Reconstructible phylogenetic networks: do not distinguish the indistinguishable

Inferring phylogenetic networks from multifurcating trees via cherry picking and machine learning

The Hybridization problem asks to reconcile a set of conflicting phylogenetic trees into a single phylogenetic network with the smallest possible number of reticulation nodes. This problem is computationally hard and previous solutions are limited to small and/or severely restricted data sets, for example, a set of binary trees with the same taxon set or only two non-binary trees with non-equal taxon sets. Building on our previous work on binary trees, we present FHyNCH, the first algorithmic framework to heuristically solve the Hybridization problem for large sets of multifurcating trees whose sets of taxa may differ. Our heuristics combine the cherry-picking technique, recently proposed to solve the same problem for binary trees, with two carefully designed machine-learning models. We demonstrate that our methods are practical and produce qualitatively good solutions through experiments on both synthetic and real data sets.

Introgression Underlies Phylogenetic Uncertainty But Not Parallel Plumage Evolution in a Recent Songbird Radiation

Instances of parallel phenotypic evolution offer great opportunities to understand the evolutionary processes underlying phenotypic changes. However, confirming parallel phenotypic evolution and studying its causes requires a robust phylogenetic framework. One such example is the "black-and-white wagtails," a group of 5 species in the songbird genus Motacilla: 1 species, Motacilla alba, shows wide intra-specific plumage variation, while the 4r others form 2 pairs of very similar-looking species (M. aguimp + M. samveasnae and M. grandis + M. maderaspatensis, respectively). However, the 2 species in each of these pairs were not recovered as sisters in previous phylogenetic inferences. Their relationships varied depending on the markers used, suggesting that gene tree heterogeneity might have hampered accurate phylogenetic inference. Here, we use whole genome resequencing data to explore the phylogenetic relationships within this group, with a special emphasis on characterizing the extent of gene tree heterogeneity and its underlying causes. We first used multispecies coalescent methods to generate a "complete evidence" phylogenetic hypothesis based on genome-wide variants, while accounting for incomplete lineage sorting (ILS) and introgression. We then investigated the variation in phylogenetic signal across the genome to quantify the extent of discordance across genomic regions and test its underlying causes. We found that wagtail genomes are mosaics of regions supporting variable genealogies, because of ILS and inter-specific introgression. The most common topology across the genome, supporting M. alba and M. aguimp as sister species, appears to be influenced by ancient introgression. Additionally, we inferred another ancient introgression event, between M. alba and M. grandis. By combining results from multiple analyses, we propose a phylogenetic network for the black-and-white wagtails that confirms that similar phenotypes evolved in non-sister lineages, supporting parallel plumage evolution. Furthermore, the inferred reticulations do not connect species with similar plumage coloration, suggesting that introgression does not underlie parallel plumage evolution in this group. Our results demonstrate the importance of investing genome-wide patterns of gene tree heterogeneity to help understand the mechanisms underlying phenotypic evolution. [Gene tree heterogeneity; incomplete lineage sorting; introgression; parallel evolution; phylogenomics; plumage evolution; wagtails.].

Detection of Ghost Introgression Requires Exploiting Topological and Branch Length Information

In recent years, the study of hybridization and introgression has made significant progress, with ghost introgression-the transfer of genetic material from extinct or unsampled lineages to extant species-emerging as a key area for research. Accurately identifying ghost introgression, however, presents a challenge. To address this issue, we focused on simple cases involving 3 species with a known phylogenetic tree. Using mathematical analyses and simulations, we evaluated the performance of popular phylogenetic methods, including HyDe and PhyloNet/MPL, and the full-likelihood method, Bayesian Phylogenetics and Phylogeography (BPP), in detecting ghost introgression. Our findings suggest that heuristic approaches relying on site-pattern counts or gene-tree topologies struggle to differentiate ghost introgression from introgression between sampled non-sister species, frequently leading to incorrect identification of donor and recipient species. The full-likelihood method BPP uses multilocus sequence alignments directly-hence taking into account both gene-tree topologies and branch lengths, by contrast, is capable of detecting ghost introgression in phylogenomic datasets. We analyzed a real-world phylogenomic dataset of 14 species of Jaltomata (Solanaceae) to showcase the potential of full-likelihood methods for accurate inference of introgression.

Botany and geogenomics: Constraining geological hypotheses in the neotropics with large-scale genetic data derived from plants

Decades of empirical research have revealed how the geological history of our planet shaped plant evolution by establishing well-known patterns (e.g., how mountain uplift resulted in high rates of diversification and replicate radiations in montane plant taxa). This follows a traditional approach where botanical data are interpreted in light of geological events. In this synthesis, I instead describe how by integrating natural history, phylogenetics, and population genetics, botanical research can be applied alongside geology and paleontology to inform our understanding of past geological and climatic processes. This conceptual shift aligns with the goals of the emerging field of geogenomics. In the neotropics, plant geogenomics is a powerful tool for the reciprocal exploration of two long standing questions in biology and geology: how the dynamic landscape of the region came to be and how it shaped the evolution of the richest flora. Current challenges that are specific to analytical approaches for plant geogenomics are discussed. I describe the scale at which various geological questions can be addressed from biological data and what makes some groups of plants excellent model systems for geogenomics research. Although plant geogenomics is discussed with reference to the neotropics, the recommendations given here for approaches to plant geogenomics can and should be expanded to exploring long-standing questions on how the earth evolved with the use of plant DNA.

