, that is, when each gene tree coalesces within a species tree displayed in the network, we prove that 4-taxon networks are never anomalous. Under independent and various levels of correlated inheritance, we use simulations under realistic parameters to quantify the prevalence of anomalous 4-taxon networks, finding that truly anomalous networks are rare. At the same time, however, we find a significant fraction of networks close enough to the anomaly zone to appear anomalous, when considering the quartet concordance factors observed from a few hundred genes. These apparent anomalies may challenge network inference methods.

Phylogenetic discordance and integrative species delimitation in the Mammillaria haageana species complex (Cactaceae)

Species complexes consist of very close phylogenetic relatives, where morphological similarities make it difficult to distinguish between them using traditional taxonomic methods. Here, we focused on the long-standing challenge of species delimitation in the Mammillaria haageana complex, a group that presents great morphological diversity that makes its taxonomy a puzzle. Our work integrates genomic, morphological, and ecological data to establish the taxonomic limits in the M. haageana complex, and we also studied the evolutionary relationships with the remainder of the M. ser. Supertextae species. Our genetic analyses, as well as morphological and ecological evidence, led us to propose that the M. haageana complex is made up of six distinct entities (M. acultzingensis, M. conspicua, M. haageana, M. lanigera, M. meissneri, and M. san-angelensis), mainly as a result of ecological speciation. A recent taxonomic proposal considered these taxa as a single species; therefore, we propose their recognition at the species level. Our results also show a high level of incomplete lineage sorting rather than reticulation, which is especially likely in recently diverged species such as those comprising M. ser. Supertextae. The species hypotheses proposed here may be useful in future extinction risk assessments and conservation strategies.

Hybridization despite elaborate courtship behavior and female choice in Neotropical tree frogs

The mechanisms of hybridization can be elucidated by analyzing genotypes as well as phenotypes that could act as premating barriers, as the reproductive interactions among heterospecifics can alter the evolutionary history of species. In frogs, hybrids typically occur among species that reproduce explosively (in dense aggregations) with few opportunities for mate selection but are rare in species with elaborate courtship behaviors that may prevent erroneous mating. Using 21 microsatellite markers, we examined hybridization in the prolonged-breeding tree frogs Bokermannohyla ibitiguara and B. sazimai sampled within a contact zone in the Brazilian savanna (72 tadpoles; 74 adults). We also compared acoustic and morphological data. We confirmed both parental species genetically; STRUCTURE results confirmed 14 hybrids, 11 of which were second-generation according to NEWHYBRIDS, all with intermediate values of genetic dissimilarities compared to the parentals. Morphological and acoustic analyses revealed that hybrids showed variable but not necessarily intermediate phenotypes. Moreover, 2 hybrids exhibited call types different from parentals. The reproduction of B. ibitiguara involves territorial and aggressive males, elaborate courtships with acoustic and tactile stimuli, choosy females, and opportunistic strategies. Our study uncovers a rare case of viable hybridization among closely related frogs with such a combination of complex courtship behaviors and mate choice. We discuss the likely directionality and mechanisms behind this phenomenon, and highlight the importance of investigating hybridization even in species that show elaborate reproduction and female choice to advance our understanding of animal diversification.

Evolution of a hybrid zone of two willow species (Salix L.) in the European Alps analyzed by RAD-seq and morphometrics

Natural hybridization of plants can result in many outcomes with several evolutionary consequences, such as hybrid speciation and introgression. Natural hybrid zones can arise in mountain systems as a result of fluctuating climate during the exchange of glacial and interglacial periods, where species retract and expand their territories, resulting in secondary contacts. Willows are a large genus of woody plants with an immense capability of interspecific crossing. In this study, the sympatric area of two diploid sister species, S. foetida and S. waldsteiniana in the eastern European Alps, was investigated to study the genomic structure of populations within and outside their contact zone and to analyze congruence of morphological phenotypes with genetic data. Eleven populations of the two species were sampled across the Alps and examined using phylogenetic network and population genetic structure analyses of RAD Seq data and morphometric analyses of leaves. The results showed that a homoploid hybrid zone between the two species was established within their sympatric area. Patterns of genetic admixture in homoploid hybrids indicated introgression with asymmetric backcrossing to not only one of the parental species but also one hybrid population forming a separate lineage. The lack of F1 hybrids indicated a long-term persistence of the hybrid populations. Insignificant isolation by distance suggests that gene flow can act over large geographical scales. Morphometric characteristics of hybrids supported the molecular data and clearly separated populations of the parental species, but showed intermediacy in the hybrid zone populations with a bias toward S. waldsteiniana. The homoploid hybrid zone might have been established via secondary contact hybridization, and its establishment was fostered by the low genetic divergence of parental species and a lack of strong intrinsic crossing barriers. Incomplete ecological separation and the ability of long-distance dispersal of willows could have contributed to the spatial expansion of the hybrid zone.

