Presence Of Incomplete Lineage Sorting Research Articles

DISCO+QR: rooting species trees in the presence of GDL and ILS.

Genes evolve under processes such as gene duplication and loss (GDL), so that gene family trees are multi-copy, as well as incomplete lineage sorting (ILS); both processes produce gene trees that differ from the species tree. The estimation of species trees from sets of gene family trees is challenging, and the estimation of rooted species trees presents additional analytical challenges. Two of the methods developed for this problem are STRIDE, which roots species trees by considering GDL events, and Quintet Rooting (QR), which roots species trees by considering ILS. We present DISCO+QR, a new approach to rooting species trees that first uses DISCO to address GDL and then uses QR to perform rooting in the presence of ILS. DISCO+QR operates by taking the input gene family trees and decomposing them into single-copy trees using DISCO and then roots the given species tree using the information in the single-copy gene trees using QR. We show that the relative accuracy of STRIDE and DISCO+QR depend on the properties of the dataset (number of species, genes, rate of gene duplication, degree of ILS and gene tree estimation error), and that each provides advantages over the other under some conditions. DISCO and QR are available in github. Supplementary data are available at Bioinformatics Advances online.

Bayesian-Weighted Triplet and Quartet Methods for Species Tree Inference

Inference of the evolutionary histories of species, commonly represented by a species tree, is complicated by the divergent evolutionary history of different parts of the genome. Different loci on the genome can have different histories from the underlying species tree (and each other) due to processes such as incomplete lineage sorting (ILS), gene duplication and loss, and horizontal gene transfer. The multispecies coalescent is a commonly used model for performing inference on species and gene trees in the presence of ILS. This paper introduces Lily-T and Lily-Q, two new methods for species tree inference under the multispecies coalescent. We then compare them to two frequently used methods, SVDQuartets and ASTRAL, using simulated and empirical data. Both methods generally showed improvement over SVDQuartets, and Lily-Q was superior to Lily-T for most simulation settings. The comparison to ASTRAL was more mixed-Lily-Q tended to be better than ASTRAL when the length of recombination-free loci was short, when the coalescent population parameter [Formula: see text] was small, or when the internal branch lengths were longer.

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.

Diversification of HawaiianCyrtandra(Gesneriaceae) under the influence of incomplete lineage sorting and hybridization

AbstractCyrtandra(Gesneriaceae) is a genus of flowering plants with over 800 species distributed throughout Southeast Asia and the Pacific Islands. On the Hawaiian Islands, 60 named species and over 89 putative hybrids exist, most of which are identified on the basis of morphology. Despite many previous studies on the HawaiianCyrtandralineage, questions regarding the reconciliation of morphology and genetics remain, many of which can be attributed to the relatively young age and evidence of hybridization between species. We utilized targeted enrichment, high‐throughput sequencing, and modern phylogenomics tools to test 31 HawaiianCyrtandrasamples (22 species, two putative hybrids, four species with two samples each, one species with four samples) and two outgroups for species relationships and hybridization in the presence of incomplete lineage sorting (ILS). Both concatenated and species‐tree methods were used to reconstruct species relationships, and network analyses were conducted to test for hybridization. We expected to see high levels of ILS and putative hybrids intermediate to their parent species. Phylogenies reconstructed from the concatenated and species‐tree methods were highly incongruent, most likely due to high levels of incomplete lineage sorting. Network analyses inferred gene flow within this lineage, but not always between taxa that we expected. Multiple hybridizations were inferred, but many were on deeper branches of the island lineages suggesting a long history of hybridization. We demonstrated the utility of high‐throughput sequencing and a phylogenomic approach using 569 loci to understanding species relationships and gene flow in the presence of ILS.

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.

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.

To Include or Not to Include: The Impact of Gene Filtering on Species Tree Estimation Methods.

