Coalescent Units Research Articles

PhyloCoalSimulations: A Simulator for Network Multispecies Coalescent Models, Including a New Extension for the Inheritance of Gene Flow.

We consider the evolution of phylogenetic gene trees along phylogenetic species networks, according to the network multispecies coalescent process, and introduce a new network coalescent model with correlated inheritance of gene flow. This model generalizes two traditional versions of the network coalescent: with independent or common inheritance. At each reticulation, multiple lineages of a given locus are inherited from parental populations chosen at random, either independently across lineages or with positive correlation according to a Dirichlet process. This process may account for locus-specific probabilities of inheritance, for example. We implemented the simulation of gene trees under these network coalescent models in the Julia package PhyloCoalSimulations, which depends on PhyloNetworks and its powerful network manipulation tools. Input species phylogenies can be read in extended Newick format, either in numbers of generations or in coalescent units. Simulated gene trees can be written in Newick format, and in a way that preserves information about their embedding within the species network. This embedding can be used for downstream purposes, such as to simulate species-specific processes like rate variation across species, or for other scenarios as illustrated in this note. This package should be useful for simulation studies and simulation-based inference methods. The software is available open source with documentation and a tutorial at https://github.com/cecileane/PhyloCoalSimulations.jl.

Phylogenomic Coalescent Analyses of Avian Retroelements Infer Zero-Length Branches at the Base of Neoaves, Emergent Support for Controversial Clades, and Ancient Introgressive Hybridization in Afroaves.

Retroelement insertions (RIs) are low-homoplasy characters that are ideal data for addressing deep evolutionary radiations, where gene tree reconstruction errors can severely hinder phylogenetic inference with DNA and protein sequence data. Phylogenomic studies of Neoaves, a large clade of birds (>9000 species) that first diversified near the Cretaceous–Paleogene boundary, have yielded an array of robustly supported, contradictory relationships among deep lineages. Here, we reanalyzed a large RI matrix for birds using recently proposed quartet-based coalescent methods that enable inference of large species trees including branch lengths in coalescent units, clade-support, statistical tests for gene flow, and combined analysis with DNA-sequence-based gene trees. Genome-scale coalescent analyses revealed extremely short branches at the base of Neoaves, meager branch support, and limited congruence with previous work at the most challenging nodes. Despite widespread topological conflicts with DNA-sequence-based trees, combined analyses of RIs with thousands of gene trees show emergent support for multiple higher-level clades (Columbea, Passerea, Columbimorphae, Otidimorphae, Phaethoquornithes). RIs express asymmetrical support for deep relationships within the subclade Afroaves that hints at ancient gene flow involving the owl lineage (Strigiformes). Because DNA-sequence data are challenged by gene tree-reconstruction error, analysis of RIs represents one approach for improving gene tree-based methods when divergences are deep, internodes are short, terminal branches are long, and introgressive hybridization further confounds species–tree inference.

Theoretical and Practical Considerations when using Retroelement Insertions to Estimate Species Trees in the Anomaly Zone.

