Multispecies Coalescent Model Research Articles

Comprehending Cornales: phylogenetic reconstruction of the order using the Angiosperms353 probe set.

PremiseCornales is an order of flowering plants containing ecologically and horticulturally important families, including Cornaceae (dogwoods) and Hydrangeaceae (hydrangeas), among others. While many relationships in Cornales are strongly supported by previous studies, some uncertainty remains with regards to the placement of Hydrostachyaceae and to relationships among families in Cornales and within Cornaceae. Here we analyzed hundreds of nuclear loci to test published phylogenetic hypotheses and estimated a robust species tree for Cornales.MethodsUsing the Angiosperms353 probe set and existing data sets, we generated phylogenomic data for 158 samples, representing all families in the Cornales, with intensive sampling in the Cornaceae.ResultsWe curated an average of 312 genes per sample, constructed maximum likelihood gene trees, and inferred a species tree using the summary approach implemented in ASTRAL‐III, a method statistically consistent with the multispecies coalescent model.ConclusionsThe species tree we constructed generally shows high support values and a high degree of concordance among individual nuclear gene trees. Relationships among families are largely congruent with previous molecular studies, except for the placement of the nyssoids and the Grubbiaceae‐Curtisiaceae clades. Furthermore, we were able to place Hydrostachyaceae within Cornales, and within Cornaceae, the monophyly of known morphogroups was well supported. However, patterns of gene tree discordance suggest potential ancient reticulation, gene flow, and/or ILS in the Hydrostachyaceae lineage and the early diversification of Cornus. Our findings reveal new insights into the diversification process across Cornales and demonstrate the utility of the Angiosperms353 probe set.

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.]

Quartet-based inference is statistically consistent under the unified duplication-loss-coalescence model.

MotivationThe classic multispecies coalescent (MSC) model provides the means for theoretical justification of incomplete lineage sorting-aware species tree inference methods. This has motivated an extensive body of work on phylogenetic methods that are statistically consistent under MSC. One such particularly popular method is ASTRAL, a quartet-based species tree inference method. Novel studies suggest that ASTRAL also performs well when given multi-locus gene trees in simulation studies. Further, Legried et al. recently demonstrated that ASTRAL is statistically consistent under the gene duplication and loss model (GDL). GDL is prevalent in evolutionary histories and is the first core process in the powerful duplication-loss-coalescence evolutionary model (DLCoal) by Rasmussen and Kellis.ResultsIn this work, we prove that ASTRAL is statistically consistent under the general DLCoal model. Therefore, our result supports the empirical evidence from the simulation-based studies. More broadly, we prove that the quartet-based inference approach is statistically consistent under DLCoal.Supplementary information Supplementary data are available at Bioinformatics online.

Statistical inconsistency of the unrooted minimize deep coalescence criterion.

Species trees, which describe the evolutionary relationships between species, are often inferred from gene trees, which describe the ancestral relationships between sequences sampled at different loci from the species of interest. A common approach to inferring species trees from gene trees is motivated by supposing that gene tree variation is due to incomplete lineage sorting, also known as deep coalescence. One of the earliest methods motivated by deep coalescence is to find the species tree that minimizes the number of deep coalescent events needed to explain discrepancies between the species tree and input gene trees. This minimize deep coalescence (MDC) criterion can be applied in both rooted and unrooted settings. where either rooted or unrooted gene trees can be used to infer a rooted species tree. Previous work has shown that MDC is statistically inconsistent in the rooted setting, meaning that under a probabilistic model for deep coalescence, the multispecies coalescent, for some species trees, increasing the number of input gene trees does not make the method more likely to return a correct species tree. Here, we obtain analogous results in the unrooted setting, showing conditions leading to inconsistency of the MDC criterion using the multispecies coalescent model with unrooted gene trees for four taxa and five taxa.