PhyloCoalSimulations: A Simulator for Network Multispecies Coalescent Models, Including a New Extension for the Inheritance of Gene Flow

We consider the evolution of phylogenetic gene trees along phylogenetic species networks, according to the network multispecies coalescent process, and introduce a new network coalescent model with correlated inheritance of gene flow. This model generalizes two traditional versions of the network coalescent: with independent or common inheritance. At each reticulation, multiple lineages of a given locus are inherited from parental populations chosen at random, either independently across lineages or with positive correlation according to a Dirichlet process. This process may account for locus-specific probabilities of inheritance, for example. We implemented the simulation of gene trees under these network coalescent models in the Julia package PhyloCoalSimulations, which depends on PhyloNetworks and its powerful network manipulation tools. Input species phylogenies can be read in extended Newick format, either in numbers of generations or in coalescent units. Simulated gene trees can be written in Newick format, and in a way that preserves information about their embedding within the species network. This embedding can be used for downstream purposes, such as to simulate species-specific processes like rate variation across species, or for other scenarios as illustrated in this note. This package should be useful for simulation studies and simulation-based inference methods. The software is available open source with documentation and a tutorial at https://github.com/cecileane/PhyloCoalSimulations.jl.

Constructing phylogenetic networks via cherry picking and machine learning

BACKGROUND

Combining a set of phylogenetic trees into a single phylogenetic network that explains all of them is a fundamental challenge in evolutionary studies. Existing methods are computationally expensive and can either handle only small numbers of phylogenetic trees or are limited to severely restricted classes of networks.

RESULTS

In this paper, we apply the recently-introduced theoretical framework of cherry picking to design a class of efficient heuristics that are guaranteed to produce a network containing each of the input trees, for practical-size datasets consisting of binary trees. Some of the heuristics in this framework are based on the design and training of a machine learning model that captures essential information on the structure of the input trees and guides the algorithms towards better solutions. We also propose simple and fast randomised heuristics that prove to be very effective when run multiple times.

CONCLUSIONS

Unlike the existing exact methods, our heuristics are applicable to datasets of practical size, and the experimental study we conducted on both simulated and real data shows that these solutions are qualitatively good, always within some small constant factor from the optimum. Moreover, our machine-learned heuristics are one of the first applications of machine learning to phylogenetics and show its promise.

Phylogenomics reveals widespread hybridization and polyploidization in Henckelia (Gesneriaceae)

BACKGROUND AND AIMS

Hybridization has long been recognized as an important process for plant evolution and is often accompanied by polyploidization, another prominent force in generating biodiversity. Despite its pivotal importance in evolution, the actual prevalence and distribution of hybridization across the tree of life remain unclear.

METHODS

We used whole-genome shotgun (WGS) sequencing and cytological data to investigate the evolutionary history of Henckelia, a large genus in the family Gesneriaceae with a high frequency of suspected hybridization and polyploidization events. We generated WGS sequencing data at about 10× coverage for 26 Chinese Henckelia species plus one Sri Lankan species. To untangle the hybridization history, we separately extracted whole plastomes and thousands of single-copy nuclear genes from the sequencing data, and reconstructed phylogenies based on both nuclear and plastid data. We also explored sources of both genealogical and cytonuclear conflicts and identified signals of hybridization and introgression within our phylogenomic dataset using several statistical methods. Additionally, to test the polyploidization history, we evaluated chromosome counts for 45 populations of the 27 Henckelia species studied.

KEY RESULTS

We obtained well-supported phylogenetic relationships using both concatenation- and coalescent-based methods. However, the nuclear phylogenies were highly inconsistent with the plastid phylogeny, and we observed intensive discordance among nuclear gene trees. Further analyses suggested that both incomplete lineage sorting and gene flow contributed to the observed cytonuclear and genealogical discordance. Our analyses of introgression and phylogenetic networks revealed a complex history of hybridization within the genus Henckelia. In addition, based on chromosome counts for 27 Henckelia species, we found independent polyploidization events occurred within Henckelia after different hybridization events.

CONCLUSIONS

Our findings demonstrated that hybridization and polyploidization are common in Henckelia. Furthermore, our results revealed that H. oblongifolia is not a member of the redefined Henckelia and they suggested several other taxonomic treatments in this genus.

Identifiability of local and global features of phylogenetic networks from average distances

Phylogenetic networks extend phylogenetic trees to model non-vertical inheritance, by which a lineage inherits material from multiple parents. The computational complexity of estimating phylogenetic networks from genome-wide data with likelihood-based methods limits the size of networks that can be handled. Methods based on pairwise distances could offer faster alternatives. We study here the information that average pairwise distances contain on the underlying phylogenetic network, by characterizing local and global features that can or cannot be identified. For general networks, we clarify that the root and edge lengths adjacent to reticulations are not identifiable, and then focus on the class of zipped-up semidirected networks. We provide a criterion to swap subgraphs locally, such as 3-cycles, resulting in indistinguishable networks. We propose the "distance split tree", which can be constructed from pairwise distances, and prove that it is a refinement of the network's tree of blobs, capturing the tree-like features of the network. For level-1 networks, this distance split tree is equal to the tree of blobs refined to separate polytomies from blobs, and we prove that the mixed representation of the network is identifiable. The information loss is localized around 4-cycles, for which the placement of the reticulation is unidentifiable. The mixed representation combines split edges for 4-cycles, regular tree and hybrid edges from the semidirected network, and edge parameters that encode all information identifiable from average pairwise distances.

