Bayesian Inference of Species Networks from Multilocus Sequence Data

Phase Resolution of Heterozygous Sites in Diploid Genomes is Important to Phylogenomic Analysis under the Multispecies Coalescent Model

Genome sequencing projects routinely generate haploid consensus sequences from diploid genomes, which are effectively chimeric sequences with the phase at heterozygous sites resolved at random. The impact of phasing errors on phylogenomic analyses under the multispecies coalescent (MSC) model is largely unknown. Here, we conduct a computer simulation to evaluate the performance of four phase-resolution strategies (the true phase resolution, the diploid analytical integration algorithm which averages over all phase resolutions, computational phase resolution using the program PHASE, and random resolution) on estimation of the species tree and evolutionary parameters in analysis of multilocus genomic data under the MSC model. We found that species tree estimation is robust to phasing errors when species divergences were much older than average coalescent times but may be affected by phasing errors when the species tree is shallow. Estimation of parameters under the MSC model with and without introgression is affected by phasing errors. In particular, random phase resolution causes serious overestimation of population sizes for modern species and biased estimation of cross-species introgression probability. In general, the impact of phasing errors is greater when the mutation rate is higher, the data include more samples per species, and the species tree is shallower with recent divergences. Use of phased sequences inferred by the PHASE program produced small biases in parameter estimates. We analyze two real data sets, one of East Asian brown frogs and another of Rocky Mountains chipmunks, to demonstrate that heterozygote phase-resolution strategies have similar impacts on practical data analyses. We suggest that genome sequencing projects should produce unphased diploid genotype sequences if fully phased data are too challenging to generate, and avoid haploid consensus sequences, which have heterozygous sites phased at random. In case the analytical integration algorithm is computationally unfeasible, computational phasing prior to population genomic analyses is an acceptable alternative. [BPP; introgression; multispecies coalescent; phase; species tree.]

Assessing the fit of the multi-species network coalescent to multi-locus data

MOTIVATION

With growing genome-wide molecular datasets from next-generation sequencing, phylogenetic networks can be estimated using a variety of approaches. These phylogenetic networks include events like hybridization, gene flow or horizontal gene transfer explicitly. However, the most accurate network inference methods are computationally heavy. Methods that scale to larger datasets do not calculate a full likelihood, such that traditional likelihood-based tools for model selection are not applicable to decide how many past hybridization events best fit the data. We propose here a goodness-of-fit test to quantify the fit between data observed from genome-wide multi-locus data, and patterns expected under the multi-species coalescent model on a candidate phylogenetic network.

RESULTS

We identified weaknesses in the previously proposed TICR test, and proposed corrections. The performance of our new test was validated by simulations on real-world phylogenetic networks. Our test provides one of the first rigorous tools for model selection, to select the adequate network complexity for the data at hand. The test can also work for identifying poorly inferred areas on a network.

AVAILABILITY AND IMPLEMENTATION

Software for the goodness-of-fit test is available as a Julia package at https://github.com/cecileane/QuartetNetworkGoodnessFit.jl.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Introgression is widespread in the radiation of carnivorous Nepenthes pitcher plants

Introgression and hybridization are important processes in plant evolution, but they are difficult to study from a phylogenetic perspective, because they conflict with the bifurcating evolutionary history typically depicted in phylogenetic models. The role of hybridization in plant evolution is best documented in the form of allo-polyploidizations. In contrast, homoploid hybridization and introgression are less explored, although they may be crucial in adaptive radiations. Here we employ genome-wide data (ddRAD-seq, transcriptomes) to investigate the evolutionary history of Nepenthes, a radiation of c. 160 species of iconic carnivorous plants mainly from tropical Asia. Our data indicates that the main radiation is only c. 5 million years old, and confirms previous bifurcating phylogenies. However, due to a greatly expanded number of loci, we were able test for the first time the long-standing hypotheses of introgression and historical hybridization. The genus presents one very clear case of organellar capture between two distantly related but sympatric groups. Furthermore, all Nepenthes species show introgression signals in their nuclear genomes, as uncovered by a general survey of ABBA-BABA-like statistics. The ancestor of the rapid main radiation shows ancestry from two deeply diverged lineages, as indicated by phylogenetic network analyses. All major clades of the main radiation show further introgression both within and between each other, as suggested by admixture graphs. Our study supports the hypothesis that rapid adaptive radiations are hotspots of introgression in the tree of life, and highlights the need to consider non-treelike processes in evolutionary studies of Nepenthes in particular.

Practical Speedup of Bayesian Inference of Species Phylogenies by Restricting the Space of Gene Trees

Species tree inference from multilocus data has emerged as a powerful paradigm in the postgenomic era, both in terms of the accuracy of the species tree it produces as well as in terms of elucidating the processes that shaped the evolutionary history. Bayesian methods for species tree inference are desirable in this area as they have been shown not only to yield accurate estimates, but also to naturally provide measures of confidence in those estimates. However, the heavy computational requirements of Bayesian inference have limited the applicability of such methods to very small data sets. In this article, we show that the computational efficiency of Bayesian inference under the multispecies coalescent can be improved in practice by restricting the space of the gene trees explored during the random walk, without sacrificing accuracy as measured by various metrics. The idea is to first infer constraints on the trees of the individual loci in the form of unresolved gene trees, and then to restrict the sampler to consider only resolutions of the constrained trees. We demonstrate the improvements gained by such an approach on both simulated and biological data.

Polyploid phylogenetics

Polyploidy is a dominant feature of extant plant diversity. However, major research questions, including whether polyploidy is important to long-term evolution or is just 'evolutionary noise', remain unresolved due to difficulties associated with the generation and analysis of data from polyploid lineages. Many of these difficulties have been recently overcome, such that it is now often relatively straightforward to infer the full and often reticulate phylogenetic history of groups with recently formed polyploids. This nascent field of 'polyploid phylogenetics' allows researchers to tackle long-standing questions of polyploid macroevolution, supplies the foundation for mechanistic models of ploidy change, and provides the opportunity to include a more complete and representative sample of plant taxa in our analyses in general.