With the increasing availability of whole genome data, many species trees are being constructed from hundreds to thousands of loci. Although concatenation analysis using maximum likelihood is a standard approach for estimating species trees, it does not account for gene tree heterogeneity, which can occur due to many biological processes, such as incomplete lineage sorting. Coalescent species tree estimation methods, many of which are statistically consistent in the presence of incomplete lineage sorting, include Bayesian methods that coestimate the gene trees and the species tree, summary methods that compute the species tree by combining estimated gene trees, and site-based methods that infer the species tree from site patterns in the alignments of different loci. Due to concerns that poor quality loci will reduce the accuracy of estimated species trees, many recent phylogenomic studies have removed or filtered genes on the basis of phylogenetic signal and/or missing data prior to inferring species trees; little is known about the performance of species tree estimation methods when gene filtering is performed. We examine how incomplete lineage sorting, phylogenetic signal of individual loci, and missing data affect the absolute and the relative accuracy of species tree estimation methods and show how these properties affect methods' responses to gene filtering strategies. In particular, summary methods (ASTRAL-II, ASTRID, and MP-EST), a site-based coalescent method (SVDquartets within PAUP*), and an unpartitioned concatenation analysis using maximum likelihood (RAxML) were evaluated on a heterogeneous collection of simulated multilocus data sets, and the following trends were observed. Filtering genes based on gene tree estimation error improved the accuracy of the summary methods when levels of incomplete lineage sorting were low to moderate but did not benefit the summary methods under higher levels of incomplete lineage sorting, unless gene tree estimation error was also extremely high (a model condition with few replicates). Neither SVDquartets nor concatenation analysis using RAxML benefited from filtering genes on the basis of gene tree estimation error. Finally, filtering genes based on missing data was either neutral (i.e., did not impact accuracy) or else reduced the accuracy of all five methods. By providing insight into the consequences of gene filtering, we offer recommendations for estimating species tree in the presence of incomplete lineage sorting and reconcile seemingly conflicting observations made in prior studies regarding the impact of gene filtering.

Simulation-Based Evaluation of Hybridization Network Reconstruction Methods in the Presence of Incomplete Lineage Sorting.

Hybridization events generate reticulate species relationships, giving rise to species networks rather than species trees. We report a comparative study of consensus, maximum parsimony, and maximum likelihood methods of species network reconstruction using gene trees simulated assuming a known species history. We evaluate the role of the divergence time between species involved in a hybridization event, the relative contributions of the hybridizing species, and the error in gene tree estimation. When gene tree discordance is mostly due to hybridization and not due to incomplete lineage sorting (ILS), most of the methods can detect even highly skewed hybridization events between highly divergent species. For recent divergences between hybridizing species, when the influence of ILS is sufficiently high, likelihood methods outperform parsimony and consensus methods, which erroneously identify extra hybridizations. The more sophisticated likelihood methods, however, are affected by gene tree errors to a greater extent than are consensus and parsimony.

A maximum pseudo-likelihood approach for phylogenetic networks.

BackgroundSeveral phylogenomic analyses have recently demonstrated the need to account simultaneously for incomplete lineage sorting (ILS) and hybridization when inferring a species phylogeny. A maximum likelihood approach was introduced recently for inferring species phylogenies in the presence of both processes, and showed very good results. However, computing the likelihood of a model in this case is computationally infeasible except for very small data sets.ResultsInspired by recent work on the pseudo-likelihood of species trees based on rooted triples, we introduce the pseudo-likelihood of a phylogenetic network, which, when combined with a search heuristic, provides a statistical method for phylogenetic network inference in the presence of ILS. Unlike trees, networks are not always uniquely encoded by a set of rooted triples. Therefore, even when given sufficient data, the method might converge to a network that is equivalent under rooted triples to the true one, but not the true one itself. The method is computationally efficient and has produced very good results on the data sets we analyzed. The method is implemented in PhyloNet, which is publicly available in open source.ConclusionsMaximum pseudo-likelihood allows for inferring species phylogenies in the presence of hybridization and ILS, while scaling to much larger data sets than is currently feasible under full maximum likelihood. The nonuniqueness of phylogenetic networks encoded by a system of rooted triples notwithstanding, the proposed method infers the correct network under certain scenarios, and provides candidates for further exploration under other criteria and/or data in other scenarios.