New taxonomic framework for Arthrodermataceae: a comprehensive analysis based on their phylogenetic reconstruction, divergence time estimation, phylogenetic split network, and phylogeography

The Arthrodermataceae, or dermatophytes, are a major family in the Onygenales and important from a public health safety perspective. Here, based on sequenced and downloaded from GenBank sequences, the evolutionary relationships of Arthrodermataceae were comprehensively studied via phylogenetic reconstruction, divergence time estimation, phylogenetic split network, and phylogeography analysis. These results showed the clades Ctenomyces, Epidermophyton, Guarromyces, Lophophyton, Microsporum, Paraphyton, and Trichophyton were all monophyletic groups, whereas Arthroderma and Nannizzia were polyphyletic. Among them, Arthroderma includes at least four different clades, Arthroderma I, III and IV are new clades in Arthrodermataceae. Nannizzia contains at least two different clades, Nannizzia I and Nannizzia II, but Nannizzia II was a new clade in Arthrodermataceae. The unclassified group, distributed in Japan and India, was incorrectly identified; it should be a new clade in Arthrodermataceae. The phylogenetic split network based on the ITS sequences provided strong support for the true relationships among the lineages in the reconstructed phylogenetic tree. A haplotype phylogenetic network based on the ITS sequences was used to visualize species evolution and geographic lineages relationships in all genera except Trichophyton. The new framework provided here for the phylogeny and taxonomy of Arthrodermataceae will facilitate the rapid identification of species in the family, which should useful for evaluating the results of preventive measures and interventions, as well as for conducting epidemiological studies.

NetRAX: accurate and fast maximum likelihood phylogenetic network inference

MOTIVATION

Phylogenetic networks can represent non-treelike evolutionary scenarios. Current, actively developed approaches for phylogenetic network inference jointly account for non-treelike evolution and incomplete lineage sorting (ILS). Unfortunately, this induces a very high computational complexity and current tools can only analyze small datasets.

RESULTS

We present NetRAX, a tool for maximum likelihood (ML) inference of phylogenetic networks in the absence of ILS. Our tool leverages state-of-the-art methods for efficiently computing the phylogenetic likelihood function on trees, and extends them to phylogenetic networks via the notion of 'displayed trees'. NetRAX can infer ML phylogenetic networks from partitioned multiple sequence alignments and returns the inferred networks in Extended Newick format. On simulated data, our results show a very low relative difference in Bayesian Information Criterion (BIC) score and a near-zero unrooted softwired cluster distance to the true, simulated networks. With NetRAX, a network inference on a partitioned alignment with 8000 sites, 30 taxa and 3 reticulations completes within a few minutes on a standard laptop.

AVAILABILITY AND IMPLEMENTATION

Our implementation is available under the GNU General Public License v3.0 at https://github.com/lutteropp/NetRAX.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

NetRAX: Accurate and Fast Maximum Likelihood Phylogenetic Network Inference

Motivation

Phylogenetic networks can represent non-treelike evolutionary scenarios. Current, actively developed approaches for phylogenetic network inference jointly account for non-treelike evolution and incomplete lineage sorting (ILS). Unfortunately, this induces a very high computational complexity and current tools can only analyze small datasets.

Results

We present NetRAX, a tool for maximum likelihood (ML) inference of phylogenetic networks in the absence of ILS. Our tool leverages state-of-the-art methods for efficiently computing the phylogenetic likelihood function on trees, and extends them to phylogenetic networks via the notion of ‘displayed trees’. NetRAX can infer ML phylogenetic networks from partitioned multiple sequence alignments and returns the inferred networks in Extended Newick format. On simulated data, our results show a very low relative difference in Bayesian Information Criterion (BIC) score and a near-zero unrooted softwired cluster distance to the true, simulated networks. With NetRAX, a network inference on a partitioned alignment with 8000 sites, 30 taxa and 3 reticulations completes within a few minutes on a standard laptop.

Availability and implementation

Our implementation is available under the GNU General Public License v3.0 at https://github.com/lutteropp/NetRAX.

Supplementary information

Supplementary data are available at Bioinformatics online.

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.

Candidate‐species delimitation in Desmognathus salamanders reveals gene flow across lineage boundaries, confounding phylogenetic estimation and clarifying hybrid zones

Dusky Salamanders (genus Desmognathus) currently comprise only 22 described, extant species. However, recent mitochondrial and nuclear estimates indicate the presence of up to 49 candidate species based on ecogeographic sampling. Previous studies also suggest a complex history of hybridization between these lineages. Studies in other groups suggest that disregarding admixture may affect both phylogenetic inference and clustering‐based species delimitation. With a dataset comprising 233 Anchored Hybrid Enrichment (AHE) loci sequenced for 896 Desmognathus specimens from all 49 candidate species, we test three hypotheses regarding (i) species‐level diversity, (ii) hybridization and admixture, and (iii) misleading phylogenetic inference. Using phylogenetic and population‐clustering analyses considering gene flow, we find support for at least 47 candidate species in the phylogenomic dataset, some of which are newly characterized here while others represent combinations of previously named lineages that are collapsed in the current dataset. Within these, we observe significant phylogeographic structure, with up to 64 total geographic genetic lineages, many of which hybridize either narrowly at contact zones or extensively across ecological gradients. We find strong support for both recent admixture between terminal lineages and ancient hybridization across internal branches. This signal appears to distort concatenated phylogenetic inference, wherein more heavily admixed terminal specimens occupy apparently artifactual early‐diverging topological positions, occasionally to the extent of forming false clades of intermediate hybrids. Additional geographic and genetic sampling and more robust computational approaches will be needed to clarify taxonomy, and to reconstruct a network topology to display evolutionary relationships in a manner that is consistent with their complex history of reticulation.

