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.

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 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.

Evolutionary and Phylogenetic Dynamics of SARS-CoV-2 Variants: A Genetic Comparative Study of Taiyuan and Wuhan Cities of China.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a positive-sense, single-stranded RNA genome-containing virus which has infected millions of people all over the world. The virus has been mutating rapidly enough, resulting in the emergence of new variants and sub-variants which have reportedly been spread from Wuhan city in China, the epicenter of the virus, to the rest of China and all over the world. The occurrence of mutations in the viral genome, especially in the viral spike protein region, has resulted in the evolution of multiple variants and sub-variants which gives the virus the benefit of host immune evasion and thus renders modern-day vaccines and therapeutics ineffective. Therefore, there is a continuous need to study the genetic characteristics and evolutionary dynamics of the SARS-CoV-2 variants. Hence, in this study, a total of 832 complete genomes of SARS-CoV-2 variants from the cities of Taiyuan and Wuhan in China was genetically characterized and their phylogenetic and evolutionary dynamics studied using phylogenetics, genetic similarity, and phylogenetic network analyses. This study shows that the four most prevalent lineages in Taiyuan and Wuhan are as follows: the Omicron lineages EG.5.1.1, followed by HK.3, FY.3, and XBB.1.16 (Pangolin classification), and clades 23F (EG.5.1), followed by 23H (HK.3), 22F (XBB), and 23D (XBB.1.9) (Nextclade classification), and lineage B followed by the Omicron FY.3, lineage A, and Omicron FL.2.3 (Pangolin classification), and the clades 19A, followed by 22F (XBB), 23F (EG.5.1), and 23H (HK.3) (Nextclade classification), respectively. Furthermore, our genetic similarity analysis show that the SARS-CoV-2 clade 19A-B.4 from Wuhan (name starting with 412981) has the least genetic similarity of about 95.5% in the spike region of the genome as compared to the query sequence of Omicron XBB.2.3.2 from Taiyuan (name starting with 18495234), followed by the Omicron FR.1.4 from Taiyuan (name starting with 18495199) with ~97.2% similarity and Omicron DY.3 (name starting with 17485740) with ~97.9% similarity. The rest of the variants showed ≥98% similarity with the query sequence of Omicron XBB.2.3.2 from Taiyuan (name starting with 18495234). In addition, our recombination analysis results show that the SARS-CoV-2 variants have three statistically significant recombinant events which could have possibly resulted in the emergence of Omicron XBB.1.16 (recombination event 3), FY.3 (recombination event 5), and FL.2.4 (recombination event 7), suggesting some very important information regarding viral evolution. Also, our phylogenetic tree and network analyses show that there are a total of 14 clusters and more than 10,000 mutations which may have probably resulted in the emergence of cluster-I, followed by 47 mutations resulting in the emergence of cluster-II and so on. The clustering of the viral variants of both cities reveals significant information regarding the phylodynamics of the virus among them. The results of our temporal phylogenetic analysis suggest that the variants of Taiyuan have likely emerged as independent variants separate from the variants of Wuhan. This study, to the best of our knowledge, is the first ever genetic comparative study between Taiyuan and Wuhan cities in China. This study will help us better understand the virus and cope with the emergence and spread of new variants at a local as well as an international level, and keep the public health authorities informed for them to make better decisions in designing new viral vaccines and therapeutics. It will also help the outbreak investigators to better examine any future outbreak.

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.

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.

TINNiK: Inference of the Tree of Blobs of a Species Network Under the Coalescent.

The tree of blobs of a species network shows only the tree-like aspects of relationships of taxa on a network, omitting information on network substructures where hybridization or other types of lateral transfer of genetic information occur. By isolating such regions of a network, inference of the tree of blobs can serve as a starting point for a more detailed investigation, or indicate the limit of what may be inferrable without additional assumptions. Building on our theoretical work on the identifiability of the tree of blobs from gene quartet distributions under the Network Multispecies Coalescent model, we develop an algorithm, TINNiK, for statistically consistent tree of blobs inference. We provide examples of its application to both simulated and empirical datasets, utilizing an implementation in the MSCquartets 2.0 R package.