Phylogenomic species tree estimation in the presence of incomplete lineage sorting and horizontal gene transfer.

BackgroundSpecies tree estimation is challenged by gene tree heterogeneity resulting from biological processes such as duplication and loss, hybridization, incomplete lineage sorting (ILS), and horizontal gene transfer (HGT). Mathematical theory about reconstructing species trees in the presence of HGT alone or ILS alone suggests that quartet-based species tree methods (known to be statistically consistent under ILS, or under bounded amounts of HGT) might be effective techniques for estimating species trees when both HGT and ILS are present.ResultsWe evaluated several publicly available coalescent-based methods and concatenation under maximum likelihood on simulated datasets with moderate ILS and varying levels of HGT. Our study shows that two quartet-based species tree estimation methods (ASTRAL-2 and weighted Quartets MaxCut) are both highly accurate, even on datasets with high rates of HGT. In contrast, although NJst and concatenation using maximum likelihood are highly accurate under low HGT, they are less robust to high HGT rates.ConclusionOur study shows that quartet-based species-tree estimation methods can be highly accurate under the presence of both HGT and ILS. The study suggests the possibility that some quartet-based methods might be statistically consistent under phylogenomic models of gene tree heterogeneity with both HGT and ILS.

A comparative study of SVDquartets and other coalescent-based species tree estimation methods.

BackgroundSpecies tree estimation is challenging in the presence of incomplete lineage sorting (ILS), which can make gene trees different from the species tree. Because ILS is expected to occur and the standard concatenation approach can return incorrect trees with high support in the presence of ILS, "coalescent-based" summary methods (which first estimate gene trees and then combine gene trees into a species tree) have been developed that have theoretical guarantees of robustness to arbitrarily high amounts of ILS. Some studies have suggested that summary methods should only be used on "c-genes" (i.e., recombination-free loci) that can be extremely short (sometimes fewer than 100 sites). However, gene trees estimated on short alignments can have high estimation error, and summary methods tend to have high error on short c-genes. To address this problem, Chifman and Kubatko introduced SVDquartets, a new coalescent-based method. SVDquartets takes multi-locus unlinked single-site data, infers the quartet trees for all subsets of four species, and then combines the set of quartet trees into a species tree using a quartet amalgamation heuristic. Yet, the relative accuracy of SVDquartets to leading coalescent-based methods has not been assessed.ResultsWe compared SVDquartets to two leading coalescent-based methods (ASTRAL-2 and NJst), and to concatenation using maximum likelihood. We used a collection of simulated datasets, varying ILS levels, numbers of taxa, and number of sites per locus. Although SVDquartets was sometimes more accurate than ASTRAL-2 and NJst, most often the best results were obtained using ASTRAL-2, even on the shortest gene sequence alignments we explored (with only 10 sites per locus). Finally, concatenation was the most accurate of all methods under low ILS conditions.ConclusionsASTRAL-2 generally had the best accuracy under higher ILS conditions, and concatenation had the best accuracy under the lowest ILS conditions. However, SVDquartets was competitive with the best methods under conditions with low ILS and small numbers of sites per locus. The good performance under many conditions of ASTRAL-2 in comparison to SVDquartets is surprising given the known vulnerability of ASTRAL-2 and similar methods to short gene sequences.

ASTRID: Accurate Species TRees from Internode Distances.