Multispecies coalescent and its applications to infer species phylogenies and cross-species gene flow

Multispecies coalescent (MSC) is the extension of the single-population coalescent model to multiple species. It integrates the phylogenetic process of species divergences and the population genetic process of coalescent, and provides a powerful framework for a number of inference problems using genomic sequence data from multiple species, including estimation of species divergence times and population sizes, estimation of species trees accommodating discordant gene trees, inference of cross-species gene flow and species delimitation. In this review, we introduce the major features of the MSC model, discuss full-likelihood and heuristic methods of species tree estimation and summarize recent methodological advances in inference of cross-species gene flow. We discuss the statistical and computational challenges in the field and research directions where breakthroughs may be likely in the next few years.

Merging Arcs to Produce Acyclic Phylogenetic Networks and Normal Networks

As phylogenetic networks grow increasingly complicated, systematic methods for simplifying them to reveal properties will become more useful. This paper considers how to modify acyclic phylogenetic networks into other acyclic networks by contracting specific arcs that include a set D. The networks need not be binary, so vertices in the networks may have more than two parents and/or more than two children. In general, in order to make the resulting network acyclic, additional arcs not in D must also be contracted. This paper shows how to choose D so that the resulting acyclic network is “pre-normal”. As a result, removal of all redundant arcs yields a normal network. The set D can be selected based only on the geometry of the network, giving a well-defined normal phylogenetic network depending only on the given network. There are CSD maps relating most of the networks. The resulting network can be visualized as a “wired lift” in the original network, which appears as the original network with each arc drawn in one of three ways.

Distinguishing level-1 phylogenetic networks on the basis of data generated by Markov processes

Phylogenetic networks can represent evolutionary events that cannot be described by phylogenetic trees. These networks are able to incorporate reticulate evolutionary events such as hybridization, introgression, and lateral gene transfer. Recently, network-based Markov models of DNA sequence evolution have been introduced along with model-based methods for reconstructing phylogenetic networks. For these methods to be consistent, the network parameter needs to be identifiable from data generated under the model. Here, we show that the semi-directed network parameter of a triangle-free, level-1 network model with any fixed number of reticulation vertices is generically identifiable under the Jukes–Cantor, Kimura 2-parameter, or Kimura 3-parameter constraints.

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.

Integrating Sequence Capture and Restriction Site-Associated DNA Sequencing to Resolve Recent Radiations of Pelagic Seabirds

The diversification of modern birds has been shaped by a number of radiations. Rapid diversification events make reconstructing the evolutionary relationships among taxa challenging due to the convoluted effects of incomplete lineage sorting (ILS) and introgression. Phylogenomic data sets have the potential to detect patterns of phylogenetic incongruence, and to address their causes. However, the footprints of ILS and introgression on sequence data can vary between different phylogenomic markers at different phylogenetic scales depending on factors such as their evolutionary rates or their selection pressures. We show that combining phylogenomic markers that evolve at different rates, such as paired-end double-digest restriction site-associated DNA (PE-ddRAD) and ultraconserved elements (UCEs), allows a comprehensive exploration of the causes of phylogenetic discordance associated with short internodes at different timescales. We used thousands of UCE and PE-ddRAD markers to produce the first well-resolved phylogeny of shearwaters, a group of medium-sized pelagic seabirds that are among the most phylogenetically controversial and endangered bird groups. We found that phylogenomic conflict was mainly derived from high levels of ILS due to rapid speciation events. We also documented a case of introgression, despite the high philopatry of shearwaters to their breeding sites, which typically limits gene flow. We integrated state-of-the-art concatenated and coalescent-based approaches to expand on previous comparisons of UCE and RAD-Seq data sets for phylogenetics, divergence time estimation, and inference of introgression, and we propose a strategy to optimize RAD-Seq data for phylogenetic analyses. Our results highlight the usefulness of combining phylogenomic markers evolving at different rates to understand the causes of phylogenetic discordance at different timescales. [Aves; incomplete lineage sorting; introgression; PE-ddRAD-Seq; phylogenomics; radiations; shearwaters; UCEs.].

A Bayesian Implementation of the Multispecies Coalescent Model with Introgression for Phylogenomic Analysis

Recent analyses suggest that cross-species gene flow or introgression is common in nature, especially during species divergences. Genomic sequence data can be used to infer introgression events and to estimate the timing and intensity of introgression, providing an important means to advance our understanding of the role of gene flow in speciation. Here, we implement the multispecies-coalescent-with-introgression model, an extension of the multispecies-coalescent model to incorporate introgression, in our Bayesian Markov chain Monte Carlo program Bpp. The multispecies-coalescent-with-introgression model accommodates deep coalescence (or incomplete lineage sorting) and introgression and provides a natural framework for inference using genomic sequence data. Computer simulation confirms the good statistical properties of the method, although hundreds or thousands of loci are typically needed to estimate introgression probabilities reliably. Reanalysis of data sets from the purple cone spruce confirms the hypothesis of homoploid hybrid speciation. We estimated the introgression probability using the genomic sequence data from six mosquito species in the Anopheles gambiae species complex, which varies considerably across the genome, likely driven by differential selection against introgressed alleles.

