Reticulation Events Research Articles

Identifiability of tree-child phylogenetic networks under a probabilistic recombination-mutation model of evolution

Phylogenetic networks are an extension of phylogenetic trees which are used to represent evolutionary histories in which reticulation events (such as recombination and hybridization) have occurred. A central question for such networks is that of identifiability, which essentially asks under what circumstances can we reliably identify the phylogenetic network that gave rise to the observed data? Recently, identifiability results have appeared for networks relative to a model of sequence evolution that generalizes the standard Markov models used for phylogenetic trees. However, these results are quite limited in terms of the complexity of the networks that are considered. In this paper, by introducing an alternative probabilistic model for evolution along a network that is based on some ground-breaking work by Thatte for pedigrees, we are able to obtain an identifiability result for a much larger class of phylogenetic networks (essentially the class of so-called tree-child networks). To prove our main theorem, we derive some new results for identifying tree-child networks combinatorially, and then adapt some techniques developed by Thatte for pedigrees to show that our combinatorial results imply identifiability in the probabilistic setting. We hope that the introduction of our new model for networks could lead to new approaches to reliably construct phylogenetic networks.

Recovering normal networks from shortest inter-taxa distance information.

Phylogenetic networks are a type of leaf-labelled, acyclic, directed graph used by biologists to represent the evolutionary history of species whose past includes reticulation events. A phylogenetic network is tree-child if each non-leaf vertex is the parent of a tree vertex or a leaf. Up to a certain equivalence, it has been recently shown that, under two different types of weightings, edge-weighted tree-child networks are determined by their collection of distances between each pair of taxa. However, the size of these collections can be exponential in the size of the taxa set. In this paper, we show that, if we have no "shortcuts", that is, the networks are normal, the same results are obtained with only a quadratic number of inter-taxa distances by using the shortest distance between each pair of taxa. The proofs are constructive and give cubic-time algorithms in the size of the taxa sets for building such weighted networks.

On the existence of a cherry-picking sequence

Recently, the minimum number of reticulation events that is required to simultaneously embed a collection P of rooted binary phylogenetic trees into a so-called temporal network has been characterized in terms of cherry-picking sequences. Such a sequence is a particular ordering on the leaves of the trees in P. However, it is well-known that not all collections of phylogenetic trees have a cherry-picking sequence. In this paper, we show that the problem of deciding whether or not P has a cherry-picking sequence is NP-complete for when P contains at least eight rooted binary phylogenetic trees. Moreover, we use automata theory to show that the problem can be solved in polynomial time if the number of trees in P and the number of cherries in each such tree are bounded by a constant.

An updated phylogeny and infrageneric classification of the genus Sisyrinchium (Iridaceae): Challenges of molecular and morphological evidence

AbstractTaxon delimitation and classification remains one of the fundamental bases of evolutionary studies and is especially challenging because processes by which new biological entities arise are complex and non‐linear over time, although continuous. Sisyrinchium (ca. 140 to 216 taxa) is one of the most species‐rich genera of Iridaceae, largely widespread in the Americas. Recent molecular phylogenetic studies have shown that the systematics of the genus is in need of substantial revision. Different data sources were investigated to establish an updated infrageneric classification based on phylogenetic principles. Monophyletic sections of Sisyrinchium were circumscribed using a new phylogenetic framework established from an increased sampling of taxa (107 species), and complementary approaches were combined to provide the most comprehensive infrageneric treatment of the genus proposed so far. Additionally, numerous molecular synapomorphies were identified to reinforce previous taxonomic treatments of tribe Sisyrinchieae (six genera) at the generic level. Major lineages of Sisyrinchium were concordantly resolved with mostly strong to full support by the DNA regions used in the study and ten sections characterized by unique combinations of molecular, morphological and geographical diagnostic characters were recognized. The phylogenetic trees respectively based on plastid + mitochondrial and nuclear ITS DNA regions were generally congruent except for two unplaced species (S. chilense, S. elegantulum) for which ancestral reticulation events were detected. New circumscriptions were provided for seven sections (sect. Cephalanthum, sect. Echthronema, sect. Hydastylus, sect. Segetia, sect. Sisyrinchium, sect. Spathirhachis, sect. Viperella) while three sections (sect. Morphanthus, sect. Rhizilineum, sect. Trichoparcus) were newly described. This work constitutes a robust contribution to elucidate the systematics of Sisyrinchium and emphasizes the need of integrative taxonomic approaches using multiple data sources, not only to improve the delimitation of taxa but also to investigate their evolutionary history.