A potential shortcoming of concatenation methods for species tree estimation is their failure to account for incomplete lineage sorting. Coalescent methods address this problem but make various assumptions that, if violated, can result in worse performance than concatenation. Given the challenges of analyzing DNA sequences with both concatenation and coalescent methods, retroelement insertions (RIs) have emerged as powerful phylogenomic markers for species tree estimation. Here, we show that two recently proposed quartet-based methods, SDPquartets and ASTRAL_BP, are statistically consistent estimators of the unrooted species tree topology under the coalescent when RIs follow a neutral infinite-sites model of mutation and the expected number of new RIs per generation is constant across the species tree. The accuracy of these (and other) methods for inferring species trees from RIs has yet to be assessed on simulated data sets, where the true species tree topology is known. Therefore, we evaluated eight methods given RIs simulated from four model species trees, all of which have short branches and at least three of which are in the anomaly zone. In our simulation study, ASTRAL_BP and SDPquartets always recovered the correct species tree topology when given a sufficiently large number of RIs, as predicted. A distance-based method (ASTRID_BP) and Dollo parsimony also performed well in recovering the species tree topology. In contrast, unordered, polymorphism, and Camin-Sokal parsimony (as well as an approach based on MDC) typically fail to recover the correct species tree topology in anomaly zone situations with more than four ingroup taxa. Of the methods studied, only ASTRAL_BP automatically estimates internal branch lengths (in coalescent units) and support values (i.e., local posterior probabilities). We examined the accuracy of branch length estimation, finding that estimated lengths were accurate for short branches but upwardly biased otherwise. This led us to derive the maximum likelihood (branch length) estimate for when RIs are given as input instead of binary gene trees; this corrected formula produced accurate estimates of branch lengths in our simulation study provided that a sufficiently large number of RIs were given as input. Lastly, we evaluated the impact of data quantity on species tree estimation by repeating the above experiments with input sizes varying from 100 to 100,000 parsimony-informative RIs. We found that, when given just 1000 parsimony-informative RIs as input, ASTRAL_BP successfully reconstructed major clades (i.e., clades separated by branches $>0.3$ coalescent units) with high support and identified rapid radiations (i.e., shorter connected branches), although not their precise branching order. The local posterior probability was effective for controlling false positive branches in these scenarios. [Coalescence; incomplete lineage sorting; Laurasiatheria; Palaeognathae; parsimony; polymorphism parsimony; retroelement insertions; species trees; transposon.].

PRANC: ML species tree estimation from the ranked gene trees under coalescence.

PRANC computes the Probabilities of RANked gene tree topologies under the multispecies coalescent. A ranked gene tree is a gene tree accounting for the temporal ordering of internal nodes. PRANC can also estimate the maximum likelihood (ML) species tree from a sample of ranked or unranked gene tree topologies. It estimates the ML tree with estimated branch lengths in coalescent units. PRANC is written in C++ and freely available at github.com/anastasiiakim/PRANC. Supplementary data are available at Bioinformatics online.

Probabilistic Species Tree Distances: Implementing the Multispecies Coalescent to Compare Species Trees Within the Same Model-Based Framework Used to Estimate Them.

Despite the ubiquitous use of statistical models for phylogenomic and population genomic inferences, this model-based rigor is rarely applied to post hoc comparison of trees. In a recent study, Garba et al. derived new methods for measuring the distance between two gene trees computed as the difference in their site pattern probability distributions. Unlike traditional metrics that compare trees solely in terms of geometry, these measures consider gene trees and associated parameters as probabilistic models that can be compared using standard information theoretic approaches. Consequently, probabilistic measures of phylogenetic tree distance can be far more informative than simply comparisons of topology and/or branch lengths alone. However, in their current form, these distance measures are not suitable for the comparison of species tree models in the presence of gene tree heterogeneity. Here, we demonstrate an approach for how the theory of Garba et al. (2018), which is based on gene tree distances, can be extended naturally to the comparison of species tree models. Multispecies coalescent (MSC) models parameterize the discrete probability distribution of gene trees conditioned upon a species tree with a particular topology and set of divergence times (in coalescent units), and thus provide a framework for measuring distances between species tree models in terms of their corresponding gene tree topology probabilities. We describe the computation of probabilistic species tree distances in the context of standard MSC models, which assume complete genetic isolation postspeciation, as well as recent theoretical extensions to the MSC in the form of network-based MSC models that relax this assumption and permit hybridization among taxa. We demonstrate these metrics using simulations and empirical species tree estimates and discuss both the benefits and limitations of these approaches. We make our species tree distance approach available as an R package called pSTDistanceR, for open use by the community.

Fast Coalescent-Based Computation of Local Branch Support from Quartet Frequencies.

Species tree reconstruction is complicated by effects of incomplete lineage sorting, commonly modeled by the multi-species coalescent model (MSC). While there has been substantial progress in developing methods that estimate a species tree given a collection of gene trees, less attention has been paid to fast and accurate methods of quantifying support. In this article, we propose a fast algorithm to compute quartet-based support for each branch of a given species tree with regard to a given set of gene trees. We then show how the quartet support can be used in the context of the MSC to compute (1) the local posterior probability (PP) that the branch is in the species tree and (2) the length of the branch in coalescent units. We evaluate the precision and recall of the local PP on a wide set of simulated and biological datasets, and show that it has very high precision and improved recall compared with multi-locus bootstrapping. The estimated branch lengths are highly accurate when gene tree estimation error is low, but are underestimated when gene tree estimation error increases. Computation of both the branch length and local PP is implemented as new features in ASTRAL.