Defining phylogenetic networks using ancestral profiles

Rooted phylogenetic networks provide a more complete representation of the ancestral relationship between species than phylogenetic trees when reticulate evolutionary processes are at play. One way to reconstruct a phylogenetic network is to consider its 'ancestral profile' (the number of paths from each ancestral vertex to each leaf). In general, this information does not uniquely determine the underlying phylogenetic network. A recent paper considered a new class of phylogenetic networks called 'orchard networks' where this uniqueness was claimed to hold. Here we show that an additional restriction on the network, that of being 'stack-free', is required in order for the original uniqueness claim to hold. On the other hand, if the additional stack-free restriction is lifted, we establish an alternative result; namely, there is uniqueness within the class of orchard networks up to the resolution of vertices of high in-degree.

Phylotranscriptomic evidence for pervasive ancient hybridization among Old World salamanders

Hybridization can leave genealogical signatures in an organism's genome, originating from the parental lineages and persisting over time. This potentially confounds phylogenetic inference methods that aim to represent evolution as a strictly bifurcating tree. We apply a phylotranscriptomic approach to study the evolutionary history of, and test for inter-lineage introgression in the Salamandridae, a Holarctic salamanders group of interest in studies of toxicity and aposematism, courtship behavior, and molecular evolution. Although the relationships between the 21 currently recognized salamandrid genera have been the subject of numerous molecular phylogenetic studies, some branches have remained controversial and sometimes affected by discordances between mitochondrial vs. nuclear trees. To resolve the phylogeny of this family, and understand the source of mito-nuclear discordance, we generated new transcriptomic (RNAseq) data for 20 salamandrids and used these along with published data, including 28 mitochondrial genomes, to obtain a comprehensive nuclear and mitochondrial perspective on salamandrid evolution. Our final phylotranscriptomic data set included 5455 gene alignments for 40 species representing 17 of the 21 salamandrid genera. Using concatenation and species-tree phylogenetic methods, we find (1) Salamandrina sister to the clade of the "True Salamanders" (consisting of Chioglossa, Mertensiella, Lyciasalamandra, and Salamandra), (2) Ichthyosaura sister to the Near Eastern genera Neurergus and Ommatotriton, (3) Triturus sister to Lissotriton, and (4) Cynops paraphyletic with respect to Paramesotriton and Pachytriton. Combining introgression tests and phylogenetic networks, we find evidence for introgression among taxa within the clades of "Modern Asian Newts" and "Modern European Newts". However, we could not unambiguously identify the number, position, and direction of introgressive events. Combining evidence from nuclear gene analysis with the observed mito-nuclear phylogenetic discordances, we hypothesize a scenario with hybridization and mitochondrial capture among ancestral lineages of (1) Lissotriton into Ichthyosaura and (2) Triturus into Calotriton, plus introgression of nuclear genes from Triturus into Lissotriton. Furthermore, both mitochondrial capture and nuclear introgression may have occurred among lineages assigned to Cynops. More comprehensive genomic data will, in the future, allow testing this against alternative scenarios involving hybridization with other, extinct lineages of newts.

Major inconsistencies of inferred population genetic structure estimated in a large set of domestic horse breeds using microsatellites

STRUCTURE remains the most applied software aimed at recovering the true, but unknown, population structure from microsatellite or other genetic markers. About 30% of structure-based studies could not be reproduced (Molecular Ecology, 21, 2012, 4925). Here we use a large set of data from 2,323 horses from 93 domestic breeds plus the Przewalski horse, typed at 15 microsatellites, to evaluate how program settings impact the estimation of the optimal number of population clusters K opt that best describe the observed data. Domestic horses are suited as a test case as there is extensive background knowledge on the history of many breeds and extensive phylogenetic analyses. Different methods based on different genetic assumptions and statistical procedures (dapc, flock, PCoA, and structure with different run scenarios) all revealed general, broad-scale breed relationships that largely reflect known breed histories but diverged how they characterized small-scale patterns. structure failed to consistently identify K opt using the most widespread approach, the ΔK method, despite very large numbers of MCMC iterations (3,000,000) and replicates (100). The interpretation of breed structure over increasing numbers of K, without assuming a K opt, was consistent with known breed histories. The over-reliance on K opt should be replaced by a qualitative description of clustering over increasing K, which is scientifically more honest and has the advantage of being much faster and less computer intensive as lower numbers of MCMC iterations and repetitions suffice for stable results. Very large data sets are highly challenging for cluster analyses, especially when populations with complex genetic histories are investigated.

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.

Reconstructing Tree-Child Networks from Reticulate-Edge-Deleted Subnetworks

Network reconstruction lies at the heart of phylogenetic research. Two well-studied classes of phylogenetic networks include tree-child networks and level-k networks. In a tree-child network, every non-leaf node has a child that is a tree node or a leaf. In a level-k network, the maximum number of reticulations contained in a biconnected component is k. Here, we show that level-k tree-child networks are encoded by their reticulate-edge-deleted subnetworks, which are subnetworks obtained by deleting a single reticulation edge, if [Formula: see text]. Following this, we provide a polynomial-time algorithm for uniquely reconstructing such networks from their reticulate-edge-deleted subnetworks. Moreover, we show that this can even be done when considering subnetworks obtained by deleting one reticulation edge from each biconnected component with k reticulations.