Inference of Gene Flow between Species under Misspecified Models

Genomic sequence data provide a rich source of information about the history of species divergence and interspecific hybridization or introgression. Despite recent advances in genomics and statistical methods, it remains challenging to infer gene flow, and as a result, one may have to estimate introgression rates and times under misspecified models. Here we use mathematical analysis and computer simulation to examine estimation bias and issues of interpretation when the model of gene flow is misspecified in analysis of genomic datasets, for example, if introgression is assigned to the wrong lineages. In the case of two species, we establish a correspondence between the migration rate in the continuous migration model and the introgression probability in the introgression model. When gene flow occurs continuously through time but in the analysis is assumed to occur at a fixed time point, common evolutionary parameters such as species divergence times are surprisingly well estimated. However, the time of introgression tends to be estimated towards the recent end of the period of continuous gene flow. When introgression events are assigned incorrectly to the parental or daughter lineages, introgression times tend to collapse onto species divergence times, with introgression probabilities underestimated. Overall, our analyses suggest that the simple introgression model is useful for extracting information concerning between-specific gene flow and divergence even when the model may be misspecified. However, for reliable inference of gene flow it is important to include multiple samples per species, in particular, from hybridizing species.

Recent progress on methods for estimating and updating large phylogenies

With the increased availability of sequence data and even of fully sequenced and assembled genomes, phylogeny estimation of very large trees (even of hundreds of thousands of sequences) is now a goal for some biologists. Yet, the construction of these phylogenies is a complex pipeline presenting analytical and computational challenges, especially when the number of sequences is very large. In the past few years, new methods have been developed that aim to enable highly accurate phylogeny estimations on these large datasets, including divide-and-conquer techniques for multiple sequence alignment and/or tree estimation, methods that can estimate species trees from multi-locus datasets while addressing heterogeneity due to biological processes (e.g. incomplete lineage sorting and gene duplication and loss), and methods to add sequences into large gene trees or species trees. Here we present some of these recent advances and discuss opportunities for future improvements. This article is part of a discussion meeting issue 'Genomic population structures of microbial pathogens'.

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.

Impact of Ghost Introgression on Coalescent-based Species Tree Inference and Estimation of Divergence Time

The species studied in any evolutionary investigation generally constitute a small proportion of all the species currently existing or that have gone extinct. It is therefore likely that introgression, which is widespread across the tree of life, involves "ghosts," i.e., unsampled, unknown, or extinct lineages. However, the impact of ghost introgression on estimations of species trees has rarely been studied and is poorly understood. Here, we use mathematical analysis and simulations to examine the robustness of species tree methods based on the multispecies coalescent model to introgression from a ghost or extant lineage. We found that many results originally obtained for introgression between extant species can easily be extended to ghost introgression, such as the strongly interactive effects of incomplete lineage sorting (ILS) and introgression on the occurrence of anomalous gene trees (AGTs). The relative performance of the summary species tree method (ASTRAL) and the full-likelihood method (*BEAST) varies under different introgression scenarios, with the former being more robust to gene flow between non-sister species whereas the latter performing better under certain conditions of ghost introgression. When an outgroup ghost (defined as a lineage that diverged before the most basal species under investigation) acts as the donor of the introgressed genes, the time of root divergence among the investigated species generally was overestimated, whereas ingroup introgression, as commonly perceived, can only lead to underestimation. In many cases of ingroup introgression that may or may not involve ghost lineages, the stronger the ILS, the higher the accuracy achieved in estimating the time of root divergence, although the topology of the species tree is more prone to be biased by the effect of introgression.