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.

A Metric on the Space of kth-order reduced Phylogenetic Networks

Phylogenetic networks can be used to describe the evolutionary history of species which experience a certain number of reticulate events, and represent conflicts in phylogenetic trees that may be due to inadequacies of the evolutionary model used in the construction of the trees. Measuring the dissimilarity between two phylogenetic networks is at the heart of our understanding of the evolutionary history of species. This paper proposes a new metric, i.e. kth-distance, for the space of kth-order reduced phylogenetic networks that can be calculated in polynomial time in the size of the compared networks.

Lost in space? Generalising subtree prune and regraft to spaces of phylogenetic networks

Over the last fifteen years, phylogenetic networks have become a popular tool to analyse relationships between species whose past includes reticulation events such as hybridisation or horizontal gene transfer. However, the space of phylogenetic networks is significantly larger than that of phylogenetic trees, and how to analyse and search this enlarged space remains a poorly understood problem. Inspired by the widely-used rooted subtree prune and regraft (rSPR) operation on rooted phylogenetic trees, we propose a new operation—called subnet prune and regraft (SNPR)—that induces a metric on the space of all rooted phylogenetic networks on a fixed set of leaves. We show that the spaces of several popular classes of rooted phylogenetic networks (e.g. tree child, reticulation visible, and tree based) are connected under SNPR and that connectedness remains for the subclasses of these networks with a fixed number of reticulations. Lastly, we bound the distance between two rooted phylogenetic networks under the SNPR operation, show that it is computationally hard to compute this distance exactly, and analyse how the SNPR-distance between two such networks relates to the rSPR-distance between rooted phylogenetic trees that are embedded in these networks.

Deep reticulation and incomplete lineage sorting obscure the diploid phylogeny of rain-lilies and allies (Amaryllidaceae tribe Hippeastreae)

Hybridization is a frequent and important force in plant evolution. Next-generation sequencing (NGS) methods offer new possibilities for clade resolution and ambitious sampling of gene genealogies, yet difficulty remains in detecting deep reticulation events using currently available methods. We reconstructed the phylogeny of diploid representatives of Amaryllidaceae tribe Hippeastreae to test the hypothesis of ancient hybridizations preceding the radiation of its major subclade, Hippeastrinae. Through hybrid enrichment of DNA libraries and NGS, we obtained data for 18 nuclear loci through a curated assembly approach and nearly complete plastid genomes for 35 ingroup taxa plus 5 outgroups. Additionally, we obtained alignments for 39 loci through an automated assembly algorithm. These data were analyzed with diverse phylogenetic methods, including concatenation, coalescence-based species tree estimation, Bayesian concordance analysis, and network reconstructions, to provide insights into the evolutionary relationships of Hippeastreae. Causes for gene tree heterogeneity and cytonuclear discordance were examined through a Bayesian posterior predictive approach (JML) and coalescent simulations. Two major clades were found, Hippeastrinae and Traubiinae, as previously reported. Our results suggest the presence of two major nuclear lineages in Hippeastrinae characterized by different chromosome numbers: (1) Tocantinia and Hippeastrum with 2n=22, and (2) Eithea, Habranthus, Rhodophiala, and Zephyranthes mostly with 2n=12, 14, and 18. Strong cytonuclear discordance was confirmed in Hippeastrinae, and a network scenario with at least six hybridization events is proposed to reconcile nuclear and plastid signals, along a backbone that may also have been affected by incomplete lineage sorting at the base of each major subclade.