Not all phylogenetic networks are leaf-reconstructible

Unrooted phylogenetic networks are graphs used to represent reticulate evolutionary relationships. Accurately reconstructing such networks is of great relevance for evolutionary biology. It has recently been conjectured that all unrooted phylogenetic networks for at least five taxa can be uniquely reconstructed from their subnetworks obtained by deleting a single taxon. Here, we show that this conjecture is false, by presenting a counter-example for each possible number of taxa that is at least 4. Moreover, we show that the conjecture is still false when restricted to binary networks. This means that, even if we are able to reconstruct the unrooted evolutionary history of each proper subset of some taxon set, this still does not give us enough information to reconstruct their full unrooted evolutionary history.

Generation of Binary Tree-Child phylogenetic networks

Phylogenetic networks generalize phylogenetic trees by allowing the modelization of events of reticulate evolution. Among the different kinds of phylogenetic networks that have been proposed in the literature, the subclass of binary tree-child networks is one of the most studied ones. However, very little is known about the combinatorial structure of these networks. In this paper we address the problem of generating all possible binary tree-child (BTC) networks with a given number of leaves in an efficient way via reduction/augmentation operations that extend and generalize analogous operations for phylogenetic trees, and are biologically relevant. Since our solution is recursive, this also provides us with a recurrence relation giving an upper bound on the number of such networks. We also show how the operations introduced in this paper can be employed to extend the evolutive history of a set of sequences, represented by a BTC network, to include a new sequence. An implementation in python of the algorithms described in this paper, along with some computational experiments, can be downloaded from https://github.com/bielcardona/TCGenerators.

Differences in flowering time maintain species boundaries in a continental radiation of Viburnum

PREMISE

We take an integrative approach in assessing how introgression and Pleistocene climate fluctuations have shaped the diversification of the core Lentago clade of Viburnum, a group of five interfertile species with broad areas of sympatry. We specifically tested whether flowering time plays a role in maintaining species isolation.

METHODS

RAD-seq data for 103 individuals were used to infer the species relationships and the genetic structure within each species. Flowering times were compared among species on the basis of historical flowering dates documented by herbarium specimens.

RESULTS

Within each species, we found a strong relationship between flowering date and latitude, such that southern populations flower earlier than northern ones. In areas of sympatry, the species flower in sequence rather than simultaneously, with flowering dates offset by ≥9 d for all species pairs. In two cases it appears that the offset in flowering times is an incidental consequence of adaptation to differing climates, but in the recently diverged sister species V. prunifolium and V. rufidulum, we find evidence that reinforcement led to reproductive character displacement. Long-term trends suggest that the two northern-most species are flowering earlier in response to recent climate change.

CONCLUSIONS

We argue that speciation in the Lentago clade has primarily occurred through ecological divergence of allopatric populations, but differences in flowering time were essential to maintain separation of incipient species when they came into secondary contact. This combination of factors may underlie diversification in many other plant clades.

Phylogenomic Signatures of Ancient Introgression in a Rogue Lineage of Darters (Teleostei: Percidae)

Evolutionary history is typically portrayed as a branching phylogenetic tree, yet not all evolution proceeds in a purely bifurcating manner. Introgressive hybridization is one process that results in reticulate evolution. Most known examples of genome-wide introgression occur among closely related species with relatively recent common ancestry; however, we present evidence for ancient hybridization and genome-wide introgression between major stem lineages of darters, a species-rich clade of North American freshwater fishes. Previous attempts to resolve the relationships of darters have been confounded by the uncertain phylogenetic resolution of the lineage Allohistium. In this study, we investigate the phylogenomics of darters, specifically the relationships of Allohistium, through analyses of approximately 30,000 RADseq loci sampled from 112 species. Our phylogenetic inferences are based on traditional approaches in combination with strategies that accommodate reticulate evolution. These analyses result in a novel phylogenetic hypothesis for darters that includes ancient introgression between Allohistium and other two major darter lineages, minimally occurring 20 million years ago. Darters offer a compelling case for the necessity of incorporating phylogenetic networks in reconstructing the evolutionary history of diversification in species-rich lineages. We anticipate that the growing wealth of genomic data for clades of non-model organisms will reveal more examples of ancient hybridization, eventually requiring a re-evaluation of how evolutionary history is visualized and utilized in macroevolutonary investigations.

Bayesian Inference of Species Networks from Multilocus Sequence Data

Reticulate species evolution, such as hybridization or introgression, is relatively common in nature. In the presence of reticulation, species relationships can be captured by a rooted phylogenetic network, and orthologous gene evolution can be modeled as bifurcating gene trees embedded in the species network. We present a Bayesian approach to jointly infer species networks and gene trees from multilocus sequence data. A novel birth-hybridization process is used as the prior for the species network, and we assume a multispecies network coalescent prior for the embedded gene trees. We verify the ability of our method to correctly sample from the posterior distribution, and thus to infer a species network, through simulations. To quantify the power of our method, we reanalyze two large data sets of genes from spruces and yeasts. For the three closely related spruces, we verify the previously suggested homoploid hybridization event in this clade; for the yeast data, we find extensive hybridization events. Our method is available within the BEAST 2 add-on SpeciesNetwork, and thus provides an extensible framework for Bayesian inference of reticulate evolution.