Orchard Networks are Trees with Additional Horizontal Arcs

Phylogenetic networks are used in biology to represent evolutionary histories. The class of orchard phylogenetic networks was recently introduced for their computational benefits, without any biological justification. Here, we show that orchard networks can be interpreted as trees with additional horizontal arcs. Therefore, they are closely related to tree-based networks, where the difference is that in tree-based networks the additional arcs do not need to be horizontal. Then, we use this new characterization to show that the space of orchard networks on n leaves with k reticulations is connected under the rNNI rearrangement move with diameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(kn+n\log (n))$$\end{document}O(kn+nlog(n)).

Classes of explicit phylogenetic networks and their biological and mathematical significance

The evolutionary relationships among organisms have traditionally been represented using rooted phylogenetic trees. However, due to reticulate processes such as hybridization or lateral gene transfer, evolution cannot always be adequately represented by a phylogenetic tree, and rooted phylogenetic networks that describe such complex processes have been introduced as a generalization of rooted phylogenetic trees. In fact, estimating rooted phylogenetic networks from genomic sequence data and analyzing their structural properties is one of the most important tasks in contemporary phylogenetics. Over the last two decades, several subclasses of rooted phylogenetic networks (characterized by certain structural constraints) have been introduced in the literature, either to model specific biological phenomena or to enable tractable mathematical and computational analyses. In the present manuscript, we provide a thorough review of these network classes, as well as provide a biological interpretation of the structural constraints underlying these networks where possible. In addition, we discuss how imposing structural constraints on the network topology can be used to address the scalability and identifiability challenges faced in the estimation of phylogenetic networks from empirical data.

Estimation of Cross-Species Introgression Rates Using Genomic Data Despite Model Unidentifiability

Full-likelihood implementations of the multispecies coalescent with introgression (MSci) model treat genealogical fluctuations across the genome as a major source of information to infer the history of species divergence and gene flow using multilocus sequence data. However, MSci models are known to have unidentifiability issues, whereby different models or parameters make the same predictions about the data and cannot be distinguished by the data. Previous studies of unidentifiability have focused on heuristic methods based on gene trees and do not make an efficient use of the information in the data. Here we study the unidentifiability of MSci models under the full-likelihood methods. We characterize the unidentifiability of the bidirectional introgression (BDI) model, which assumes that gene flow occurs in both directions. We derive simple rules for arbitrary BDI models, which create unidentifiability of the label-switching type. In general, an MSci model with k BDI events has 2k unidentifiable modes or towers in the posterior, with each BDI event between sister species creating within-model parameter unidentifiability and each BDI event between nonsister species creating between-model unidentifiability. We develop novel algorithms for processing Markov chain Monte Carlo samples to remove label-switching problems and implement them in the bpp program. We analyze real and synthetic data to illustrate the utility of the BDI models and the new algorithms. We discuss the unidentifiability of heuristic methods and provide guidelines for the use of MSci models to infer gene flow using genomic data.

Phylogenomic approaches to detecting and characterizing introgression

Phylogenomics has revealed the remarkable frequency with which introgression occurs across the tree of life. These discoveries have been enabled by the rapid growth of methods designed to detect and characterize introgression from whole-genome sequencing data. A large class of phylogenomic methods makes use of data across species to infer and characterize introgression based on expectations from the multispecies coalescent. These methods range from simple tests, such as the D-statistic, to model-based approaches for inferring phylogenetic networks. Here, we provide a detailed overview of the various signals that different modes of introgression are expected leave in the genome, and how current methods are designed to detect them. We discuss the strengths and pitfalls of these approaches and identify areas for future development, highlighting the different signals of introgression, and the power of each method to detect them. We conclude with a discussion of current challenges in inferring introgression and how they could potentially be addressed.

SpeciesRax: A Tool for Maximum Likelihood Species Tree Inference from Gene Family Trees under Duplication, Transfer, and Loss

Species tree inference from gene family trees is becoming increasingly popular because it can account for discordance between the species tree and the corresponding gene family trees. In particular, methods that can account for multiple-copy gene families exhibit potential to leverage paralogy as informative signal. At present, there does not exist any widely adopted inference method for this purpose. Here, we present SpeciesRax, the first maximum likelihood method that can infer a rooted species tree from a set of gene family trees and can account for gene duplication, loss, and transfer events. By explicitly modeling events by which gene trees can depart from the species tree, SpeciesRax leverages the phylogenetic rooting signal in gene trees. SpeciesRax infers species tree branch lengths in units of expected substitutions per site and branch support values via paralogy-aware quartets extracted from the gene family trees. Using both empirical and simulated data sets we show that SpeciesRax is at least as accurate as the best competing methods while being one order of magnitude faster on large data sets at the same time. We used SpeciesRax to infer a biologically plausible rooted phylogeny of the vertebrates comprising 188 species from 31,612 gene families in 1 h using 40 cores. SpeciesRax is available under GNU GPL at https://github.com/BenoitMorel/GeneRax and on BioConda.

