The limits of the metapopulation: Lineage fragmentation in a widespread terrestrial salamander (Plethodon cinereus).

In vicariant species formation, divergence results primarily from periods of allopatry and restricted gene flow. Widespread species harboring differentiated, geographically distinct sublineages offer a window into what may be a common mode of species formation, whereby a species originates, spreads across the landscape, then fragments into multiple units. However, incipient lineages usually lack reproductive barriers that prevent their fusion upon secondary contact, blurring the boundaries between a single, large metapopulation-level lineage and multiple independent species. Here we explore this model of species formation in the Eastern Red-backed Salamander (Plethodon cinereus), a widespread terrestrial vertebrate with at least six divergent mitochondrial clades throughout its range. Using anchored hybrid enrichment data, we applied phylogenomic and population genomic approaches to investigate patterns of divergence, gene flow, and secondary contact. Genomic data broadly match most mitochondrial groups but reveal mitochondrial introgression and extensive admixture at several contact zones. While species delimitation analyses in BPP supported five lineages of P. cinereus, genealogical divergence indices (gdi) were highly sensitive to the inclusion of admixed samples and the geographic representation of candidate species, with increasing support for multiple species when removing admixed samples or limiting sampling to a single locality per group. An analysis of morphometric data revealed differences in body size and limb proportions among groups, with a reduction of forelimb length among warmer and drier localities consistent with increased fossoriality. We conclude that P. cinereus is a single species, but one with highly structured component lineages of various degrees of independence.

Inference of Phylogenetic Networks from Sequence Data using Composite Likelihood.

While phylogenies have been essential in understanding how species evolve, they do not adequately describe some evolutionary processes. For instance, hybridization, a common phenomenon where interbreeding between two species leads to formation of a new species, must be depicted by a phylogenetic network, a structure that modifies a phylogenetic tree by allowing two branches to merge into one, resulting in reticulation. However, existing methods for estimating networks become computationally expensive as the dataset size and/or topological complexity increase. The lack of methods for scalable inference hampers phylogenetic networks from being widely used in practice, despite accumulating evidence that hybridization occurs frequently in nature. Here, we propose a novel method, PhyNEST (Phylogenetic Network Estimation using SiTe patterns), that estimates binary, level-1 phylogenetic networks with a fixed, user-specified number of reticulations directly from sequence data. By using the composite likelihood as the basis for inference, PhyNEST is able to use the full genomic data in a computationally tractable manner, eliminating the need to summarize the data as a set of gene trees prior to network estimation. To search network space, PhyNEST implements both hill climbing and simulated annealing algorithms. PhyNEST assumes that the data are composed of coalescent independent sites that evolve according to the Jukes-Cantor substitution model and that the network has a constant effective population size. Simulation studies demonstrate that PhyNEST is often more accurate than two existing composite likelihood summary methods (SNaQ and PhyloNet) and that it is robust to at least one form of model misspecification (assuming a less complex nucleotide substitution model than the true generating model). We applied PhyNEST to reconstruct the evolutionary relationships among Heliconius butterflies and Papionini primates, characterized by hybrid speciation and widespread introgression, respectively. PhyNEST is implemented in an open-source Julia package and is publicly available at https://github.com/sungsik-kong/PhyNEST.jl.

Towards Reliable Detection of Introgression in the Presence of Among-Species Rate Variation.

The role of interspecific hybridization has recently seen increasing attention, especially in the context of diversification dynamics. Genomic research has now made it abundantly clear that both hybridization and introgression-the exchange of genetic material through hybridization and backcrossing-are far more common than previously thought. Besides cases of ongoing or recent genetic exchange between taxa, an increasing number of studies report "ancient introgression"- referring to results of hybridization that took place in the distant past. However, it is not clear whether commonly used methods for the detection of introgression are applicable to such old systems, given that most of these methods were originally developed for analyses at the level of populations and recently diverged species, affected by recent or ongoing genetic exchange. In particular, the assumption of constant evolutionary rates, which is implicit in many commonly used approaches, is more likely to be violated as evolutionary divergence increases. To test the limitations of introgression detection methods when being applied to old systems, we simulated thousands of genomic datasets under a wide range of settings, with varying degrees of among-species rate variation and introgression. Using these simulated datasets, we showed that some commonly applied statistical methods, including the D-statistic and certain tests based on sets of local phylogenetic trees, can produce false-positive signals of introgression between divergent taxa that have different rates of evolution. These misleading signals are caused by the presence of homoplasies occurring at different rates in different lineages. To distinguish between the patterns caused by rate variation and genuine introgression, we developed a new test that is based on the expected clustering of introgressed sites along the genome and implemented this test in the program Dsuite.