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.

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.

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.

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.

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

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

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.

Emergence and Persistent Circulation of Highly Pathogenic Avian Influenza Virus A (H5N8) in Kosovo, May 2021-May 2022.

In this study, we report the first outbreak of highly pathogenic avian influenza (HPAI) A H5N8, clade 2.3.4.4b in Kosovo on 19 May 2021. The outbreak consisted of three phases: May-June 2021, September-November 2021, and January-May 2022. In total, 32 backyards and 10 commercial holdings tested positive for the virus. Interestingly, the third and last phase of the outbreak coincided with the massive H5N1 clade 2.3.4.4b epidemic in Europe. Phylogenetic analyses of 28 viral strains from Kosovo revealed that they were closely related to the H5N8 clade 2.3.4.4.b viruses that had been circulating in Albania, Bulgaria, Croatia, Hungary, and Russia in early 2021. Whole genome sequencing of the 25 and partial sequencing of three H5N8 viruses from Kosovo showed high nucleotide identity, forming a distinctive cluster and suggesting a single introduction. The results of the network analysis were in accordance with the three epidemic waves and suggested that the viral diffusion could have been caused by secondary spreads among farms and/or different introductions of the same virus from wild birds. The persistent circulation of the same virus over a one-year period highlights the potential risk of the virus becoming endemic, especially in settings with non-adequate biosecurity.

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.

Visualizing incompatibilities in phylogenetic trees using consensus outlines.

Phylogenetic analysis frequently leads to the creation of many phylogenetic trees, either from using multiple genes or methods, or through bootstrapping or Bayesian analysis. A consensus tree is often used to summarize what the trees have in common. Consensus networks were introduced to also allow the visualization of the main incompatibilities among the trees. However, in practice, such networks often contain a large number of nodes and edges, and can be non-planar, making them difficult to interpret. Here, we introduce the new concept of a phylogenetic consensus outline, which provides a planar visualization of incompatibilities in the input trees, without the complexities of a consensus network. Furthermore, we present an effective algorithm for its computation. We demonstrate its usage and explore how it compares to other methods on a Bayesian phylogenetic analysis of languages using data from a published database and on multiple gene trees from a published study on water lilies.

Using genomics, morphometrics, and environmental niche modeling to test the validity of a narrow-range endemic snail, Pateranantahala (Gastropoda, Polygyridae).

Terrestrial gastropods are among the most imperiled groups of organisms on Earth. Many species have a complex taxonomic history, often including poorly defined subspecies, most of which have not been the focus of modern systematics research. Genomic tools, geometric morphometrics, and environmental niche modeling were used to assess the taxonomic status of Pateraclarkiinantahala (Clench & Banks, 1932), a subspecies of high conservation concern with a restricted range of approximately 3.3 km2 in North Carolina, USA. A genome-scale dataset was generated that included individuals with morphologies matching P.c.nantahala, P.c.clarkii, and one individual with an intermediate form between P.c.nantahala and P.c.clarkii that was initially hypothesized as a potential hybrid. Mitochondrial phylogenetics, nuclear species tree inference, and phylogenetic networks were used to assess relationships and gene flow. Differences in shell shape via geometric morphometrics and whether the environmental niches of the two subspecies were significantly different were also examined. Molecular analyses indicated an absence of gene flow among lineages of P.clarkii sensu lato. Analyses rejected our hypothesis that the intermediate shelled form represented a hybrid, but instead indicated that it was a distinct lineage. Environmental niche models indicated significant differences in environmental niche between P.c.clarkii and P.c.nantahala, and geometric morphometrics indicated that P.c.nantahala had a significantly different shell shape. Given multiple lines of evidence, species-level recognition of P.nantahala is warranted.

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.

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.