Phylogenetic Comparative Methods on Phylogenetic Networks with Reticulations

The goal of phylogenetic comparative methods (PCMs) is to study the distribution of quantitative traits among related species. The observed traits are often seen as the result of a Brownian Motion (BM) along the branches of a phylogenetic tree. Reticulation events such as hybridization, gene flow or horizontal gene transfer, can substantially affect a species' traits, but are not modeled by a tree. Phylogenetic networks have been designed to represent reticulate evolution. As they become available for downstream analyses, new models of trait evolution are needed, applicable to networks. We develop here an efficient recursive algorithm to compute the phylogenetic variance matrix of a trait on a network, in only one preorder traversal of the network. We then extend the standard PCM tools to this new framework, including phylogenetic regression with covariates (or phylogenetic ANOVA), ancestral trait reconstruction, and Pagel's $\lambda$ test of phylogenetic signal. The trait of a hybrid is sometimes outside of the range of its two parents, for instance because of hybrid vigor or hybrid depression. These two phenomena are rather commonly observed in present-day hybrids. Transgressive evolution can be modeled as a shift in the trait value following a reticulation point. We develop a general framework to handle such shifts and take advantage of the phylogenetic regression view of the problem to design statistical tests for ancestral transgressive evolution in the evolutionary history of a group of species. We study the power of these tests in several scenarios and show that recent events have indeed the strongest impact on the trait distribution of present-day taxa. We apply those methods to a data set of Xiphophorus fishes, to confirm and complete previous analysis in this group. All the methods developed here are available in the Julia package PhyloNetworks.

Modeling Hybridization Under the Network Multispecies Coalescent

Simultaneously modeling hybridization and the multispecies coalescent is becoming increasingly common, and inference of species networks in this context is now implemented in several software packages. This article addresses some of the conceptual issues and decisions to be made in this modeling, including whether or not to use branch lengths and issues with model identifiability. This article is based on a talk given at a Spotlight Session at Evolution 2017 meeting in Portland, Oregon. This session included several talks about modeling hybridization and gene flow in the presence of incomplete lineage sorting. Other talks given at this meeting are also included in this special issue of Systematic Biology.

Displayed Trees Do Not Determine Distinguishability Under the Network Multispecies Coalescent

Recent work in estimating species relationships from gene trees has included inferring networks assuming that past hybridization has occurred between species. Probabilistic models using the multispecies coalescent can be used in this framework for likelihood-based inference of both network topologies and parameters, including branch lengths and hybridization parameters. A difficulty for such methods is that it is not always clear whether, or to what extent, networks are identifiable-that is whether there could be two distinct networks that lead to the same distribution of gene trees. For cases in which incomplete lineage sorting occurs in addition to hybridization, we demonstrate a new representation of the species network likelihood that expresses the probability distribution of the gene tree topologies as a linear combination of gene tree distributions given a set of species trees. This representation makes it clear that in some cases in which two distinct networks give the same distribution of gene trees when sampling one allele per species, the two networks can be distinguished theoretically when multiple individuals are sampled per species. This result means that network identifiability is not only a function of the trees displayed by the networks but also depends on allele sampling within species. We additionally give an example in which two networks that display exactly the same trees can be distinguished from their gene trees even when there is only one lineage sampled per species. [gene tree, hybridization, identifiability, maximum likelihood, species tree, phylogeny.].

Rearrangement moves on rooted phylogenetic networks

Phylogenetic tree reconstruction is usually done by local search heuristics that explore the space of the possible tree topologies via simple rearrangements of their structure. Tree rearrangement heuristics have been used in combination with practically all optimization criteria in use, from maximum likelihood and parsimony to distance-based principles, and in a Bayesian context. Their basic components are rearrangement moves that specify all possible ways of generating alternative phylogenies from a given one, and whose fundamental property is to be able to transform, by repeated application, any phylogeny into any other phylogeny. Despite their long tradition in tree-based phylogenetics, very little research has gone into studying similar rearrangement operations for phylogenetic network—that is, phylogenies explicitly representing scenarios that include reticulate events such as hybridization, horizontal gene transfer, population admixture, and recombination. To fill this gap, we propose “horizontal” moves that ensure that every network of a certain complexity can be reached from any other network of the same complexity, and “vertical” moves that ensure reachability between networks of different complexities. When applied to phylogenetic trees, our horizontal moves—named rNNI and rSPR—reduce to the best-known moves on rooted phylogenetic trees, nearest-neighbor interchange and rooted subtree pruning and regrafting. Besides a number of reachability results—separating the contributions of horizontal and vertical moves—we prove that rNNI moves are local versions of rSPR moves, and provide bounds on the sizes of the rNNI neighborhoods. The paper focuses on the most biologically meaningful versions of phylogenetic networks, where edges are oriented and reticulation events clearly identified. Moreover, our rearrangement moves are robust to the fact that networks with higher complexity usually allow a better fit with the data. Our goal is to provide a solid basis for practical phylogenetic network reconstruction.

Phylogenetic networks are used to represent reticulate evolution, that is, cases in which the tree-of-life metaphor for evolution breaks down, because some of its branches have merged at one or several points in the past. This may occur, for example, when some organisms in the phylogeny are hybrids. In this paper, we deal with an elementary question for the reconstruction of phylogenetic networks: how to explore the space of all possible networks. The fundamental component for this is the set of operations that should be employed to generate alternative hypotheses for what happened in the past—which serve as basic blocks for optimization techniques such as hill-climbing. Although these approaches have a long tradition in classic tree-based phylogenetics, their application to networks that explicitly represent reticulate evolution is relatively unexplored. This paper provides the fundamental definitions and theoretical results for subsequent work in practical methods for phylogenetic network reconstruction: we subdivide networks into layers, according to a generally-accepted measure of their complexity, and provide operations that allow both to fully explore each layer, and to move across different layers. These operations constitute natural generalizations of well-known operations for the exploration of the space of phylogenetic trees, the lowest layer in the hierarchy described above.