A cubic-time algorithm for computing the trinet distance between level-1 networks

In evolutionary biology, phylogenetic networks are constructed to represent the evolution of species in which reticulate events are thought to have occurred, such as recombination and hybridization. It is therefore useful to have efficiently computable metrics with which to systematically compare such networks. Through developing an optimal algorithm to enumerate all trinets displayed by a level-1 network (a type of network that is slightly more general than an evolutionary tree), here we propose a cubic-time algorithm to compute the trinet distance between two level-1 networks. Employing simulations, we also present a comparison between the trinet metric and the so-called Robinson–Foulds phylogenetic network metric restricted to level-1 networks. The algorithms described in this paper have been implemented in JAVA and are freely available at https://www.uea.ac.uk/computing/TriLoNet.

A program to compute the soft Robinson\u2013Foulds distance between phylogenetic networks

BackgroundOver the past two decades, phylogenetic networks have been studied to model reticulate evolutionary events. The relationships among phylogenetic networks, phylogenetic trees and clusters serve as the basis for reconstruction and comparison of phylogenetic networks. To understand these relationships, two problems are raised: the tree containment problem, which asks whether a phylogenetic tree is displayed in a phylogenetic network, and the cluster containment problem, which asks whether a cluster is represented at a node in a phylogenetic network. Both the problems are NP-complete.ResultsA fast exponential-time algorithm for the cluster containment problem on arbitrary networks is developed and implemented in C. The resulting program is further extended into a computer program for fast computation of the Soft Robinson–Foulds distance between phylogenetic networks.ConclusionsTwo computer programs are developed for facilitating reconstruction and validation of phylogenetic network models in evolutionary and comparative genomics. Our simulation tests indicated that they are fast enough for use in practice. Additionally, the distribution of the Soft Robinson–Foulds distance between phylogenetic networks is demonstrated to be unlikely normal by our simulation data.

Chloroplast and ITS phylogenies to understand the evolutionary history of southern South American Azorella, Laretia and Mulinum (Azorelloideae, Apiaceae)

Azorella, Laretia and Mulinum are taxonomically complex, and good candidates to study evolutionary radiations in the Andes and the importance of hybridizations. Previous phylogenetic studies of subfamily Azorelloideae agree that Azorella and Mulinum as currently conceived are not monophyletic, and hence a revision of their circumscription is necessary. However, these phylogenies were based only on chloroplast DNA sequence data. Here, phylogenetic relationships within Azorelloideae were inferred using sequence data from five chloroplast DNA (rps16 intron, trnQ-rps16, rps16-trnKUUU 5′ -exon, trnGGCC-trnSGCU and rpL32-trnLUAG), and from nuclear rDNA ITS regions to assess the monophyly of Azorella and Mulinum and discuss generic re-circumscriptions, determine hybridization and radiation events, identify and characterize important lineages, and propose hypotheses on evolution of key morphological characters. In total, 121 accessions of Azorelloideae were analyzed. Phylogenetic analyses of the different genomes were conducted separately and combined, with and without indels, using maximum parsimony, maximum likelihood, and Bayesian methods. To analyze the incongruence between plastid and nuclear-derived trees a consensus network from strongly supported nodes from cpDNA and ITS trees was constructed. Internode certainty values were calculated to evaluate the reliability of the relationships estimated from the individual cpDNA and ITS data sets and to examine the degree of conflict within the total evidence data set. Azorella and Mulinum were confirmed as not monophyletic. Except three Azorella species, the remaining azorellas, all species of Mulinum, and Laretia form a monophyletic group, designated here as Andean-Patagonian. The three species of Azorella that are not part of the Andean-Patagonian lineage are grouped together with Huanaca and Schizeilema in another lineage, designated here as Austral. Within the Andean-Patagonian clade, three major lineages can be recognized: Diversifolia, Trifurcata, and Spinosum. Each of these lineages have different leaf morpho-anatomies, Diversifolia species being more mesomorphic compared to species of Trifurcata, and species of Spinosum being the most xeromorphic. Hybridizations have been important in the evolution of the group, especially within Diversifolia, with at least six reticulation events resulting in putative homoploid and allopolyploid hybrid species. Evidence from branch lengths and low sequence divergences suggest a rapid radiation in the Spinosum group, probably associated with the acquisition of wings in the fruits.