Species delimitation in Noccaea densiflora species complex (Brassicaceae) based on morphological and molecular data

The accurate identification of an organism is the basis of all biological disciplines. Although there have been many different species concepts and methods proposed, researchers generally choose the most appropriate concept according to their interests. However, each species concept has both advantages and disadvantages. In such cases, an integrated concept based on evidence obtained from different species concepts and methods is suitable for the accurate delimitation of a species. The biggest dilemma of integrated species delimitation methods is the inconsistency between species concepts and methods. Herein, the congruency of the different concepts and methods was tested to reveal the relationship of the Noccaea densiflora species complex. Nuclear ribosomal internal transcribed spacer, chloroplast trnL-F, and trnQ-5′rps16 regions were used for species delimitation using the multispecies coalescent model as implemented in two developed Bayesian methods. Internal transcribed spacer and trnL-F regions were also used for Templeton, Crandall, and Singh haplotype network analyses. In addition to morphological measurements from different populations and vouchers, specific bioclimatic data values were also used for the principal component analysis. Based on the analyses, it was determined that only one population of N. densiflora (Boiss. & Kotschy) F.K. Mey. and one of Noccaea microstyla (Boiss.) F.K. Mey. were clearly distinct, whereas the rest of the specimens remain taxonomically uncertain.

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 are 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. [Gene tree discordance; hypothesis test; multispecies coalescent model; quartet concordance factor; simplex plot; species tree].

Naming and describing the diversity in the Usnea cornuta aggregate (lichenized Ascomycota, Parmeliaceae) focusing on Brazilian specimens

This study is a reassessment of the Usnea cornuta aggregate diversity mainly in Brazil. Based on previous multi-locus species delimitation analyses using the multispecies coalescent model (MSC), we carried out a posteriori morphological and anatomical studies. The following corticolous new species are described: Usnea arianae with norstictic or fatty or lobaric acids, convex and efflorescent soralia and a lax medulla; U. flabelliformis with protocetraric acid, fan-shaped main branches and a high medulla/cortex ratio; U. rubropallens with protocetraric acid and a faint orange cortical/subcortical pigment; U. stipitata with constictic acid, stipitate soralia and a high medulla/cortex ratio; and U. tenuicorticata with protocetraric acid, a thin cortex and a high medulla/cortex ratio. The newly described species were found to occur so far only in the Americas, except U. arianae which shows an amphi-atlantic distribution in Europe and on the American continent. Seven species already described belonging to the U. cornuta aggr. in Brazil are further treated here: Usnea boomiana with caperatic acid and large, concave soralia, new to South America; U. brasiliensis with protocetraric acid, minute and irregular soralia; U. cornuta with mainly salazinic acid and minute soralia fusing into consoralia; U. macaronesica (syn. nov.: U. subglabrata) with barbatic acid, large excavate soralia and a lax medulla; Usnea subpectinata, a so far european species resurrected from the U. cornuta synonymy, with stictic acid and numerous isidiofibrils, new to South America; and U. trachyclada with thamnolic acid and K+ bright yellow stipitate soralia. Full descriptions with morphological, anatomical and chemical features, geographical distributions, and illustrations are provided for each species along with an identification key.

Computing the probability of gene trees concordant with the species tree in the multispecies coalescent

The multispecies coalescent process models the genealogical relationships of genes sampled from several species, enabling useful predictions about phenomena such as the discordance between a gene tree and the species phylogeny due to incomplete lineage sorting. Conversely, knowledge of large collections of gene trees can inform us about several aspects of the species phylogeny, such as its topology and ancestral population sizes. A fundamental open problem in this context is how to efficiently compute the probability of a gene tree topology, given the species phylogeny. Although a number of algorithms for this task have been proposed, they either produce approximate results, or, when they are exact, they do not scale to large data sets. In this paper, we present some progress towards exact and efficient computation of the probability of a gene tree topology. We provide a new algorithm that, given a species tree and the number of genes sampled for each species, calculates the probability that the gene tree topology will be concordant with the species tree. Moreover, we provide an algorithm that computes the probability of any specific gene tree topology concordant with the species tree. Both algorithms run in polynomial time and have been implemented in Python. Experiments show that they are able to analyze data sets where thousands of genes are sampled in a matter of minutes to hours.