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

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

A molecularphylogeny offorktail damselflies(genus Ischnura)revealsa dynamic macroevolutionary history of female colour polymorphisms

Colour polymorphisms are popular study systems among biologists interested in evolutionary dynamics, genomics, sexual selection and sexual conflict. In many damselfly groups, such as in the globally distributed genus Ischnura (forktails), sex-limited female colour polymorphisms occur in multiple species. Female-polymorphic species contain two or three female morphs, one of which phenotypically matches the male (androchrome or male mimic) and the other(s) which are phenotypically distinct from the male (heterochrome). These female colour polymorphisms are thought to be maintained by frequency-dependent sexual conflict, but their macroevolutionary histories are unknown, due to the lack of a robust molecular phylogeny. Here, we present the first time-calibrated phylogeny of Ischnura, using a multispecies coalescent approach (StarBEAST2) and incorporating both molecular and fossil data for 41 extant species (55% of the genus). We estimate the age of Ischnura to be between 13.8 and 23.4 millions of years, i.e. Miocene. We infer the ancestral state of this genus as female monomorphism with heterochrome females, with multiple gains and losses of female polymorphisms, evidence of trans-species female polymorphisms and a significant positive relationship between female polymorphism incidence and current geographic range size. Our study provides a robust phylogenetic framework for future research on the dynamic macroevolutionary history of this clade with its extraordinary diversity of sex-limited female polymorphisms.

Ecological Specialisation and Evolutionary Reticulation in Extant Hyaenidae

During the Miocene, Hyaenidae was a highly diverse family of Carnivora that has since been severely reduced to four species: the bone-cracking spotted, striped, and brown hyenas, and the specialized insectivorous aardwolf. Previous studies investigated the evolutionary histories of the spotted and brown hyenas, but little is known about the remaining two species. Moreover, the genomic underpinnings of scavenging and insectivory, defining traits of the extant species, remain elusive. Here, we generated an aardwolf genome and analyzed it together with the remaining three species to reveal their evolutionary relationships, genomic underpinnings of their scavenging and insectivorous lifestyles, and their respective genetic diversities and demographic histories. High levels of phylogenetic discordance suggest gene flow between the aardwolf lineage and the ancestral brown/striped hyena lineage. Genes related to immunity and digestion in the bone-cracking hyenas and craniofacial development in the aardwolf showed the strongest signals of selection, suggesting putative key adaptations to carrion and termite feeding, respectively. A family-wide expansion in olfactory receptor genes suggests that an acute sense of smell was a key early adaptation. Finally, we report very low levels of genetic diversity within the brown and striped hyenas despite no signs of inbreeding, putatively linked to their similarly slow decline in effective population size over the last ∼2 million years. High levels of genetic diversity and more stable population sizes through time are seen in the spotted hyena and aardwolf. Taken together, our findings highlight how ecological specialization can impact the evolutionary history, demographics, and adaptive genetic changes of an evolutionary lineage.

Gene tree discord, simplex plots, and statistical tests under the coalescent

A simple graphical device, the simplex plot of quartet concordance factors, is introduced to aid in the exploration of a collection of gene trees on a common set of taxa. A single plot summarizes all gene tree discord, and allows for visual comparison to the expected discord from the multispecies coalescent model (MSC) of incomplete lineage sorting on a species tree. A formal statistical procedure is described that can quantify the deviation from expectation for each subset of four taxa, suggesting when the data is not in accord with the MSC, and thus that either gene tree inference error is substantial or a more complex model such as that on a network may be required. If the collection of gene trees is in accord with the MSC, the plots reveal when substantial incomplete lineage sorting is present. Applications to both simulated and empirical multilocus data sets illustrate the insights provided.

Phylogenomic Discordance in the Eared Seals is best explained by Incomplete Lineage Sorting following Explosive Radiation in the Southern Hemisphere

The phylogeny and systematics of fur seals and sea lions (Otariidae) have long been studied with diverse data types, including an increasing amount of molecular data. However, only a few phylogenetic relationships have reached acceptance because of strong gene-tree species tree discordance. Divergence times estimates in the group also vary largely between studies. These uncertainties impeded the understanding of the biogeographical history of the group, such as when and how trans-equatorial dispersal and subsequent speciation events occurred. Here, we used high-coverage genome-wide sequencing for 14 of the 15 species of Otariidae to elucidate the phylogeny of the family and its bearing on the taxonomy and biogeographical history. Despite extreme topological discordance among gene trees, we found a fully supported species tree that agrees with the few well-accepted relationships and establishes monophyly of the genus Arctocephalus. Our data support a relatively recent trans-hemispheric dispersal at the base of a southern clade, which rapidly diversified into six major lineages between 3 and 2.5 Ma. Otaria diverged first, followed by Phocarctos and then four major lineages within Arctocephalus. However, we found Zalophus to be nonmonophyletic, with California (Zalophus californianus) and Steller sea lions (Eumetopias jubatus) grouping closer than the Galapagos sea lion (Zalophus wollebaeki) with evidence for introgression between the two genera. Overall, the high degree of genealogical discordance was best explained by incomplete lineage sorting resulting from quasi-simultaneous speciation within the southern clade with introgresssion playing a subordinate role in explaining the incongruence among and within prior phylogenetic studies of the family. [Hybridization; ILS; phylogenomics; Pleistocene; Pliocene; monophyly.].

Determining the probability of hemiplasy in the presence of incomplete lineage sorting and introgression

The incongruence of character states with phylogenetic relationships is often interpreted as evidence of convergent evolution. However, trait evolution along discordant gene trees can also generate these incongruences - a phenomenon known as hemiplasy. Classic comparative methods do not account for discordance, resulting in incorrect inferences about the number, timing, and direction of trait transitions. Biological sources of discordance include incomplete lineage sorting (ILS) and introgression, but only ILS has received theoretical consideration in the context of hemiplasy. Here, we present a model that shows introgression makes hemiplasy more likely, such that methods that account for ILS alone will be conservative. We also present a method and software (HeIST) for making statistical inferences about the probability of hemiplasy and homoplasy in large datasets that contain both ILS and introgression. We apply our methods to two empirical datasets, finding that hemiplasy is likely to contribute to the observed trait incongruences in both.