Resolving the phylogenetic relationships and evolutionary history of the East Asian endemic genus Rodgersia (Saxifragaceae) using multilocus data

The East Asian endemic genus Rodgersia comprises five species and several variants. These species exhibit variation in ploidy level and a fragmented distribution across the whole of East Asia. In order to explain their present distribution pattern under a robust phylogeny, we employed multiple copy nuclear genes (ITS and ETS), cpDNA (rpl32-trnL, trnV-ndhC, ndhF-rpl32) and a low copy nuclear gene (GBSSI) to reconstruct the species’ relationships within Rodgersia. Identification of ploidy levels was also carried out for most of samples. The early-diverging positions of R. nepalensis and R. podophylla were confirmed in different gene trees. Much topological incongruence among gene trees was found in the shallower branches, which comprised the species of central-southwest China. Both incomplete lineage sorting and ancient introgression may be responsible for the incongruent pattern observed. Ancient introgressions may have occurred between diploid species and the diploid progenitors of tetraploid species in different areas of southwest China. Rodgersia probably originated in Northeast Asia during the Pliocene. This genus is a rare example in which two early-diverging species occur at opposite ends of the distribution area, likely resulting from successive vicariance events. Unlike many vicariance events shaped simply by forest fragmentation during the Pleistocene, the contemporary biogeographic pattern of Rodgersia is more the result of rapid sympatric evolution (reticulate events and polyploidization) of the taxa in the central area.

Do Branch Lengths Help to Locate a Tree in a Phylogenetic Network?

Phylogenetic networks are increasingly used in evolutionary biology to represent the history of species that have undergone reticulate events such as horizontal gene transfer, hybrid speciation and recombination. One of the most fundamental questions that arise in this context is whether the evolution of a gene with one copy in all species can be explained by a given network. In mathematical terms, this is often translated in the following way: is a given phylogenetic tree contained in a given phylogenetic network? Recently this tree containment problem has been widely investigated from a computational perspective, but most studies have only focused on the topology of the phylogenies, ignoring a piece of information that, in the case of phylogenetic trees, is routinely inferred by evolutionary analyses: branch lengths. These measure the amount of change (e.g., nucleotide substitutions) that has occurred along each branch of the phylogeny. Here, we study a number of versions of the tree containment problem that explicitly account for branch lengths. We show that, although length information has the potential to locate more precisely a tree within a network, the problem is computationally hard in its most general form. On a positive note, for a number of special cases of biological relevance, we provide algorithms that solve this problem efficiently. This includes the case of networks of limited complexity, for which it is possible to recover, among the trees contained by the network with the same topology as the input tree, the closest one in terms of branch lengths.

A graph theoretic model for prediction of reticulation events and phylogenetic networks for DNA sequences

Phylogenies are the commonly used tools for the prediction of ancestry of present day organisms from the past decades. Several methods have been developed to construct phylogenetic trees that predict the history of species by direct linkage of edges. Very few studies have been developed for the phylogenetic networks (which is the generalization of trees). Presently, the methods used to determine phylogenetic networks are based on distance measures or character measures of the sequences of species. It is a very challenging task for computational biologists to find the exact method that can predict the accurate networks of organisms. In this study, a phylogenetic network construction model based on basic graph theory concepts is reported. This model finds the distance matrix of every sequence considered in the study. The two features (positioning and stack interactions) of every DNA sequence and their combined effect have been taken into account to calculate the distances. Results suggested that reticulate events can be observed by using the distances obtained by the proposed method and no such event is predicted by using the distances calculated by the previous method. The important results obtained in the form of distances are 1.637300, 2.000000, 0.932700, 2.331300, 2.829200 and the significance of these values is to represent the different reticulation events among the sequences for different features. Hence distances calculated by this model gives better insights to study the phylogenetic networks.