Analysis of Paralogs in Target Enrichment Data Pinpoints Multiple Ancient Polyploidy Events in Alchemilla s.l. (Rosaceae)

Target enrichment is becoming increasingly popular for phylogenomic studies. Although baits for enrichment are typically designed to target single-copy genes, paralogs are often recovered with increased sequencing depth, sometimes from a significant proportion of loci, especially in groups experiencing whole-genome duplication (WGD) events. Common approaches for processing paralogs in target enrichment data sets include random selection, manual pruning, and mainly, the removal of entire genes that show any evidence of paralogy. These approaches are prone to errors in orthology inference or removing large numbers of genes. By removing entire genes, valuable information that could be used to detect and place WGD events is discarded. Here, we used an automated approach for orthology inference in a target enrichment data set of 68 species of Alchemilla s.l. (Rosaceae), a widely distributed clade of plants primarily from temperate climate regions. Previous molecular phylogenetic studies and chromosome numbers both suggested ancient WGDs in the group. However, both the phylogenetic location and putative parental lineages of these WGD events remain unknown. By taking paralogs into consideration and inferring orthologs from target enrichment data, we identified four nodes in the backbone of Alchemilla s.l. with an elevated proportion of gene duplication. Furthermore, using a gene-tree reconciliation approach, we established the autopolyploid origin of the entire Alchemilla s.l. and the nested allopolyploid origin of four major clades within the group. Here, we showed the utility of automated tree-based orthology inference methods, previously designed for genomic or transcriptomic data sets, to study complex scenarios of polyploidy and reticulate evolution from target enrichment data sets.[Alchemilla; allopolyploidy; autopolyploidy; gene tree discordance; orthology inference; paralogs; Rosaceae; target enrichment; whole genome duplication.].

Comparing the topology of phylogenetic network generators

Phylogenetic networks represent evolutionary history of species and can record natural reticulate evolutionary processes such as horizontal gene transfer and gene recombination. This makes phylogenetic networks a more comprehensive representation of evolutionary history compared to phylogenetic trees. Stochastic processes for generating random trees or networks are important tools in evolutionary analysis, especially in phylogeny reconstruction where they can be utilized for validation or serve as priors for Bayesian methods. However, as more network generators are developed, there is a lack of discussion or comparison for different generators. To bridge this gap, we compare a set of phylogenetic network generators by profiling topological summary statistics of the generated networks over the number of reticulations and comparing the topological profiles.

Prevalence and Adaptive Impact of Introgression

Alleles that introgress between species can influence the evolutionary and ecological fate of species exposed to novel environments. Hybrid offspring of different species are often unfit, and yet it has long been argued that introgression can be a potent force in evolution, especially in plants. Over the last two decades, genomic data have increasingly provided evidence that introgression is a critically important source of genetic variation and that this additional variation can be useful in adaptive evolution of both animals and plants. Here, we review factors that influence the probability that foreign genetic variants provide long-term benefits (so-called adaptive introgression) and discuss their potential benefits. We find that introgression plays an important role in adaptive evolution, particularly when a species is far from its fitness optimum, such as when they expand their range or are subject to changing environments.

Multispecies Coalescent: Theory and Applications in Phylogenetics

Species tree estimation is a basic part of many biological research projects, ranging from answering basic evolutionary questions (e.g., how did a group of species adapt to their environments?) to addressing questions in functional biology. Yet, species tree estimation is very challenging, due to processes such as incomplete lineage sorting, gene duplication and loss, horizontal gene transfer, and hybridization, which can make gene trees differ from each other and from the overall evolutionary history of the species. Over the last 10–20 years, there has been tremendous growth in methods and mathematical theory for estimating species trees and phylogenetic networks, and some of these methods are now in wide use. In this survey, we provide an overview of the current state of the art, identify the limitations of existing methods and theory, and propose additional research problems and directions.