Maximum Likelihood Estimation of Species Trees from Gene Trees in the Presence of Ancestral Population Structure

Though large multilocus genomic data sets have led to overall improvements in phylogenetic inference, they have posed the new challenge of addressing conflicting signals across the genome. In particular, ancestral population structure, which has been uncovered in a number of diverse species, can skew gene tree frequencies, thereby hindering the performance of species tree estimators. Here we develop a novel maximum likelihood method, termed TASTI (Taxa with Ancestral structure Species Tree Inference), that can infer phylogenies under such scenarios, and find that it has increasing accuracy with increasing numbers of input gene trees, contrasting with the relatively poor performances of methods not tailored for ancestral structure. Moreover, we propose a supertree approach that allows TASTI to scale computationally with increasing numbers of input taxa. We use genetic simulations to assess TASTI's performance in the three- and four-taxon settings and demonstrate the application of TASTI on a six-species Afrotropical mosquito data set. Finally, we have implemented TASTI in an open-source software package for ease of use by the scientific community.

Phylogenetic Trees and Networks Can Serve as Powerful and Complementary Approaches for Analysis of Genomic Data

Genomic data have had a profound impact on nearly every biological discipline. In systematics and phylogenetics, the thousands of loci that are now being sequenced can be analyzed under the multispecies coalescent model (MSC) to explicitly account for gene tree discordance due to incomplete lineage sorting (ILS). However, the MSC assumes no gene flow post divergence, calling for additional methods that can accommodate this limitation. Explicit phylogenetic network methods have emerged, which can simultaneously account for ILS and gene flow by representing evolutionary history as a directed acyclic graph. In this point of view, we highlight some of the strengths and limitations of phylogenetic networks and argue that tree-based inference should not be blindly abandoned in favor of networks simply because they represent more parameter rich models. Attention should be given to model selection of reticulation complexity, and the most robust conclusions regarding evolutionary history are likely obtained when combining tree- and network-based inference.

Swimming through the sands of the Sahara and Arabian deserts: Phylogeny of sandfish skinks (Scincidae, Scincus) reveals a recent and rapid diversification

Large parts of the Sahara Desert and Arabia are covered by sand seas and sand dunes, which are inhabited by specialized animal communities. For example, many lizards have developed adaptations to life in loose sand, including sand-swimming behavior. The best-known sand swimmers of the Saharo-Arabia are the sandfish skinks (genus Scincus). Although there are currently only four Scincus species recognized, their phylogenetic relationships have not yet been addressed in detail. We use eight genetic markers (three mitochondrial, five nuclear) and a complete sampling of species to infer the relationships within the genus. We employ multiple phylogenetic approaches to reconstruct the evolutionary history of these skinks and to assess the level of reticulation at the onset of their radiation. Our results indicate the presence of five strongly supported species-level lineages, four represented by the currently recognized species and the fifth by S. scincus conirostris, which does not form a clade with S. scincus. Based on these results we elevate the Iranian and northern Arabian S. conirostris to the species level. The two Saharan species, S. albifasciatus and S. scincus, are sister in all analyses. Deeper relationships within the genus, however, remained largely unresolved despite the extensive genetic data set. This basal polytomy, together with the fact that we detected no sign of hybridization in the history of the genus, indicates that the diversification of the five Scincus species was rapid, burst-like, and not followed by secondary hybridization events. Divergence time estimations show a Middle Pliocene crown radiation of the genus (3.3 Mya). We hypothesize that the aridification of the Saharo-Arabia that began in the Late Miocene triggered the initial diversification of Scincus, and that the subsequent expansion of sand deserts enabled their dispersal over the large Saharan and Arabian range. We discuss the evolution of body form in sand swimming lizards and ponder how Scincus retained their fully limbed morphology despite being sand swimmers that are typically limbless.

Evidence of introgression in endemic frogs from the campo rupestre contradicts the reduced hybridization hypothesis

The campo rupestre ecosystem is considered an old, climatically buffered, infertile landscape. As a consequence, long-term isolation is thought to have played an important role in the diversification of its biota. Here, we tested for hybridization between two endemic leaf frogs from the campo rupestre. We used sequence markers and coalescent models to verify haplotype sharing between the species, to test the existence and direction of gene flow, and to reconstruct the spatiotemporal dynamics of gene flow. Additionally, ecological niche modelling (ENM) was used to assess for potential co-occurrence by overlapping the climatic niche of these species since the middle Pleistocene. We found haplotype sharing and/or lack of differentiation in four nuclear fragments, one of them associated with introgression. The coalescent models support introgressive hybridization unidirectionally from Pithecopus megacephalus to P. ayeaye, occurring ~300 kya. ENM corroborates this scenario, revealing areas of potential environmental niche overlap for the species at about 787 kya. These results contradict the expectation of reduced hybridization, while ENM suggests climatic fluctuation rather than stability for the two species. The reduced hybridization hypothesis needs to be further investigated because our results suggest that it may have unrealistic premises at least for animals.

A Simulation Study to Examine the Information Content in Phylogenomic Data Sets under the Multispecies Coalescent Model

We use computer simulation to examine the information content in multilocus data sets for inference under the multispecies coalescent model. Inference problems considered include estimation of evolutionary parameters (such as species divergence times, population sizes, and cross-species introgression probabilities), species tree estimation, and species delimitation based on Bayesian comparison of delimitation models. We found that the number of loci is the most influential factor for almost all inference problems examined. Although the number of sequences per species does not appear to be important to species tree estimation, it is very influential to species delimitation. Increasing the number of sites and the per-site mutation rate both increase the mutation rate for the whole locus and these have the same effect on estimation of parameters, but the sequence length has a greater effect than the per-site mutation rate for species tree estimation. We discuss the computational costs when the data size increases and provide guidelines concerning the subsampling of genomic data to enable the application of full-likelihood methods of inference.

Defining Species When There is Gene Flow

Whatever one's definition of species, it is generally expected that individuals of the same species should be genetically more similar to each other than they are to individuals of another species. Here, we show that in the presence of cross-species gene flow, this expectation may be incorrect. We use the multispecies coalescent model with continuous-time migration or episodic introgression to study the impact of gene flow on genetic differences within and between species and highlight a surprising but plausible scenario in which different population sizes and asymmetrical migration rates cause a genetic sequence to be on average more closely related to a sequence from another species than to a sequence from the same species. Our results highlight the extraordinary impact that even a small amount of gene flow may have on the genetic history of the species. We suggest that contrasting long-term migration rate and short-term hybridization rate, both of which can be estimated using genetic data, may be a powerful approach to detecting the presence of reproductive barriers and to define species boundaries.[Gene flow; introgression; migration; multispecies coalescent; species concept; species delimitation.].