Bayesian Inference of Reticulate Phylogenies under the Multispecies Network Coalescent.

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

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.

Phylogenetic origin of limes and lemons revealed by cytoplasmic and nuclear markers.

The origin of limes and lemons has been a source of conflicting taxonomic opinions. Biochemical studies, numerical taxonomy and recent molecular studies suggested that cultivated Citrus species result from interspecific hybridization between four basic taxa (C. reticulata,C. maxima,C. medica and C. micrantha). However, the origin of most lemons and limes remains controversial or unknown. The aim of this study was to perform extended analyses of the diversity, genetic structure and origin of limes and lemons. The study was based on 133 Citrus accessions. It combined maternal phylogeny studies based on mitochondrial and chloroplastic markers, and nuclear structure analysis based on the evaluation of ploidy level and the use of 123 markers, including 73 basic taxa diagnostic single nucleotide polymorphism (SNP) and indel markers. The lime and lemon horticultural group appears to be highly polymorphic, with diploid, triploid and tetraploid varieties, and to result from many independent reticulation events which defined the sub-groups. Maternal phylogeny involves four cytoplasmic types out of the six encountered in the Citrus genus. All lime and lemon accessions were highly heterozygous, with interspecific admixture of two, three and even the four ancestral taxa genomes. Molecular polymorphism between varieties of the same sub-group was very low. Citrus medica contributed to all limes and lemons and was the direct male parent for the main sub-groups in combination with C. micrantha or close papeda species (for C. aurata, C. excelsa, C. macrophylla and C. aurantifolia--'Mexican' lime types of Tanaka's taxa), C. reticulata(for C. limonia, C. karna and C. jambhiri varieties of Tanaka's taxa, including popular citrus rootstocks such as 'Rangpur' lime, 'Volkamer' and 'Rough' lemons), C. aurantium (for C. limetta and C. limon--yellow lemon types--varieties of Tanaka's taxa) or the C. maxima × C. reticulate hybrid (for C. limettioides--'Palestine sweet' lime types--and C. meyeri). Among triploid limes, C. latifolia accessions ('Tahiti' and 'Persian' lime types) result from the fertilization of a haploid ovule of C. limon by a diploid gamete of C. aurantifolia, while C. aurantifolia triploid accessions ('Tanepao' lime types and 'Madagascar' lemon) probably result from an interspecific backcross (a diploid ovule of C. aurantifolia fertilized by C. medica). As limes and lemons were vegetatively propagated (apomixis, horticultural practices) the intra-sub-group phenotypic diversity results from asexual variations.

A Resolution of the Static Formulation Question for the Problem of Computing the History Bound.

Evolutionary data has been traditionally modeled via phylogenetic trees; however, branching alone cannot model conflicting phylogenetic signals, so networks are used instead. Ancestral recombination graphs (ARGs) are used to model the evolution of incompatible sets of SNP data, allowing each site to mutate only once. The model often aims to minimize the number of recombinations. Similarly, incompatible cluster data can be represented by a reticulation network that minimizes reticulation events. The ARG literature has traditionally been disjoint from the reticulation network literature. By building on results from the reticulation network literature, we resolve an open question of interest to the ARG community. We explicitly prove that the History Bound, a lower bound on the number of recombinations in an ARG for a binary matrix, which was previously only defined procedurally, is equal to the minimum number of reticulation nodes in a network for the corresponding cluster data. To facilitate the proof, we give an algorithm that constructs this network using intermediate values from the procedural History Bound definition. We then develop a top-down algorithm for computing the History Bound, which has the same worst-case runtime as the known dynamic program, and show that it is likely to run faster in typical cases.