Molecular characterization of recombinant LSDV isolates from 2022 outbreak in Indonesia through phylogenetic networks and whole-genome SNP-based analysis.

Lumpy skin disease (LSD) is a transboundary viral disease of cattle and water buffaloes caused by the LSD virus, leading to high morbidity, low mortality, and a significant economic impact. Initially endemic to Africa only, LSD has spread to the Middle East, Europe, and Asia in the past decade. The most effective control strategy for LSD is the vaccination of cattle with live-attenuated LSDV vaccines. Consequently, the emergence of two groups of LSDV strains in Asian countries, one closely related to the ancient Kenyan LSDV isolates and the second made of recombinant viruses with a backbone of Neethling-vaccine and field isolates, emphasized the need for constant molecular surveillance. This current study investigated the first outbreak of LSD in Indonesia in 2022. Molecular characterization of the isolate circulating in the country based on selected LSDV-marker genes: RPO30, GPCR, EEV glycoprotein gene, and B22R, as well as whole genome analysis using several analytical tools, indicated the Indonesia LSDV isolate as a recombinant of LSDV_Neethling_vaccine_LW_1959 and LSDV_NI-2490. The analysis clustered the Indonesia_LSDV with the previously reported LSDV recombinants circulating in East and Southeast Asia, but different from the recombinant viruses in Russia and the field isolates in South-Asian countries. Additionally, this study has demonstrated alternative accurate ways of LSDV whole genome analysis and clustering of isolates, including the recombinants, instead of whole-genome phylogenetic tree analysis. These data will strengthen our understanding of the pathogens' origin, the extent of their spread, and determination of suitable control measures required.

Divergence and reticulation in the Mexican white oaks: ecological and phylogenomic evidence on species limits and phylogenetic networks in the Quercus laeta complex (Fagaceae).

BACKGROUND AND AIMS: Introgressive hybridization poses a challenge to taxonomic and phylogenetic understanding of taxa, particularly when there are high numbers of co-occurring, intercrossable species. The genus Quercus exemplifies this situation. Oaks are highly diverse in sympatry and cross freely, creating syngameons of interfertile species. Although a well-resolved, dated phylogeny is available for the American oak clade, evolutionary relationships within many of the more recently derived clades remain to be defined, particularly for the young and exceptionally diverse Mexican white oak clade. Here, we adopted an approach bridging micro- and macroevolutionary scales to resolve evolutionary relationships in a rapidly diversifying clade endemic to Mexico. METHODS: Ecological data and sequences of 155 low-copy nuclear genes were used to identify distinct lineages within the Quercus laeta complex. Concatenated and coalescent approaches were used to assess the phylogenetic placement of these lineages relative to the Mexican white oak clade. Phylogenetic network methods were applied to evaluate the timing and genomic significance of recent or historical introgression among lineages. KEY RESULTS: The Q. laeta complex comprises six well-supported lineages, each restricted geographically and with mostly divergent climatic niches. Species trees corroborated that the different lineages are more closely related to other species of Mexican white oaks than to each other, suggesting that this complex is polyphyletic. Phylogenetic networks estimated events of ancient introgression that involved the ancestors of three present-day Q. laeta lineages. CONCLUSIONS: The Q. laeta complex is a morphologically and ecologically related group of species rather than a clade. Currently, oak phylogenetics is at a turning point, at which it is necessary to integrate phylogenetics and ecology in broad regional samples to figure out species boundaries. Our study illuminates one of the more complicated of the Mexican white oak groups and lays groundwork for further taxonomic study.

Counting Phylogenetic Networks with Few Reticulation Vertices: Galled and Reticulation-Visible Networks.

We give exact and asymptotic counting results for the number of galled networks and reticulation-visible networks with few reticulation vertices. Our results are obtained with the component graph method, which was introduced by L. Zhang and his coauthors, and generating function techniques. For galled networks, we in addition use analytic combinatorics. Moreover, in an appendix, we consider maximally reticulated reticulation-visible networks and derive their number, too.