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

Motivation

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

Results

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

Availability and implementation

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

Supplementary information

Supplementary data are available at Bioinformatics online.

Phylogenetic tree building in the genomic age

Knowing phylogenetic relationships among species is fundamental for many studies in biology. An accurate phylogenetic tree underpins our understanding of the major transitions in evolution, such as the emergence of new body plans or metabolism, and is key to inferring the origin of new genes, detecting molecular adaptation, understanding morphological character evolution and reconstructing demographic changes in recently diverged species. Although data are ever more plentiful and powerful analysis methods are available, there remain many challenges to reliable tree building. Here, we discuss the major steps of phylogenetic analysis, including identification of orthologous genes or proteins, multiple sequence alignment, and choice of substitution models and inference methodologies. Understanding the different sources of errors and the strategies to mitigate them is essential for assembling an accurate tree of life.

Uncovering the genomic signature of ancient introgression between white oak lineages (Quercus)

Botanists have long recognised interspecific gene flow as a common occurrence within white oaks (Quercus section Quercus). Historical allele exchange, however, has not been fully characterised and the complex genomic signals resulting from the combination of vertical and horizontal gene transmission may confound phylogenetic inference and obscure our ability to accurately infer the deep evolutionary history of oaks. Using anchored enrichment, we obtained a phylogenomic dataset consisting of hundreds of single-copy nuclear loci. Concatenation, species-tree and network analyses were carried out in an attempt to uncover the genomic signal of ancient introgression and infer the divergent phylogenetic topology for the white oak clade. Locus and site-level likelihood comparisons were then conducted to further explore the introgressed signal within our dataset. Historical, intersectional gene flow is suggested to have occurred between an ancestor of the Eurasian Roburoid lineage and Quercus pontica and North American Dumosae and Prinoideae lineages. Despite extensive time past, our approach proved successful in detecting the genomic signature of ancient introgression. Our results, however, highlight the importance of sampling and the use of a plurality of analytical tools and methods to sufficiently explore genomic datasets, uncover this signal, and accurately infer evolutionary history.

Genomic landscape of the global oak phylogeny

The tree of life is highly reticulate, with the history of population divergence emerging from populations of gene phylogenies that reflect histories of introgression, lineage sorting and divergence. In this study, we investigate global patterns of oak diversity and test the hypothesis that there are regions of the oak genome that are broadly informative about phylogeny. We utilize fossil data and restriction-site associated DNA sequencing (RAD-seq) for 632 individuals representing nearly 250 Quercus species to infer a time-calibrated phylogeny of the world's oaks. We use a reversible-jump Markov chain Monte Carlo method to reconstruct shifts in lineage diversification rates, accounting for among-clade sampling biases. We then map the > 20 000 RAD-seq loci back to an annotated oak genome and investigate genomic distribution of introgression and phylogenetic support across the phylogeny. Oak lineages have diversified among geographic regions, followed by ecological divergence within regions, in the Americas and Eurasia. Roughly 60% of oak diversity traces back to four clades that experienced increases in net diversification, probably in response to climatic transitions or ecological opportunity. The strong support for the phylogeny contrasts with high genomic heterogeneity in phylogenetic signal and introgression. Oaks are phylogenomic mosaics, and their diversity may in fact depend on the gene flow that shapes the oak genome.

Genome-wide sequence information reveals recurrent hybridization among diploid wheat wild relatives

Many conflicting hypotheses regarding the relationships among crops and wild species closely related to wheat (the genera Aegilops, Amblyopyrum, and Triticum) have been postulated. The contribution of hybridization to the evolution of these taxa is intensely discussed. To determine possible causes for this, and provide a phylogeny of the diploid taxa based on genome-wide sequence information, independent data were obtained from genotyping-by-sequencing and a target-enrichment experiment that returned 244 low-copy nuclear loci. The data were analyzed using Bayesian, likelihood and coalescent-based methods. D statistics were used to test if incomplete lineage sorting alone or together with hybridization is the source for incongruent gene trees. Here we present the phylogeny of all diploid species of the wheat wild relatives. We hypothesize that most of the wheat-group species were shaped by a primordial homoploid hybrid speciation event involving the ancestral Triticum and Am. muticum lineages to form all other species except Ae. speltoides. This hybridization event was followed by multiple introgressions affecting all taxa except Triticum. Mostly progenitors of the extant species were involved in these processes, while recent interspecific gene flow seems insignificant. The composite nature of many genomes of wheat-group taxa results in complicated patterns of diploid contributions when these lineages are involved in polyploid formation, which is, for example, the case for tetraploid and hexaploid wheats. Our analysis provides phylogenetic relationships and a testable hypothesis for the genome compositions in the basic evolutionary units within the wheat group of Triticeae.

Implementing Large Genomic Single Nucleotide Polymorphism Data Sets in Phylogenetic Network Reconstructions: A Case Study of Particularly Rapid Radiations of Cichlid Fish

The Midas cichlids of the Amphilophus citrinellus spp. species complex from Nicaragua (13 species) are an extraordinary example of adaptive and rapid radiation ($<$24,000 years old). These cichlids are a very challenging group to infer its evolutionary history in phylogenetic analyses, due to the apparent prevalence of incomplete lineage sorting (ILS), as well as past and current gene flow. Assuming solely a vertical transfer of genetic material from an ancestral lineage to new lineages is not appropriate in many cases of genes transferred horizontally in nature. Recently developed methods to infer phylogenetic networks under such circumstances might be able to circumvent these problems. These models accommodate not just ILS, but also gene flow, under the multispecies network coalescent (MSNC) model, processes that are at work in young, hybridizing, and/or rapidly diversifying lineages. There are currently only a few programs available that implement MSNC for estimating phylogenetic networks. Here, we present a novel way to incorporate single nucleotide polymorphism (SNP) data into the currently available PhyloNetworks program. Based on simulations, we demonstrate that SNPs can provide enough power to recover the true phylogenetic network. We also show that it can accurately infer the true network more often than other similar SNP-based programs (PhyloNet and HyDe). Moreover, our approach results in a faster algorithm compared to the original pipeline in PhyloNetworks, without losing power. We also applied our new approach to infer the phylogenetic network of Midas cichlid radiation. We implemented the most comprehensive genomic data set to date (RADseq data set of 679 individuals and $>$37K SNPs from 19 ingroup lineages) and present estimated phylogenetic networks for this extremely young and fast-evolving radiation of cichlid fish. We demonstrate that the MSNC is more appropriate than the multispecies coalescent alone for the analysis of this rapid radiation. [Genomics; multispecies network coalescent; phylogenetic networks; phylogenomics; RADseq; SNPs.]