Hybrid-Lambda: simulation of multiple merger and Kingman gene genealogies in species networks and species trees

BackgroundThere has been increasing interest in coalescent models which admit multiple mergers of ancestral lineages; and to model hybridization and coalescence simultaneously.Results Hybrid-Lambda is a software package that simulates gene genealogies under multiple merger and Kingman’s coalescent processes within species networks or species trees. Hybrid-Lambda allows different coalescent processes to be specified for different populations, and allows for time to be converted between generations and coalescent units, by specifying a population size for each population. In addition, Hybrid-Lambda can generate simulated datasets, assuming the infinitely many sites mutation model, and compute the F ST statistic. As an illustration, we apply Hybrid-Lambda to infer the time of subdivision of certain marine invertebrates under different coalescent processes.Conclusions Hybrid-Lambda makes it possible to investigate biogeographic concordance among high fecundity species exhibiting skewed offspring distribution.

Land plant origins and coalescence confusion

Coalescence methods have emerged as an alternative toconcatenation methods for reconstructing species trees[1,2]. Zhong et al. [3] advocated the coalescence approachfor resolving early branching events in plant phylogeny.We show that different coalescence methods yield discor-dant results and call attention to fundamental problemswith the application of coalescence to deep phylogeneticquestions such as the origin of land plants.Streptophyte algae (Figure 1) are the closest livingrelatives of land plants, but elucidation of the lineage thatrepresents the sister group to land plants remains contro-versial [3]. Zhong et al. [3] argued that concatenationanalyses bearing on land plant origins are fundamentallyflawed owing to conflicts among gene trees and suggestedthat coalescence methods that accommodate gene treeheterogeneity can overcome these problems. Zhong et al.[3] applied one of these methods, MP-EST [2], to sixphylogenomic data sets (42 to 289 genes) and uniformlyrecovered Zygnematalesasthesistergrouptolandplants(Figure 1A), albeit with low bootstrap support (28–65%).The authors concluded that Zygnematales is the sistergroup of land plants based on consistent MP-EST sup-port. However, uniform results should not be equatedwith accuracy and instead may reflect methodologicalbiases [4].A conspicuous feature of Zhong et al.’s [3] data set ismissing sequences; for example, 119 genes in the preferred184 gene data set were unsampled for the same 24 taxaincluding all three outgroups. This potentially debilitatingcircumstance required rooting >100 gene trees within theingroup for these trees (Figure 1). Liu et al. (pp. 4–5 in [2])cautioned that,forMP-EST,missinglineages‘insomegenetrees areallowediflineagesaremissingrandomly,butalotof missing lineages may dramatically reduce the perfor-mance of the pseudo-likelihood approach.’ Zhong et al. [3]ignored this advice and their data sets are plagued withmassive blocks of nonrandomly distributed, missingsequences (Figure 1).We performed coalescence analyses on the six phyloge-nomic data sets from Zhong et al. [3] with another method,STAR [1], andrecoveredZygnematales +Coleochaetales asthe sistergrouptolandplantsinfiveofsixcases(Figure1B).Given the manifest disagreement between MP-EST andSTAR, these results undermine Zhong et al.’s [3] majorconclusions regarding land plant origins and the utility ofcoalescence methods for deep phylogenetic problems.MP-EST and STAR are both statistically consistentmethods when their underlying assumptions are upheldand in these instances may yield more accurate speciestreesthanconcatenation[1,2].However,theoreticalguar-antees are empty when assumptions are violated andshould be trumped by empirical performance. Zhonget al.[3]extolledthevirtuesofcoalescencemethodsbasedonsimulations,buttoourknowledgetheonlysimulationswhere MP-EST or STAR outperformed concatenation in-volveasingletreethatissmall(5taxa),asymmetrical,andshallow (3.1 coalescent units fromroot to tip) [1,2]. Simu-lations that have modeled ancient diversifications andlarger sets of taxa have uniformly favored concatenationto‘shortcut’coalescencemethods(STAR,MP-EST,STEM,STEAC, MDC) [5–8] even when data were simulated viacoalescencemodels[6–8]. Pateletal.[7]foundthatSTEMoutperformedconcatenationwithtruegenetrees,buttruegene trees are unknown outside simulationsand insteadgene trees must be inferred from sequences. The poorperformance of coalescence methods [5–8] presumablyreflects theirincorrectassumptionthat allconflictamonggene trees is attributable to deep coalescence, whereas amultitude of other problems (long branches, mutationalsaturation,weakphylogeneticsignal, modelmisspecifica-tion, poor taxon sampling) negatively impact reconstruc-tion of accurate gene trees and provide more cogentexplanations for incongruence [6,7].Zhongetal.’s[3]genetreesimplyunrealisticretentionsof ancestral polymorphism that in one case exceed 500million years [9] (Figure 1C). A consequence of highlyinaccurategenetreesforcoalescenceanalysesisa speciestrees with branch lengths (in coalescent units) that areimpossibly short (Figure 1D). The interval that extendsfrom the common ancestor of green plants to the commonancestor of land plants encompasses >500 million years(MY)(Figure1).Yet,inZhongetal.’s[3]MP-ESTtree,thislineage spans only 3.9 coalescent units, which is equiva-lent to 0.4–19.2 MY for an annual plant with N