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.

Phylogenomic assessment of the role of hybridization and introgression in trait evolution

Trait evolution among a set of species-a central theme in evolutionary biology-has long been understood and analyzed with respect to a species tree. However, the field of phylogenomics, which has been propelled by advances in sequencing technologies, has ushered in the era of species/gene tree incongruence and, consequently, a more nuanced understanding of trait evolution. For a trait whose states are incongruent with the branching patterns in the species tree, the same state could have arisen independently in different species (homoplasy) or followed the branching patterns of gene trees, incongruent with the species tree (hemiplasy). Another evolutionary process whose extent and significance are better revealed by phylogenomic studies is gene flow between different species. In this work, we present a phylogenomic method for assessing the role of hybridization and introgression in the evolution of polymorphic or monomorphic binary traits. We apply the method to simulated evolutionary scenarios to demonstrate the interplay between the parameters of the evolutionary history and the role of introgression in a binary trait's evolution (which we call xenoplasy). Very importantly, we demonstrate, including on a biological data set, that inferring a species tree and using it for trait evolution analysis in the presence of gene flow could lead to misleading hypotheses about trait 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.

The Perfect Storm: Gene Tree Estimation Error, Incomplete Lineage Sorting, and Ancient Gene Flow Explain the Most Recalcitrant Ancient Angiosperm Clade, Malpighiales

The genomic revolution offers renewed hope of resolving rapid radiations in the Tree of Life. The development of the multispecies coalescent model and improved gene tree estimation methods can better accommodate gene tree heterogeneity caused by incomplete lineage sorting (ILS) and gene tree estimation error stemming from the short internal branches. However, the relative influence of these factors in species tree inference is not well understood. Using anchored hybrid enrichment, we generated a data set including 423 single-copy loci from 64 taxa representing 39 families to infer the species tree of the flowering plant order Malpighiales. This order includes 9 of the top 10 most unstable nodes in angiosperms, which have been hypothesized to arise from the rapid radiation during the Cretaceous. Here, we show that coalescent-based methods do not resolve the backbone of Malpighiales and concatenation methods yield inconsistent estimations, providing evidence that gene tree heterogeneity is high in this clade. Despite high levels of ILS and gene tree estimation error, our simulations demonstrate that these two factors alone are insufficient to explain the lack of resolution in this order. To explore this further, we examined triplet frequencies among empirical gene trees and discovered some of them deviated significantly from those attributed to ILS and estimation error, suggesting gene flow as an additional and previously unappreciated phenomenon promoting gene tree variation in Malpighiales. Finally, we applied a novel method to quantify the relative contribution of these three primary sources of gene tree heterogeneity and demonstrated that ILS, gene tree estimation error, and gene flow contributed to 10.0$\%$, 34.8$\%$, and 21.4$\%$ of the variation, respectively. Together, our results suggest that a perfect storm of factors likely influence this lack of resolution, and further indicate that recalcitrant phylogenetic relationships like the backbone of Malpighiales may be better represented as phylogenetic networks. Thus, reducing such groups solely to existing models that adhere strictly to bifurcating trees greatly oversimplifies reality, and obscures our ability to more clearly discern the process of evolution. [Coalescent; concatenation; flanking region; hybrid enrichment, introgression; phylogenomics; rapid radiation, triplet frequency.].

A divide-and-conquer method for scalable phylogenetic network inference from multilocus data

Motivation

Reticulate evolutionary histories, such as those arising in the presence of hybridization, are best modeled as phylogenetic networks. Recently developed methods allow for statistical inference of phylogenetic networks while also accounting for other processes, such as incomplete lineage sorting. However, these methods can only handle a small number of loci from a handful of genomes.

Results

In this article, we introduce a novel two-step method for scalable inference of phylogenetic networks from the sequence alignments of multiple, unlinked loci. The method infers networks on subproblems and then merges them into a network on the full set of taxa. To reduce the number of trinets to infer, we formulate a Hitting Set version of the problem of finding a small number of subsets, and implement a simple heuristic to solve it. We studied their performance, in terms of both running time and accuracy, on simulated as well as on biological datasets. The two-step method accurately infers phylogenetic networks at a scale that is infeasible with existing methods. The results are a significant and promising step towards accurate, large-scale phylogenetic network inference.