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

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

The Multilocus Multispecies Coalescent: A Flexible New Model of Gene Family Evolution.

Incomplete lineage sorting (ILS), the interaction between coalescence and speciation, can generate incongruence between gene trees and species trees, as can gene duplication (D), transfer (T), and loss (L). These processes are usually modeled independently, but in reality, ILS can affect gene copy number polymorphism, that is, interfere with DTL. This has been previously recognized, but not treated in a satisfactory way, mainly because DTL events are naturally modeled forward-in-time, while ILS is naturally modeled backward-in-time with the coalescent. Here, we consider the joint action of ILS and DTL on the gene tree/species tree problem in all its complexity. In particular, we show that the interaction between ILS and duplications/transfers (without losses) can result in patterns usually interpreted as resulting from gene loss, and that the realized rate of D, T, and L becomes nonhomogeneous in time when ILS is taken into account. We introduce algorithmic solutions to these problems. Our new model, the multilocus multispecies coalescent, which also accounts for any level of linkage between loci, generalizes the multispecies coalescent (MSC) model and offers a versatile, powerful framework for proper simulation, and inference of gene family evolution. [Gene duplication; gene loss; horizontal gene transfer; incomplete lineage sorting; multispecies coalescent; hemiplasy; recombination.].

The Perfect Storm: Gene Tree Estimation Error, Incomplete Lineage Sorting, and Ancient Gene Flow Explain the Most Recalcitrant Ancient Angiosperm Clade, Malpighiales.

The genomic revolution offers renewed hope of resolving rapid radiations in the Tree of Life. The development of the multispecies coalescent model and improved gene tree estimation methods can better accommodate gene tree heterogeneity caused by incomplete lineage sorting (ILS) and gene tree estimation error stemming from the short internal branches. However, the relative influence of these factors in species tree inference is not well understood. Using anchored hybrid enrichment, we generated a data set including 423 single-copy loci from 64 taxa representing 39 families to infer the species tree of the flowering plant order Malpighiales. This order includes 9 of the top 10 most unstable nodes in angiosperms, which have been hypothesized to arise from the rapid radiation during the Cretaceous. Here, we show that coalescent-based methods do not resolve the backbone of Malpighiales and concatenation methods yield inconsistent estimations, providing evidence that gene tree heterogeneity is high in this clade. Despite high levels of ILS and gene tree estimation error, our simulations demonstrate that these two factors alone are insufficient to explain the lack of resolution in this order. To explore this further, we examined triplet frequencies among empirical gene trees and discovered some of them deviated significantly from those attributed to ILS and estimation error, suggesting gene flow as an additional and previously unappreciated phenomenon promoting gene tree variation in Malpighiales. Finally, we applied a novel method to quantify the relative contribution of these three primary sources of gene tree heterogeneity and demonstrated that ILS, gene tree estimation error, and gene flow contributed to 10.0$\%$, 34.8$\%$, and 21.4$\%$ of the variation, respectively. Together, our results suggest that a perfect storm of factors likely influence this lack of resolution, and further indicate that recalcitrant phylogenetic relationships like the backbone of Malpighiales may be better represented as phylogenetic networks. Thus, reducing such groups solely to existing models that adhere strictly to bifurcating trees greatly oversimplifies reality, and obscures our ability to more clearly discern the process of evolution. [Coalescent; concatenation; flanking region; hybrid enrichment, introgression; phylogenomics; rapid radiation, triplet frequency.].

Topological Metrizations of Trees, and New Quartet Methods of Tree Inference.