The Impact of Cross-Species Gene Flow on Species Tree Estimation

Recent analyses of genomic sequence data suggest cross-species gene flow is common in both plants and animals, posing challenges to species tree estimation. We examine the levels of gene flow needed to mislead species tree estimation with three species and either episodic introgressive hybridization or continuous migration between an outgroup and one ingroup species. Several species tree estimation methods are examined, including the majority-vote method based on the most common gene tree topology (with either the true or reconstructed gene trees used), the UPGMA method based on the average sequence distances (or average coalescent times) between species, and the full-likelihood method based on multilocus sequence data. Our results suggest that the majority-vote method based on gene tree topologies is more robust to gene flow than the UPGMA method based on coalescent times and both are more robust than likelihood assuming a multispecies coalescent (MSC) model with no cross-species gene flow. Comparison of the continuous migration model with the episodic introgression model suggests that a small amount of gene flow per generation can cause drastic changes to the genetic history of the species and mislead species tree methods, especially if the species diverged through radiative speciation events. Estimates of parameters under the MSC with gene flow suggest that African mosquito species in the Anopheles gambiae species complex constitute such an example of extreme impact of gene flow on species phylogeny. [IM; introgression; migration; MSci; multispecies coalescent; species tree.]

Identifying model violations under the multispecies coalescent model using P2C2M.SNAPP

Phylogenetic estimation under the multispecies coalescent model (MSCM) assumes all incongruence among loci is caused by incomplete lineage sorting. Therefore, applying the MSCM to datasets that contain incongruence that is caused by other processes, such as gene flow, can lead to biased phylogeny estimates. To identify possible bias when using the MSCM, we present P2C2M.SNAPP. P2C2M.SNAPP is an R package that identifies model violations using posterior predictive simulation. P2C2M.SNAPP uses the posterior distribution of species trees output by the software package SNAPP to simulate posterior predictive datasets under the MSCM, and then uses summary statistics to compare either the empirical data or the posterior distribution to the posterior predictive distribution to identify model violations. In simulation testing, P2C2M.SNAPP correctly classified up to 83% of datasets (depending on the summary statistic used) as to whether or not they violated the MSCM model. P2C2M.SNAPP represents a user-friendly way for researchers to perform posterior predictive model checks when using the popular SNAPP phylogenetic estimation program. It is freely available as an R package, along with additional program details and tutorials.

Unraveling Reticulate Evolution in Opuntia (Cactaceae) From Southern Mexico

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

NANUQ: a method for inferring species networks from gene trees under the coalescent model

Species networks generalize the notion of species trees to allow for hybridization or other lateral gene transfer. Under the network multispecies coalescent model, individual gene trees arising from a network can have any topology, but arise with frequencies dependent on the network structure and numerical parameters. We propose a new algorithm for statistical inference of a level-1 species network under this model, from data consisting of gene tree topologies, and provide the theoretical justification for it. The algorithm is based on an analysis of quartets displayed on gene trees, combining several statistical hypothesis tests with combinatorial ideas such as a quartet-based intertaxon distance appropriate to networks, the NeighborNet algorithm for circular split systems, and the Circular Network algorithm for constructing a splits graph.

Reticulate Evolution Helps Explain Apparent Homoplasy in Floral Biology and Pollination in Baobabs (Adansonia; Bombacoideae; Malvaceae)

Baobabs (Adansonia) are a cohesive group of tropical trees with a disjunct distribution in Australia, Madagascar, and continental Africa, and diverse flowers associated with two pollination modes. We used custom-targeted sequence capture in conjunction with new and existing phylogenetic comparative methods to explore the evolution of floral traits and pollination systems while allowing for reticulate evolution. Our analyses suggest that relationships in Adansonia are confounded by reticulation, with network inference methods supporting at least one reticulation event. The best supported hypothesis involves introgression between Adansonia rubrostipa and core Longitubae, both of which are hawkmoth pollinated with yellow/red flowers, but there is also some support for introgression between the African lineage and Malagasy Brevitubae, which are both mammal-pollinated with white flowers. New comparative methods for phylogenetic networks were developed that allow maximum-likelihood inference of ancestral states and were applied to study the apparent homoplasy in floral biology and pollination mode seen in Adansonia. This analysis supports a role for introgressive hybridization in morphological evolution even in a clade with highly divergent and geographically widespread species. Our new comparative methods for discrete traits on species networks are implemented in the software PhyloNetworks. [Comparative methods; Hyb-Seq; introgression; network inference; population trees; reticulate evolution; species tree inference; targeted sequence capture.]

Evolutionary networks from RADseq loci point to hybrid origins of Medicago carstiensis and Medicago cretacea

PREMISE

Although hybridization has played an important role in the evolution of many plant species, phylogenetic reconstructions that include hybridizing lineages have been historically constrained by the available models and data. Restriction-site-associated DNA sequencing (RADseq) has been a popular sequencing technique for the reconstruction of hybridization in the next-generation sequencing era. However, the utility of RADseq for the reconstruction of complex evolutionary networks has not been thoroughly investigated. Conflicting phylogenetic relationships in the genus Medicago have been mainly attributed to hybridization, but the specific hybrid origins of taxa have not been yet clarified.

METHODS

We obtained new molecular data from diploid species of Medicago section Medicago using single-digest RADseq to reconstruct evolutionary networks from gene trees, an approach that is computationally tractable with data sets that include several species and complex hybridization patterns.

RESULTS

Our analyses revealed that assembly filters to exclusively select a small set of loci with high phylogenetic information led to the most-divergent network topologies. Conversely, alternative clustering thresholds or filters on the number of samples per locus had a lower impact on networks. A strong hybridization signal was detected for M. carstiensis and M. cretacea, while signals were less clear for M. rugosa, M. rhodopea, M. suffruticosa, M. marina, M. scutellata, and M. sativa.