Phylogenetic network classes through the lens of expanding covers.

It was recently shown that a large class of phylogenetic networks, the 'labellable' networks, is in bijection with the set of 'expanding' covers of finite sets. In this paper, we show how several prominent classes of phylogenetic networks can be characterised purely in terms of properties of their associated covers. These classes include the tree-based, tree-child, orchard, tree-sibling, and normal networks. In the opposite direction, we give an example of how a restriction on the set of expanding covers can define a new class of networks, which we call 'spinal' phylogenetic networks.

An interchange property for the rooted phylogenetic subnet diversity on phylogenetic networks.

Faith's Phylogenetic Diversity (PD) on rooted phylogenetic trees satisfies the so-called strong exchange property that guarantees that, for every two sets of leaves of different cardinalities, a leaf can always be moved from the larger set to the smaller set in such a way that the sum of the PD values does not decrease. This strong exchange property entails a simple polynomial-time greedy solution to the PD optimization problem on rooted phylogenetic trees. In this paper we obtain an exchange property for the rooted Phylogenetic Subnet Diversity (rPSD) on rooted phylogenetic networks, which involves a more complicated exchange of leaves. We derive from it a polynomial-time greedy solution to the rPSD optimization problem on rooted semibinary level-2 phylogenetic networks.

The Space of Equidistant Phylogenetic Cactuses.

An equidistant X-cactus is a type of rooted, arc-weighted, directed acyclic graph with leaf set X, that is used in biology to represent the evolutionary history of a set X of species. In this paper, we introduce and investigate the space of equidistant X-cactuses. This space contains, as a subset, the space of ultrametric trees on X that was introduced by Gavryushkin and Drummond. We show that equidistant-cactus space is a CAT(0)-metric space which implies, for example, that there are unique geodesic paths between points. As a key step to proving this, we present a combinatorial result concerning ranked rooted X-cactuses. In particular, we show that such graphs can be encoded in terms of a pairwise compatibility condition arising from a poset of collections of pairs of subsets of X that satisfy certain set-theoretic properties. As a corollary, we also obtain an encoding of ranked, rooted X-trees in terms of partitions of X, which provides an alternative proof that the space of ultrametric trees on X is CAT(0). We expect that our results will provide the basis for novel ways to perform statistical analyses on collections of equidistant X-cactuses, as well as new directions for defining and understanding spaces of more general, arc-weighted phylogenetic networks.

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

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

Labellable Phylogenetic Networks.

Phylogenetic networks are mathematical representations of evolutionary history that are able to capture both tree-like evolutionary processes (speciations) and non-tree-like 'reticulate' processes such as hybridization or horizontal gene transfer. The additional complexity that comes with this capacity, however, makes networks harder to infer from data, and more complicated to work with as mathematical objects. In this paper, we define a new, large class of phylogenetic networks, that we call labellable, and show that they are in bijection with the set of 'expanding covers' of finite sets. This correspondence is a generalisation of the encoding of phylogenetic forests by partitions of finite sets. Labellable networks can be characterised by a simple combinatorial condition, and we describe the relationship between this large class and other commonly studied classes. Furthermore, we show that all phylogenetic networks have a quotient network that is labellable.

Generation of Orchard and Tree-Child Networks.

Phylogenetic networks are an extension of phylogenetic trees that allow for the representation of reticulate evolution events. One of the classes of networks that has gained the attention of the scientific community over the last years is the class of orchard networks, that generalizes tree-child networks, one of the most studied classes of networks. In this paper we focus on the combinatorial and algorithmic problem of the generation of binary orchard networks, and also of binary tree-child networks. To this end, we use that these networks are defined as those that can be recovered by reversing a certain reduction process. Then, we show how to choose a "minimum" reduction process among all that can be applied to a network, and hence we get a unique representation of the network that, in fact, can be given in terms of sequences of pairs of integers, whose length is related to the number of leaves and reticulations of the network. Therefore, the generation of networks is reduced to the generation of such sequences of pairs. Our main result is a recursive method for the efficient generation of all minimum sequences, and hence of all orchard (or tree-child) networks with a given number of leaves and reticulations. An implementation in C of the algorithms described in this paper, along with some computational experiments, can be downloaded from the public repository  https://github.com/gerardet46/OrchardGenerator . Using this implementation, we have computed the number of binary orchard networks with at most 6 leaves and 8 reticulations.