Topological phylogenetic trees can be assigned edge weights in several natural ways, highlighting different aspects of the tree. Here, the rooted triple and quartet metrizations are introduced, and applied to formulate novel methods of inferring large trees from rooted triple and quartet data. These methods lead to new statistically consistent procedures for inference of a species tree from gene trees under the multispecies coalescent model.

Multiple species delimitation approaches applied to the avian lark genus Alaudala

Species delimitation has advanced from a purely phenotypic exercise to a branch of science that integrates multiple sources of data to identify independently evolving lineages that can be treated as species. We here test species limits in the avian Lesser Short-toed Lark Alaudala rufesens–Sand Lark A. raytal complex, which has an intricate taxonomic history, ranging from a single to three recognised species, with different inclusiveness in different treatments. Our integrative taxonomic approach is based on a combination of DNA sequences, plumage, biometrics, songs, song-flights, geographical distributions, habitat, and bioclimatic data, and using various methods including a species delimitation program (STACEY) based on the multispecies coalescent model. We propose that four species should be recognised: Lesser Short-toed Lark A. rufescens (sensu stricto), Heine’s Short-toed Lark A. heinei, Asian Short-toed Lark A. cheleensis and Sand Lark A. raytal. There is also some evidence suggesting lineage separation within A. cheleensis and A. raytal, but additional data are required to evaluate this. The species delimitation based on STACEY agrees well with the non-genetic data. Although computer-based species delimitation programs can be useful in identifying independently evolving lineages, we stress that whenever possible, species hypotheses proposed by these programs should be tested by independent, non-genetic data. Our results highlight the difficulty and subjectivity of delimiting lineages and species, especially at early stages in the speciation process.

MSCquartets 1.0: quartet methods for species trees and networks under the multispecies coalescent model in R.

MSCquartets is an R package for species tree hypothesis testing, inference of species trees and inference of species networks under the Multispecies Coalescent model of incomplete lineage sorting and its network analog. Input for these analyses are collections of metric or topological locus trees which are then summarized by the quartets displayed on them. Results of hypothesis tests at user-supplied levels are displayed in a simplex plot by color-coded points. The package implements the QDC and WQDC algorithms for topological and metric species tree inference, and the NANUQ algorithm for level-1 topological species network inference, all of which give statistically consistent estimators under the model. MSCquartets is available through the Comprehensive R Archive Network: https://CRAN.R-project.org/package=MSCquartets.

The genomic view of diversification.

The process of species diversification is traditionally summarized by a single tree, the species tree, whose reconstruction from molecular data is hindered by frequent conflicts between gene genealogies. Here, we argue that instead of seeing these conflicts as nuisances, we can exploit them to inform the diversification process itself. We adopt a gene-based view of diversification to model the ubiquitous presence of gene flow between diverging lineages, one of the most important processes explaining disagreements among gene trees. We propose a new framework for modelling the joint evolution of gene and species lineages relaxing the hierarchy between the species tree and gene trees inherent to the standard view, as embodied in a popular model known as the multispecies coalescent (MSC). We implement this framework in two alternative models called the gene-based diversification models (GBD): (a) GBD-forward following all evolving genomes through time and (b) GBD-backward based on coalescent theory. They feature four parameters tuning colonization, gene flow, genetic drift and genetic differentiation. We propose an inference method based on differences between gene trees. Applied to two empirical data sets prone to gene flow, we find better support for the GBD-backward model than for the MSC model. Along with the increasing awareness of the extent of gene flow, this work shows the importance of considering the richer signal contained in genomic histories, rather than in the mere species tree, to better apprehend the complex evolutionary history of species.

UglyTrees: a browser-based multispecies coalescent tree visualizer.