In the light of deep coalescence: revisiting trees within networks

BACKGROUND

Phylogenetic networks model reticulate evolutionary histories. The last two decades have seen an increased interest in establishing mathematical results and developing computational methods for inferring and analyzing these networks. A salient concept underlying a great majority of these developments has been the notion that a network displays a set of trees and those trees can be used to infer, analyze, and study the network.

RESULTS

In this paper, we show that in the presence of coalescence effects, the set of displayed trees is not sufficient to capture the network. We formally define the set of parental trees of a network and make three contributions based on this definition. First, we extend the notion of anomaly zone to phylogenetic networks and report on anomaly results for different networks. Second, we demonstrate how coalescence events could negatively affect the ability to infer a species tree that could be augmented into the correct network. Third, we demonstrate how a phylogenetic network can be viewed as a mixture model that lends itself to a novel inference approach via gene tree clustering.

CONCLUSIONS

Our results demonstrate the limitations of focusing on the set of trees displayed by a network when analyzing and inferring the network. Our findings can form the basis for achieving higher accuracy when inferring phylogenetic networks and open up new venues for research in this area, including new problem formulations based on the notion of a network's parental trees.

TriLoNet: Piecing Together Small Networks to Reconstruct Reticulate Evolutionary Histories

Phylogenetic networks are a generalization of evolutionary trees that can be used to represent reticulate processes such as hybridization and recombination. Here, we introduce a new approach called TriLoNet (Trinet Level- one Network algorithm) to construct such networks directly from sequence alignments which works by piecing together smaller phylogenetic networks. More specifically, using a bottom up approach similar to Neighbor-Joining, TriLoNet constructs level-1 networks (networks that are somewhat more general than trees) from smaller level-1 networks on three taxa. In simulations, we show that TriLoNet compares well with Lev1athan, a method for reconstructing level-1 networks from three-leaved trees. In particular, in simulations we find that Lev1athan tends to generate networks that overestimate the number of reticulate events as compared with those generated by TriLoNet. We also illustrate TriLoNet's applicability using simulated and real sequence data involving recombination, demonstrating that it has the potential to reconstruct informative reticulate evolutionary histories. TriLoNet has been implemented in JAVA and is freely available at https://www.uea.ac.uk/computing/TriLoNet.

Folding and unfolding phylogenetic trees and networks

Phylogenetic networks are rooted, labelled directed acyclic graphswhich are commonly used to represent reticulate evolution. There is a close relationship between phylogenetic networks and multi-labelled trees (MUL-trees). Indeed, any phylogenetic network N can be “unfolded” to obtain a MUL-tree U(N) and, conversely, a MUL-tree T can in certain circumstances be “folded” to obtain aphylogenetic network F(T) that exhibits T. In this paper, we study properties of the operations U and F in more detail. In particular, we introduce the class of stable networks, phylogenetic networks N for which F(U(N)) is isomorphic to N, characterise such networks, and show that they are related to the well-known class of tree-sibling networks. We also explore how the concept of displaying a tree in a network N can be related to displaying the tree in the MUL-tree U(N). To do this, we develop aphylogenetic analogue of graph fibrations. This allows us to view U(N) as the analogue of the universal cover of a digraph, and to establish a close connection between displaying trees in U(N) and reconciling phylogenetic trees with networks.

Inferring Phylogenetic Networks with Maximum Pseudolikelihood under Incomplete Lineage Sorting

Phylogenetic networks are necessary to represent the tree of life expanded by edges to represent events such as horizontal gene transfers, hybridizations or gene flow. Not all species follow the paradigm of vertical inheritance of their genetic material. While a great deal of research has flourished into the inference of phylogenetic trees, statistical methods to infer phylogenetic networks are still limited and under development. The main disadvantage of existing methods is a lack of scalability. Here, we present a statistical method to infer phylogenetic networks from multi-locus genetic data in a pseudolikelihood framework. Our model accounts for incomplete lineage sorting through the coalescent model, and for horizontal inheritance of genes through reticulation nodes in the network. Computation of the pseudolikelihood is fast and simple, and it avoids the burdensome calculation of the full likelihood which can be intractable with many species. Moreover, estimation at the quartet-level has the added computational benefit that it is easily parallelizable. Simulation studies comparing our method to a full likelihood approach show that our pseudolikelihood approach is much faster without compromising accuracy. We applied our method to reconstruct the evolutionary relationships among swordtails and platyfishes (Xiphophorus: Poeciliidae), which is characterized by widespread hybridizations.

Phylogenetic networks display the evolutionary history of groups of individuals (species or populations) including reticulation events such as hybridization, horizontal gene transfer or migration. Here, we present a likelihood method to learn networks from molecular sequences at multiple genes. Our model accounts for several biological processes: mutations, incomplete lineage sorting of alleles in ancestral populations, and reticulations in the network. The likelihood is decomposed into 4-taxon subsets to make the analyses scale to many species and many genes. Our work makes it possible to learn large phylogenetic networks from large data sets, with a statistical approach and a biologically relevant model.

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.