Availability and implementation

We implemented the algorithms in the publicly available software package PhyloNet (https://bioinfocs.rice.edu/PhyloNet).

Supplementary information

Supplementary data are available at Bioinformatics online.

Disentangling Sources of Gene Tree Discordance in Phylogenomic Data Sets: Testing Ancient Hybridizations in Amaranthaceae s.l

Gene tree discordance in large genomic data sets can be caused by evolutionary processes such as incomplete lineage sorting and hybridization, as well as model violation, and errors in data processing, orthology inference, and gene tree estimation. Species tree methods that identify and accommodate all sources of conflict are not available, but a combination of multiple approaches can help tease apart alternative sources of conflict. Here, using a phylotranscriptomic analysis in combination with reference genomes, we test a hypothesis of ancient hybridization events within the plant family Amaranthaceae s.l. that was previously supported by morphological, ecological, and Sanger-based molecular data. The data set included seven genomes and 88 transcriptomes, 17 generated for this study. We examined gene-tree discordance using coalescent-based species trees and network inference, gene tree discordance analyses, site pattern tests of introgression, topology tests, synteny analyses, and simulations. We found that a combination of processes might have generated the high levels of gene tree discordance in the backbone of Amaranthaceae s.l. Furthermore, we found evidence that three consecutive short internal branches produce anomalous trees contributing to the discordance. Overall, our results suggest that Amaranthaceae s.l. might be a product of an ancient and rapid lineage diversification, and remains, and probably will remain, unresolved. This work highlights the potential problems of identifiability associated with the sources of gene tree discordance including, in particular, phylogenetic network methods. Our results also demonstrate the importance of thoroughly testing for multiple sources of conflict in phylogenomic analyses, especially in the context of ancient, rapid radiations. We provide several recommendations for exploring conflicting signals in such situations. [Amaranthaceae; gene tree discordance; hybridization; incomplete lineage sorting; phylogenomics; species network; species tree; transcriptomics.]

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.

Unraveling Reticulate Evolution in Opuntia (Cactaceae) From Southern Mexico

The process of hybridization occurs in approximately 40% of vascular plants, and this exchange of genetic material between non-conspecific individuals occurs unequally among plant lineages, being more frequent in certain groups such as Opuntia (Cactaceae). This genus is known for multiple taxonomic controversies due to widespread polyploidy and probable hybrid origin of several of its species. Southern Mexico species of this genus have been poorly studied despite their great diversity in regions such as the Tehuacán-Cuicatlán Valley which contains around 12% of recognized Mexico's native Opuntia species. In this work, we focus on testing the hybrid status of two putative hybrids from this region, Opuntia tehuacana and Opuntia pilifera, and estimate if hybridization occurs among sampled southern opuntias using two newly identified nuclear intron markers to construct phylogenetic networks with HyDe and Dsuite and perform invariant analysis under the coalescent model with HyDe and Dsuite. For the test of hybrid origin in O. tehuacana, our results could not recover hybridization as proposed in the literature, but we found introgression into O. tehuacana individuals involving O. decumbens and O. huajuapensis. Regarding O. pilifera, we identified O. decumbens as probable parental species, supported by our analysis, which sustains the previous hybridization hypothesis between Nopalea and Basilares clades. Finally, we suggest new hybridization and introgression cases among southern Mexican species involving O. tehuantepecana and O. depressa as parental species of O. velutina and O. decumbens.

Comparative Phylogenomics, a Stepping Stone for Bird Biodiversity Studies

Birds are a group with immense availability of genomic resources, and hundreds of forthcoming genomes at the doorstep. We review recent developments in whole genome sequencing, phylogenomics, and comparative genomics of birds. Short read based genome assemblies are common, largely due to efforts of the Bird 10K genome project (B10K). Chromosome-level assemblies are expected to increase due to improved long-read sequencing. The available genomic data has enabled the reconstruction of the bird tree of life with increasing confidence and resolution, but challenges remain in the early splits of Neoaves due to their explosive diversification after the Cretaceous-Paleogene (K-Pg) event. Continued genomic sampling of the bird tree of life will not just better reflect their evolutionary history but also shine new light onto the organization of phylogenetic signal and conflict across the genome. The comparatively simple architecture of avian genomes makes them a powerful system to study the molecular foundation of bird specific traits. Birds are on the verge of becoming an extremely resourceful system to study biodiversity from the nucleotide up.