The Accuracy of Species Tree Estimation under Simulation: A Comparison of Methods

Numerous simulation studies have investigated the accuracy of phylogenetic inference of gene trees under maximum parsimony, maximum likelihood, and Bayesian techniques. The relative accuracy of species tree inference methods under simulation has received less study. The number of analytical techniques available for inferring species trees is increasing rapidly, and in this paper, we compare the performance of several species tree inference techniques at estimating recent species divergences using computer simulation. Simulating gene trees within species trees of different shapes and with varying tree lengths (T) and population sizes (), and evolving sequences on those gene trees, allows us to determine how phylogenetic accuracy changes in relation to different levels of deep coalescence and phylogenetic signal. When the probability of discordance between the gene trees and the species tree is high (i.e., T is small and/or is large), Bayesian species tree inference using the multispecies coalescent (BEST) outperforms other methods. The performance of all methods improves as the total length of the species tree is increased, which reflects the combined benefits of decreasing the probability of discordance between species trees and gene trees and gaining more accurate estimates for gene trees. Decreasing the probability of deep coalescences by reducing also leads to accuracy gains for most methods. Increasing the number of loci from 10 to 100 improves accuracy under difficult demographic scenarios (i.e., coalescent units ≤ 4N(e)), but 10 loci are adequate for estimating the correct species tree in cases where deep coalescence is limited or absent. In general, the correlation between the phylogenetic accuracy and the posterior probability values obtained from BEST is high, although posterior probabilities are overestimated when the prior distribution for is misspecified.

BUCKy: Gene tree/species tree reconciliation with Bayesian concordance analysis

BUCKy is a C++ program that implements Bayesian concordance analysis. The method uses a non-parametric clustering of genes with compatible trees, and reconstructs the primary concordance tree from clades supported by the largest proportions of genes. A population tree with branch lengths in coalescent units is estimated from quartet concordance factors. BUCKy is open source and distributed under the GNU general public license at www.stat.wisc.edu/∼ane/bucky/.

Gene tree reconciliation: new developments in Bayesian concordance analysis with BUCKy

AbstractWhen phylogenetic trees inferred from different genes are incongruent, several methods are available to reconcile gene trees and extract the shared phylogenetic information from the sequence data. Bayesian Concordance Analysis, implemented in BUCKy, aims to extract the vertical signal and to infer clusters of genes that share the same tree topology. The new version of BUCKy includes a quartet-based estimate of the species tree with branch lengths in coalescent units.