Reconstructible phylogenetic networks: do not distinguish the indistinguishable.

Phylogenetic networks represent the evolution of organisms that have undergone reticulate events, such as recombination, hybrid speciation or lateral gene transfer. An important way to interpret a phylogenetic network is in terms of the trees it displays, which represent all the possible histories of the characters carried by the organisms in the network. Interestingly, however, different networks may display exactly the same set of trees, an observation that poses a problem for network reconstruction: from the perspective of many inference methods such networks are indistinguishable. This is true for all methods that evaluate a phylogenetic network solely on the basis of how well the displayed trees fit the available data, including all methods based on input data consisting of clades, triples, quartets, or trees with any number of taxa, and also sequence-based approaches such as popular formalisations of maximum parsimony and maximum likelihood for networks. This identifiability problem is partially solved by accounting for branch lengths, although this merely reduces the frequency of the problem. Here we propose that network inference methods should only attempt to reconstruct what they can uniquely identify. To this end, we introduce a novel definition of what constitutes a uniquely reconstructible network. For any given set of indistinguishable networks, we define a canonical network that, under mild assumptions, is unique and thus representative of the entire set. Given data that underwent reticulate evolution, only the canonical form of the underlying phylogenetic network can be uniquely reconstructed. While on the methodological side this will imply a drastic reduction of the solution space in network inference, for the study of reticulate evolution this is a fundamental limitation that will require an important change of perspective when interpreting phylogenetic networks.

Phylogeny of Salix subgenus Salix s.l. (Salicaceae): delimitation, biogeography, and reticulate evolution.

BackgroundThe taxonomy and systematics of Salix subgenus Salix s.l. is difficult. The reliability and evolutionary implications of two important morphological characters (number of stamens, and morphology of bud scales) used in subgeneric classification within Salix remain untested, and a disjunct Old–New World distribution pattern of a main clade of subgenus Salix s.l., revealed by a previous study, lacks a reasonable explanation. To study these questions, we conducted phylogenetic analyses based on 4,688 bp of sequence data from four plastid (rbcL, trnD–T, matK, and atpB–rbcL) and two nuclear markers (ETS and ITS) covering all subgenera of Salix, and all sections of subgenus Salix s.l.ResultsSubgenus Salix came out as para- or polyphyletic in both nrDNA and plastid trees. The plastid phylogeny successfully resolved relationships among the major clades of Salix, but resolution within subgenus Salix s.l. remained low. Nevertheless, three monophyletic groups were identifiable in subgenus Salix s.l.: the ‘main clade’ of subgenus Salix s.l., with New and Old World species being reciprocally monophyletic; the section Triandroides clade; and the subgenus Pleuradenia clade. While nrDNA regions showed higher resolution within subgenus Salix s.l., they failed to resolve subgeneric relationships. Extensive, statistically significant gene-tree incongruence was detected across nrDNA–plastid as well as nrDNA ETS–ITS phylogenies, suggesting reticulate evolution or hybridization within the group. The results were supported by network analyses. Ancestral-state reconstructions indicated that multiple stamens and free bud scales represent the plesiomorphic states within Salix, and that several significant shifts in stamen number and bud scale morphology have occurred.ConclusionsSubgenus Salix s.l. is not monophyletic, and the evolutionary history of the subgenus has involved multiple reticulation events that may mainly be due to hybridization. The delimitation of subgenus Salix s.l. should be redefined by excluding section Triandrae and subgenus Pleuradenia from it. The evolutionary lability of bud-scale morphology and stamen number means that these characters are unreliable bases for classification. The disjunct Old–New World distribution of subgenus Salix s.l. appears to be linked to the profound climatic cooling during the Tertiary, which cut off gene exchange between New and Old World lineages.Electronic supplementary materialThe online version of this article (doi:10.1186/s12862-015-0311-7) contains supplementary material, which is available to authorized users.