CONCLUSIONS

Complex network reconstructions from RADseq gene trees were not robust under variations of the assembly parameters and filters. But when the most-divergent networks were discarded, all remaining analyses consistently supported a hybrid origin for M. carstiensis and M. cretacea.

Historical faunal exchange between the Pontocaspian Basin and North America

Ecrobia is a genus of small brackish-water mud snails with an amphi-Atlantic distribution. Interestingly, the species occurring in the northwestern Atlantic, Ecrobia truncata, is more closely related to the Pontocaspian taxa, Ecrobia grimmi and Ecrobia maritima, than to the species occurring in the northeastern Atlantic and Mediterranean Sea. At least three colonization scenarios may account for this peculiar biogeographical pattern: (1) a recent human-mediated dispersal, (2) a historical transatlantic interchange, and (3) a historical transpolar interchange. To test these three scenarios, we used five operational criteria-time of species divergence, first appearance in the fossil record, dispersal limitation as well as environmental filtering and biotic interactions along the potential migration routes. Specifically, we inferred a time-calibrated molecular phylogeny for Ecrobia and reconstructed a paleogeographical map of the Arctic Ocean at 2.5 million years ago (Mya). Based on the five operational criteria, scenarios 1 and 2 can likely be rejected. In contrast, all criteria support scenario 3 (historical transpolar interchange). It is therefore suggested that a bird-mediated and/or ocean current-mediated faunal interchange via the Arctic Ocean occurred during the Late Pliocene or Early Pleistocene. This dispersal was likely facilitated by reduced distances between the Eurasian and North American/Greenland landmasses, marine introgressions, and/or a stepping-stone system of brackish-water habitats in northern Siberia, as well as a lack of competition along the migration route. As for the direction of dispersal, the scientific data presented are not conclusive. However, there is clearly more support for the scenario of dispersal from the Pontocaspian Basin to North America than vice versa. This is the first study providing evidence for a natural faunal exchange between the Pontocaspian Basin and North America via the Arctic Ocean.

Inference of species phylogenies from bi-allelic markers using pseudo-likelihood

Motivation

Phylogenetic networks represent reticulate evolutionary histories. Statistical methods for their inference under the multispecies coalescent have recently been developed. A particularly powerful approach uses data that consist of bi-allelic markers (e.g. single nucleotide polymorphism data) and allows for exact likelihood computations of phylogenetic networks while numerically integrating over all possible gene trees per marker. While the approach has good accuracy in terms of estimating the network and its parameters, likelihood computations remain a major computational bottleneck and limit the method’s applicability.

Results

In this article, we first demonstrate why likelihood computations of networks take orders of magnitude more time when compared to trees. We then propose an approach for inference of phylogenetic networks based on pseudo-likelihood using bi-allelic markers. We demonstrate the scalability and accuracy of phylogenetic network inference via pseudo-likelihood computations on simulated data. Furthermore, we demonstrate aspects of robustness of the method to violations in the underlying assumptions of the employed statistical model. Finally, we demonstrate the application of the method to biological data. The proposed method allows for analyzing larger datasets in terms of the numbers of taxa and reticulation events. While pseudo-likelihood had been proposed before for data consisting of gene trees, the work here uses sequence data directly, offering several advantages as we discuss.

Availability and implementation

The methods have been implemented in PhyloNet (http://bioinfocs.rice.edu/phylonet).

Patterns, Mechanisms and Genetics of Speciation in Reptiles and Amphibians

In this contribution, the aspects of reptile and amphibian speciation that emerged from research performed over the past decade are reviewed. First, this study assesses how patterns and processes of speciation depend on knowing the taxonomy of the group in question, and discuss how integrative taxonomy has contributed to speciation research in these groups. This study then reviews the research on different aspects of speciation in reptiles and amphibians, including biogeography and climatic niches, ecological speciation, the relationship between speciation rates and phenotypic traits, and genetics and genomics. Further, several case studies of speciation in reptiles and amphibians that exemplify many of these themes are discussed. These include studies of integrative taxonomy and biogeography in South American lizards, ecological speciation in European salamanders, speciation and phenotypic evolution in frogs and lizards. The final case study combines genomics and biogeography in tortoises. The field of amphibian and reptile speciation research has steadily moved forward from the assessment of geographic and ecological aspects, to incorporating other dimensions of speciation, such as genetic mechanisms and evolutionary forces. A higher degree of integration among all these dimensions emerges as a goal for future research.

QS-Net: Reconstructing Phylogenetic Networks Based on Quartet and Sextet

Phylogenetic networks are used to estimate evolutionary relationships among biological entities or taxa involving reticulate events such as horizontal gene transfer, hybridization, recombination, and reassortment. In the past decade, many phylogenetic tree and network reconstruction methods have been proposed. Despite that they are highly accurate in reconstructing simple to moderate complex reticulate events, the performance decreases when several reticulate events are present simultaneously. In this paper, we proposed QS-Net, a phylogenetic network reconstruction method taking advantage of information on the relationship among six taxa. To evaluate the performance of QS-Net, we conducted experiments on three artificial sequence data simulated from an evolutionary tree, an evolutionary network involving three reticulate events, and a complex evolutionary network involving five reticulate events. Comparison with popular phylogenetic methods including Neighbor-Joining, Split-Decomposition, Neighbor-Net, and Quartet-Net suggests that QS-Net is comparable with other methods in reconstructing tree-like evolutionary histories, while it outperforms them in reconstructing reticulate events. In addition, we also applied QS-Net in real data including a bacterial taxonomy data consisting of 36 bacterial species and the whole genome sequences of 22 H7N9 influenza A viruses. The results indicate that QS-Net is capable of inferring commonly believed bacterial taxonomy and influenza evolution as well as identifying novel reticulate events. The software QS-Net is publically available at https://github.com/Tmyiri/QS-Net.