SummaryVisualization is a vital task in phylogenetics and yet there is a deficit in programs which visualize the multispecies coalescent (MSC) model. UglyTrees (UT) is an easy-to-use program for visualizing multiple gene trees embedded within a single species trees. The mapping between gene and species nodes is automatically detected allowing for ready access to the program. UT can scrape the contents of a website for MSC analyses, enabling the sharing of interactive MSC figures through optional parameters in the URL. If a posterior distribution is uploaded, the transitions between MSC states are animated allowing the visual tracking of trees throughout the sequence.Availability and implementationUT runs in all major web browsers including mobile devices, and is hosted at www.uglytrees.nz. The MIT-licensed code is available at https://github.com/UglyTrees/uglytrees.github.io.

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.].

Inference of population admixture network from local gene genealogies: a coalescent-based maximum likelihood approach.

MotivationPopulation admixture is an important subject in population genetics. Inferring population demographic history with admixture under the so-called admixture network model from population genetic data is an established problem in genetics. Existing admixture network inference approaches work with single genetic polymorphisms. While these methods are usually very fast, they do not fully utilize the information [e.g. linkage disequilibrium (LD)] contained in population genetic data.ResultsIn this article, we develop a new admixture network inference method called GTmix. Different from existing methods, GTmix works with local gene genealogies that can be inferred from population haplotypes. Local gene genealogies represent the evolutionary history of sampled haplotypes and contain the LD information. GTmix performs coalescent-based maximum likelihood inference of admixture networks with inferred local genealogies based on the well-known multispecies coalescent (MSC) model. GTmix utilizes various techniques to speed up the likelihood computation on the MSC model and the optimal network search. Our simulations show that GTmix can infer more accurate admixture networks with much smaller data than existing methods, even when these existing methods are given much larger data. GTmix is reasonably efficient and can analyze population genetic datasets of current interests.Availability and implementationThe program GTmix is available for download at: https://github.com/yufengwudcs/GTmix.Supplementary information Supplementary data are available at Bioinformatics online.

Inferring Metric Trees from Weighted Quartets via an Intertaxon Distance.

A metric phylogenetic tree relating a collection of taxa induces weighted rooted triples and weighted quartets for all subsets of three and four taxa, respectively. New intertaxon distances are defined that can be calculated from these weights, and shown to exactly fit the same tree topology, but with edge weights rescaled by certain factors dependent on the associated split size. These distances are analogs for metric trees of similar ones recently introduced for topological trees that are based on induced unweighted rooted triples and quartets. The distances introduced here lead to new statistically consistent methods of inferring a metric species tree from a collection of topological gene trees generated under the multispecies coalescent model of incomplete lineage sorting. Simulations provide insight into their potential.

Consistency of SVDQuartets and Maximum Likelihood for Coalescent-Based Species Tree Estimation.

Numerous methods for inferring species-level phylogenies under the coalescent model have been proposed within the last 20 years, and debates continue about the relative strengths and weaknesses of these methods. One desirable property of a phylogenetic estimator is that of statistical consistency, which means intuitively that as more data are collected, the probability that the estimated tree has the same topology as the true tree goes to 1. To date, consistency results for species tree inference under the multispecies coalescent (MSC) have been derived only for summary statistics methods, such as ASTRAL and MP-EST. These methods have been found to be consistent given true gene trees but may be inconsistent when gene trees are estimated from data for loci of finite length. Here, we consider the question of statistical consistency for four taxa for SVDQuartets for general data types, as well as for the maximum likelihood (ML) method in the case in which the data are a collection of sites generated under the MSC model such that the sites are conditionally independent given the species tree (we call these data coalescent independent sites [CIS] data). We show that SVDQuartets is statistically consistent for all data types (i.e., for both CIS data and for multilocus data), and we derive its rate of convergence. We additionally show that ML is consistent for CIS data under the JC69 model and discuss why a proof for the more general multilocus case is difficult. Finally, we compare the performance of ML and SDVQuartets using simulation for both data types. [Consistency; gene tree; maximum likelihood; multilocus data; hylogenetic inference; species tree; SVDQuartets.].