Autopolyploidy, Allopolyploidy, and Phylogenetic Networks with Horizontal Arcs.

Polyploidization is an evolutionary process by which a species acquires multiple copies of its complete set of chromosomes. The reticulate nature of the signal left behind by it means that phylogenetic networks offer themselves as a framework to reconstruct the evolutionary past of species affected by it. The main strategy for doing this is to first construct a so-called multiple-labelled tree and to then somehow derive such a network from it. The following question therefore arises: How much can be said about that past if such a tree is not readily available? By viewing a polyploid dataset as a certain vector which we call a ploidy (level) profile, we show that among other results, there always exists a phylogenetic network in the form of a beaded phylogenetic tree with additional arcs that realizes a given ploidy profile. Intriguingly, the two end vertices of almost all of these additional arcs can be interpreted as having co-existed in time thereby adding biological realism to our network, a feature that is, in general, not enjoyed by phylogenetic networks. In addition, we show that our network may be viewed as a generator of ploidy profile space, a novel concept similar to phylogenetic tree space that we introduce to be able to compare phylogenetic networks that realize one and the same ploidy profile. We illustrate our findings in terms of a publicly available Viola dataset.

Evolutionary adaptation of bovine coronavirus (BCoV): Screening of natural recombinations across the complete genomes.

Bovine coronavirus (BCoV) is a member of pathogenic Betacoronaviruses that has been circulating for several decades in multiple host species. Given the similarity between BCoV and human coronaviruses, the current study aimed to review the complete genomes of 107 BCoV strains available on the GenBank database, collected between 1983 and 2017 from different countries. The maximum-likelihood based phylogenetic analysis revealed three main BCoV genogroups: GI, GII, and GIII. GI is further divided into nine subgenogroups: GI-a to GI-i. The GI-a to GI-d are restricted to Japan, and GI-e to GI-i to the USA. The evolutionary relationships were also inferred using phylogenetic network analysis, revealing two major distinct networks dominated by viruses identified in the USA and Japan, respectively. The USA strains-dominated Network Cluster includes two sub-branches: France/Germany and Japan/China in addition to the United States, while Japan strains-dominated Network Cluster is limited to Japan. Twelve recombination events were determined, including 11 intragenogroup (GI) and one intergenogroup (GII vs. GI-g). The breakpoints of the recombination events were mainly located in ORF1ab and the spike glycoprotein ORF. Interestingly, 10 of 12 recombination events occurred between Japan strains, one between the USA strains, and one from intercontinental recombination (Japan vs. USA). These findings suggest that geographical characteristics, and population density with closer contact, might significantly impact the BCoV infection and co-infection and boost the emergence of more complex virus lineages.

Phylotranscriptomics of Theaceae: generic-level relationships, reticulation and whole-genome duplication.

BACKGROUND AND AIMS: Theaceae, with three tribes, nine genera and more than 200 species, are of great economic and ecological importance. Recent phylogenetic analyses based on plastomic data resolved the relationships among the three tribes and the intergeneric relationships within two of those tribes. However, generic-level relationships within the largest tribe, Theeae, were not fully resolved. The role of putative whole-genome duplication (WGD) events in the family and possible hybridization events among genera within Theeae also remain to be tested further. METHODS: Transcriptomes or low-depth whole-genome sequencing of 57 species of Theaceae, as well as additional plastome sequence data, were generated. Using a dataset of low-copy nuclear genes, we reconstructed phylogenetic relationships using concatenated, species tree and phylogenetic network approaches. We further conducted molecular dating analyses and inferred possible WGD events by examining the distribution of the number of synonymous substitutions per synonymous site (Ks) for paralogues in each species. For plastid protein-coding sequences , phylogenies were reconstructed for comparison with the results obtained from analysis of the nuclear dataset. RESULTS: Based on the 610 low-copy nuclear genes (858 606 bp in length) investigated, Stewartieae was resolved as sister to the other two tribes. Within Theeae, the Apterosperma-Laplacea clade grouped with Pyrenaria, leaving Camellia and Polyspora as sister. The estimated ages within Theaceae were largely consistent with previous studies based mainly on plastome data. Two reticulation events within Camellia and one between the common ancestor of Gordonia and Schima were found. All members of the tea family shared two WGD events, an older At-γ and a recent Ad-ß; both events were also shared with the outgroups (Diapensiaceae, Pentaphylacaceae, Styracaceae and Symplocaceae). CONCLUSIONS: Our analyses using low-copy nuclear genes improved understanding of phylogenetic relationships at the tribal and generic levels previously proposed based on plastome data, but the phylogenetic position of the Apterosperma-Laplacea clade needs more attention. There is no evidence for extensive intergeneric hybridization within Theeae or for a Theaceae-specific WGD event. Land bridges (e.g. the Bering land bridge) during the Late Oligocene may have permitted the intercontinental plant movements that facilitated the putative ancient introgression between the common ancestor of Gordonia and Schima.