Hybridization preceded radiation in diploid wheats

Evolutionary relationships among the Aegilops-Triticum relatives of cultivated wheats have been difficult to resolve owing to incomplete lineage sorting and reticulate evolution. Recent studies have suggested that the wheat D-genome lineage (progenitor of Ae. tauschii) originated through homoploid hybridization between the A-genome lineage (progenitor of Triticum s.str.) and the B-genome lineage (progenitor of Ae. speltoides). This scenario of reticulation has been debated, calling for adequate phylogenetic analyses based on comprehensive sampling. To reconstruct the evolution of Aegilops-Triticum diploids, we here combined high-throughput sequencing of 38 nuclear low-copy loci of multiple accessions of all 13 species with inferences of the species phylogeny using the full-parameterized MCMC_SEQ method. Phylogenies recovered a monophyletic Aegilops-Triticum lineage that began diversifying ~6.6 Ma ago and gave rise to four sublineages, i.e. the A- (2 species), B- (1 species), D- (9 species) and T- (Ae. mutica) genome lineage. Full-parameterized phylogenies as well as patterns of tree dilation and tree compression supported a hybrid origin of the D-genome lineage from A and B ~3.0-4.0 Ma ago, and did not indicate additional hybridization events. Conflicting ABBA-BABA tests suggestive of further reticulation were shown here to result from ancestral population structure rather than hybridization. This comprehensive and dated phylogeny of wheat relatives indicates that the origin of the hybrid D-genome was followed by intense diversification into the majority of extant diploid as well as allopolyploid wild wheats.

Fungal species boundaries in the genomics era

Genomic data has opened new possibilities to understand how organisms change over time, and could enable the discovery of previously undescribed species. Although taxonomy used to be based on phenotypes, molecular data has frequently revealed that morphological traits are insufficient to describe biodiversity. Genomics holds the promise of revealing even more genetic discontinuities, but the parameters on how to describe species from genomic data remain unclear. Fungi have been a successful case in which the use of molecular markers has uncovered the existence of genetic boundaries where no crosses are possible. In this minireview, we highlight recent advances, propose a set of standards to use genomic sequences to uncover species boundaries, point out potential pitfalls, and present possible future research directions.

Coalescent Analysis of Phylogenomic Data Confidently Resolves the Species Relationships in the Anopheles gambiae Species Complex

Deep coalescence and introgression make it challenging to infer phylogenetic relationships among closely related species that arose through radiative speciation events. Despite numerous phylogenetic analyses and the availability of whole genomes, the phylogeny in the Anopheles gambiae species complex has not been confidently resolved. Here we extract over 80, 000 coding and noncoding short segments (called loci) from the genomes of six members of the species complex and use a Bayesian method under the multispecies coalescent model to infer the species tree, which takes into account genealogical heterogeneity across the genome and uncertainty in the gene trees. We obtained a robust estimate of the species tree from the distal region of the X chromosome: (A. merus, ((A. melas, (A. arabiensis, A. quadriannulatus)), (A. gambiae, A. coluzzii))), with A. merus to be the earliest branching species. This species tree agrees with the chromosome inversion phylogeny and provides a parsimonious interpretation of inversion and introgression events. Simulation informed by the real data suggest that the coalescent approach is reliable while the sliding-window analysis used in a previous phylogenomic study generates artifactual species trees. Likelihood ratio test of gene flow revealed strong evidence of autosomal introgression from A. arabiensis into A. gambiae (at the average rate of ∼0.2 migrants per generation), but not in the opposite direction, and introgression of the 3 L chromosomal region from A. merus into A. quadriannulatus. Our results highlight the importance of accommodating incomplete lineage sorting and introgression in phylogenomic analyses of species that arose through recent radiative speciation events.

BEAST 2.5: An advanced software platform for Bayesian evolutionary analysis

Elaboration of Bayesian phylogenetic inference methods has continued at pace in recent years with major new advances in nearly all aspects of the joint modelling of evolutionary data. It is increasingly appreciated that some evolutionary questions can only be adequately answered by combining evidence from multiple independent sources of data, including genome sequences, sampling dates, phenotypic data, radiocarbon dates, fossil occurrences, and biogeographic range information among others. Including all relevant data into a single joint model is very challenging both conceptually and computationally. Advanced computational software packages that allow robust development of compatible (sub-)models which can be composed into a full model hierarchy have played a key role in these developments. Developing such software frameworks is increasingly a major scientific activity in its own right, and comes with specific challenges, from practical software design, development and engineering challenges to statistical and conceptual modelling challenges. BEAST 2 is one such computational software platform, and was first announced over 4 years ago. Here we describe a series of major new developments in the BEAST 2 core platform and model hierarchy that have occurred since the first release of the software, culminating in the recent 2.5 release.

Embracing heterogeneity: coalescing the Tree of Life and the future of phylogenomics

Building the Tree of Life (ToL) is a major challenge of modern biology, requiring advances in cyberinfrastructure, data collection, theory, and more. Here, we argue that phylogenomics stands to benefit by embracing the many heterogeneous genomic signals emerging from the first decade of large-scale phylogenetic analysis spawned by high-throughput sequencing (HTS). Such signals include those most commonly encountered in phylogenomic datasets, such as incomplete lineage sorting, but also those reticulate processes emerging with greater frequency, such as recombination and introgression. Here we focus specifically on how phylogenetic methods can accommodate the heterogeneity incurred by such population genetic processes; we do not discuss phylogenetic methods that ignore such processes, such as concatenation or supermatrix approaches or supertrees. We suggest that methods of data acquisition and the types of markers used in phylogenomics will remain restricted until a posteriori methods of marker choice are made possible with routine whole-genome sequencing of taxa of interest. We discuss limitations and potential extensions of a model supporting innovation in phylogenomics today, the multispecies coalescent model (MSC). Macroevolutionary models that use phylogenies, such as character mapping, often ignore the heterogeneity on which building phylogenies increasingly rely and suggest that assimilating such heterogeneity is an important goal moving forward. Finally, we argue that an integrative cyberinfrastructure linking all steps of the process of building the ToL, from specimen acquisition in the field to publication and tracking of phylogenomic data, as well as a culture that values contributors at each step, are essential for progress.

Identifying Species Network Features from Gene Tree Quartets Under the Coalescent Model

We show that many topological features of level-1 species networks are identifiable from the distribution of the gene tree quartets under the network multi-species coalescent model. In particular, every cycle of size at least 4 and every hybrid node in a cycle of size at least 5 are identifiable. This is a step toward justifying the inference of such networks which was recently implemented by Solís-Lemus and Ané. We show additionally how to compute quartet concordance factors for a network in terms of simpler networks, and explore some circumstances in which cycles of size 3 and hybrid nodes in 4-cycles can be detected.