A maximum pseudo-likelihood approach for estimating species trees under the coalescent model

BackgroundSeveral phylogenetic approaches have been developed to estimate species trees from collections of gene trees. However, maximum likelihood approaches for estimating species trees under the coalescent model are limited. Although the likelihood of a species tree under the multispecies coalescent model has already been derived by Rannala and Yang, it can be shown that the maximum likelihood estimate (MLE) of the species tree (topology, branch lengths, and population sizes) from gene trees under this formula does not exist. In this paper, we develop a pseudo-likelihood function of the species tree to obtain maximum pseudo-likelihood estimates (MPE) of species trees, with branch lengths of the species tree in coalescent units.ResultsWe show that the MPE of the species tree is statistically consistent as the number M of genes goes to infinity. In addition, the probability that the MPE of the species tree matches the true species tree converges to 1 at rate O(M -1). The simulation results confirm that the maximum pseudo-likelihood approach is statistically consistent even when the species tree is in the anomaly zone. We applied our method, Maximum Pseudo-likelihood for Estimating Species Trees (MP-EST) to a mammal dataset. The four major clades found in the MP-EST tree are consistent with those in the Bayesian concatenation tree. The bootstrap supports for the species tree estimated by the MP-EST method are more reasonable than the posterior probability supports given by the Bayesian concatenation method in reflecting the level of uncertainty in gene trees and controversies over the relationship of four major groups of placental mammals.ConclusionsMP-EST can consistently estimate the topology and branch lengths (in coalescent units) of the species tree. Although the pseudo-likelihood is derived from coalescent theory, and assumes no gene flow or horizontal gene transfer (HGT), the MP-EST method is robust to a small amount of HGT in the dataset. In addition, increasing the number of genes does not increase the computational time substantially. The MP-EST method is fast for analyzing datasets that involve a large number of genes but a moderate number of species.

Discordance of Species Trees with Their Most Likely Gene Trees: The Case of Five Taxa

Under a coalescent model for within-species evolution, gene trees may differ from species trees to such an extent that the gene tree topology most likely to evolve along the branches of a species tree can disagree with the species tree topology. Gene tree topologies that are more likely to be produced than the topology that matches that of the species tree are termed anomalous, and the region of branch-length space that gives rise to anomalous gene trees (AGTs) is the anomaly zone. We examine the occurrence of anomalous gene trees for the case of five taxa, the smallest number of taxa for which every species tree topology has a nonempty anomaly zone. Considering all sets of branch lengths that give rise to anomalous gene trees, the largest value possible for the smallest branch length in the species tree is greater in the five-taxon case (0.1934 coalescent time units) than in the previously studied case of four taxa (0.1568). The five-taxon case demonstrates the existence of three phenomena that do not occur in the four-taxon case. First, anomalous gene trees can have the same unlabeled topology as the species tree. Second, the anomaly zone does not necessarily enclose a ball centered at the origin in branch-length space, in which all branches are short. Third, as a branch length increases, it is possible for the number of AGTs to increase rather than decrease or remain constant. These results, which help to describe how the properties of anomalous gene trees increase in complexity as the number of taxa increases, will be useful in formulating strategies for evading the problem of anomalous gene trees during species tree inference from multilocus data.

The packaging unit: a basic structural feature for the condensation of late cricket spermatid nuclei.

The alignment, folding and packaging of cricket chromatin was examined during late spermiogenesis by an electron-microscope study of nuclei dispersed by air--liquid surface tension forces after detergent treatment. Late developing spermatid genomes arrange themselves in multiple packaging units in a stepwise process which includes: (1) a loss of the beaded repeating structure of chromatin as nucleoprotein fibres become smooth and gradually assume a uniform diameter; (2) a side-by--side alignment of structurally modified chromatin fibres; and (3) a regular folding into packaging units. Alignment and folding of chromatin fibres are presumably mediated by intermolecular bonds easily disrupted by spreading forces. In very late spermatids, interfibre binding forces are difficult to overrride by spreading alone, indicating a stronger cross-linking of increasingly coalescent packaging units. 'Unit to unit' coalescence stabilizes the nuclear structure, first limiting and afterwards denying penetration of phosphotungstic acid, as displayed in thin sections of extremely cricket spermatid nuclei. Binding of phosphotungstate by nuclear basic proteins can be facilitated by limited protein solubilization after disulphide reduction of unfixed cricket tests with sodium dodecyl sulphate and dithiothreitol. Results of this study permit the proposal of model experiments useful for clarifying the organization of highly condensed spermatid genomes and for evaluating the structure of genome segments in systems wherein changes of chromatin-associated protein occur.