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.

Forest-Based Networks.

In evolutionary studies, it is common to use phylogenetic trees to represent the evolutionary history of a set of species. However, in case the transfer of genes or other genetic information between the species or their ancestors has occurred in the past, a tree may not provide a complete picture of their history. In such cases, tree-based phylogenetic networks can provide a useful, more refined representation of the species' evolution. Such a network is essentially a phylogenetic tree with some arcs added between the tree's edges so as to represent reticulate events such as gene transfer, hybridization and recombination. Even so, this model does not permit the direct representation of evolutionary scenarios where reticulate events have taken place between different subfamilies or lineages of species. To represent such scenarios, in this paper we introduce the notion of a forest-based network, that is, a collection of leaf-disjoint phylogenetic trees on a set of species with arcs added between the edges of distinct trees within the collection. Forest-based networks include the recently introduced class of overlaid species forests which can be used to model introgression. As we shall see, even though the definition of forest-based networks is closely related to that of tree-based networks, they lead to new mathematical theory which complements that of tree-based networks. As well as studying the relationship of forest-based networks with other classes of phylogenetic networks, such as tree-child networks and universal tree-based networks, we present some characterizations of some special classes of forest-based networks. We expect that our results will be useful for developing new models and algorithms to understand reticulate evolution, such as introgression and gene transfer between species.

Distinct-Cluster Tree-Child Phylogenetic Networks and Possible Uses to Study Polyploidy.

As phylogenetic networks become more widely studied and the networks grow larger, it may be useful to "simplify" such networks into especially tractable networks. Recent results have found methods to simplify networks into normal networks. By definition, normal networks contain no redundant arcs. Nevertheless, there may be redundant arcs in networks where speciation events involving allopolyploidy occur. It is therefore desirable to find a different tractable class of networks that may contain redundant arcs. This paper proposes distinct-cluster tree-child networks as such a class, here abbreviated as DCTC networks. They are shown to have a number of useful properties, such as quadratic growth of the number of vertices with the number of leaves. A DCTC network is shown to be essentially a normal network to which some redundant arcs may have been added without losing the tree-child property. Every phylogenetic network can be simplified into a DCTC network depending only on the structure of the original network. There is always a CSD map from the original network to the resulting DCTC network. As a result, the simplified network can readily be interpreted via a "wired lift" in which the original network is redrawn with each arc represented in one of two ways.

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.

The hybrid number of a ploidy profile.

Polyploidization, whereby an organism inherits multiple copies of the genome of their parents, is an important evolutionary event that has been observed in plants and animals. One way to study such events is in terms of the ploidy number of the species that make up a dataset of interest. It is therefore natural to ask: How much information about the evolutionary past of the set of species that form a dataset can be gleaned from the ploidy numbers of the species? To help answer this question, we introduce and study the novel concept of a ploidy profile which allows us to formalize it in terms of a multiplicity vector indexed by the species the dataset is comprised of. Using the framework of a phylogenetic network, we present a closed formula for computing the hybrid number (i.e. the minimal number of polyploidization events required to explain a ploidy profile) of a large class of ploidy profiles. This formula relies on the construction of a certain phylogenetic network from the simplification sequence of a ploidy profile and the hybrid number of the ploidy profile with which this construction is initialized. Both of them can be computed easily in case the ploidy numbers that make up the ploidy profile are not too large. To help illustrate the applicability of our approach, we apply it to a simplified version of a publicly available Viola dataset.