The Timing and Direction of Introgression Under the Multispecies Network Coalescent

Introgression is a pervasive biological process, and many statistical methods have been developed to infer its presence from genomic data. However, many of the consequences and genomic signatures of introgression remain unexplored from a methodological standpoint. Here, we develop a model for the timing and direction of introgression based on the multispecies network coalescent, and from it suggest new approaches for testing introgression hypotheses. We suggest two new statistics, D ₁ and D ₂, which can be used in conjunction with other information to test hypotheses relating to the timing and direction of introgression, respectively. D ₁ may find use in evaluating cases of homoploid hybrid speciation (HHS), while D ₂ provides a four-taxon test for polarizing introgression. Although analytical expectations for our statistics require a number of assumptions to be met, we show how simulations can be used to test hypotheses about introgression when these assumptions are violated. We apply the D ₁ statistic to genomic data from the wild yeast Saccharomyces paradoxus-a proposed example of HHS-demonstrating its use as a test of this model. These methods provide new and powerful ways to address questions relating to the timing and direction of introgression.

Divergence Estimation in the Presence of Incomplete Lineage Sorting and Migration

This article focuses on the problem of estimating a species tree from multilocus data in the presence of incomplete lineage sorting and migration. I develop a mathematical model similar to IMa2 (Hey 2010) for the relevant evolutionary processes which allows both the population size parameters and the migration rates between pairs of species tree branches to be integrated out. I then describe a BEAST2 package DENIM (Divergence estimation notwithstanding ILS and migration) which is based on this model and which uses an approximation to sample from the posterior. The approximation is based on the assumption that migrations are rare, and it only samples from certain regions of the posterior which seem likely given this assumption. The method breaks down if there is a lot of migration. Using simulations, Leaché et al. (2014) showed that using the standard multispecies coalescent model to infer a species tree can result in poor accuracy if migration is present. I reanalyze this simulated data to explore DENIM's performance and demonstrate substantial improvements in accuracy over *BEAST. I also reanalyze an empirical data set.

Phylogeny Estimation by Integration over Isolation with Migration Models

Phylogeny estimation is difficult for closely related populations and species, especially if they have been exchanging genes. We present a hierarchical Bayesian, Markov-chain Monte Carlo method with a state space that includes all possible phylogenies in a full Isolation-with-Migration model framework. The method is based on a new type of genealogy augmentation called a "hidden genealogy" that enables efficient updating of the phylogeny. This is the first likelihood-based method to fully incorporate directional gene flow and genetic drift for estimation of a species or population phylogeny. Application to human hunter-gatherer populations from Africa revealed a clear phylogenetic history, with strong support for gene exchange with an unsampled ghost population, and relatively ancient divergence between a ghost population and modern human populations, consistent with human/archaic divergence. In contrast, a study of five chimpanzee populations reveals a clear phylogeny with several pairs of populations having exchanged DNA, but does not support a history with an unsampled ghost population.

Inferring Phylogenetic Networks Using PhyloNet

PhyloNet was released in 2008 as a software package for representing and analyzing phylogenetic networks. At the time of its release, the main functionalities in PhyloNet consisted of measures for comparing network topologies and a single heuristic for reconciling gene trees with a species tree. Since then, PhyloNet has grown significantly. The software package now includes a wide array of methods for inferring phylogenetic networks from data sets of unlinked loci while accounting for both reticulation (e.g., hybridization) and incomplete lineage sorting. In particular, PhyloNet now allows for maximum parsimony, maximum likelihood, and Bayesian inference of phylogenetic networks from gene tree estimates. Furthermore, Bayesian inference directly from sequence data (sequence alignments or biallelic markers) is implemented. Maximum parsimony is based on an extension of the "minimizing deep coalescences" criterion to phylogenetic networks, whereas maximum likelihood and Bayesian inference are based on the multispecies network coalescent. All methods allow for multiple individuals per species. As computing the likelihood of a phylogenetic network is computationally hard, PhyloNet allows for evaluation and inference of networks using a pseudolikelihood measure. PhyloNet summarizes the results of the various analyzes and generates phylogenetic networks in the extended Newick format that is readily viewable by existing visualization software.

Modeling Hybridization Under the Network Multispecies Coalescent

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

Finding a most parsimonious or likely tree in a network with respect to an alignment

Phylogenetic networks are often constructed by merging multiple conflicting phylogenetic signals into a directed acyclic graph. It is interesting to explore whether a network constructed in this way induces biologically-relevant phylogenetic signals that were not present in the input. Here we show that, given a multiple alignment A for a set of taxa X and a rooted phylogenetic network N whose leaves are labelled by X, it is NP-hard to locate a most parsimonious phylogenetic tree displayed by N (with respect to A) even when the level of N—the maximum number of reticulation nodes within a biconnected component—is 1 and A contains only 2 distinct states. (If, additionally, gaps are allowed the problem becomes APX-hard.) We also show that under the same conditions, and assuming a simple binary symmetric model of character evolution, finding a most likely tree displayed by the network is NP-hard. These negative results contrast with earlier work on parsimony in which it is shown that if A consists of a single column the problem is fixed parameter tractable in the level. We conclude with a discussion of why, despite the NP-hardness, both the parsimony and likelihood problem can likely be well-solved in practice.

Exploring the Tiers of Rooted Phylogenetic Network Space Using Tail Moves

Popular methods for exploring the space of rooted phylogenetic trees use rearrangement moves such as rooted Nearest Neighbour Interchange (rNNI) and rooted Subtree Prune and Regraft (rSPR). Recently, these moves were generalized to rooted phylogenetic networks, which are a more suitable representation of reticulate evolutionary histories, and it was shown that any two rooted phylogenetic networks of the same complexity are connected by a sequence of either rSPR or rNNI moves. Here, we show that this is possible using only tail moves, which are a restricted version of rSPR moves on networks that are more closely related to rSPR moves on trees. The connectedness still holds even when we restrict to distance-1 tail moves (a localized version of tail moves). Moreover, we give bounds on the number of (distance-1) tail moves necessary to turn one network into another, which in turn yield new bounds for rSPR, rNNI and SPR (i.e. the equivalent of rSPR on unrooted networks). The upper bounds are constructive, meaning that we can actually find a sequence with at most this length for any pair of networks. Finally, we show that finding a shortest sequence of tail or rSPR moves is NP-hard.