BackgroundIncomplete lineage sorting (ILS), modelled by the multi-species coalescent (MSC), is known to create discordance between gene trees and species trees, and lead to inaccurate species tree estimations unless appropriate methods are used to estimate the species tree. While many statistically consistent methods have been developed to estimate the species tree in the presence of ILS, only ASTRAL-2 and NJst have been shown to have good accuracy on large datasets. Yet, NJst is generally slower and less accurate than ASTRAL-2, and cannot run on some datasets.ResultsWe have redesigned NJst to enable it to run on all datasets, and we have expanded its design space so that it can be used with different distance-based tree estimation methods. The resultant method, ASTRID, is statistically consistent under the MSC model, and has accuracy that is competitive with ASTRAL-2. Furthermore, ASTRID is much faster than ASTRAL-2, completing in minutes on some datasets for which ASTRAL-2 used hours.ConclusionsASTRID is a new coalescent-based method for species tree estimation that is competitive with the best current method in terms of accuracy, while being much faster. ASTRID is available in open source form on github.

Species-Level Phylogeny and Polyploid Relationships in Hordeum (Poaceae) Inferred by Next-Generation Sequencing and In Silico Cloning of Multiple Nuclear Loci.

Polyploidization is an important speciation mechanism in the barley genus Hordeum. To analyze evolutionary changes after allopolyploidization, knowledge of parental relationships is essential. One chloroplast and 12 nuclear single-copy loci were amplified by polymerase chain reaction (PCR) in all Hordeum plus six out-group species. Amplicons from each of 96 individuals were pooled, sheared, labeled with individual-specific barcodes and sequenced in a single run on a 454 platform. Reference sequences were obtained by cloning and Sanger sequencing of all loci for nine supplementary individuals. The 454 reads were assembled into contigs representing the 13 loci and, for polyploids, also homoeologues. Phylogenetic analyses were conducted for all loci separately and for a concatenated data matrix of all loci. For diploid taxa, a Bayesian concordance analysis and a coalescent-based dated species tree was inferred from all gene trees. Chloroplast matK was used to determine the maternal parent in allopolyploid taxa. The relative performance of different multilocus analyses in the presence of incomplete lineage sorting and hybridization was also assessed. The resulting multilocus phylogeny reveals for the first time species phylogeny and progenitor-derivative relationships of all di- and polyploid Hordeum taxa within a single analysis. Our study proves that it is possible to obtain a multilocus species-level phylogeny for di- and polyploid taxa by combining PCR with next-generation sequencing, without cloning and without creating a heavy load of sequence data.

On the Robustness to Gene Tree Estimation Error (or lack thereof) of Coalescent-Based Species Tree Methods.

The estimation of species trees using multiple loci has become increasingly common. Because different loci can have different phylogenetic histories (reflected in different gene tree topologies) for multiple biological causes, new approaches to species tree estimation have been developed that take gene tree heterogeneity into account. Among these multiple causes, incomplete lineage sorting (ILS), modeled by the multi-species coalescent, is potentially the most common cause of gene tree heterogeneity, and much of the focus of the recent literature has been on how to estimate species trees in the presence of ILS. Despite progress in developing statistically consistent techniques for estimating species trees when gene trees can differ due to ILS, there is substantial controversy in the systematics community as to whether to use the new coalescent-based methods or the traditional concatenation methods. One of the key issues that has been raised is understanding the impact of gene tree estimation error on coalescent-based methods that operate by combining gene trees. Here we explore the mathematical guarantees of coalescent-based methods when analyzing estimated rather than true gene trees. Our results provide some insight into the differences between promise of coalescent-based methods in theory and their performance in practice.

Assignment of homoeologs to parental genomes in allopolyploids for species tree inference, with an example from Fumaria (papaveraceae).

There is a rising awareness that species trees are best inferred from multiple loci while taking into account processes affecting individual gene trees, such as substitution model error (failure of the model to account for the complexity of the data) and coalescent stochasticity (presence of incomplete lineage sorting [ILS]). Although most studies have been carried out in the context of dichotomous species trees, these processes operate also in more complex evolutionary histories involving multiple hybridizations and polyploidy. Recently, methods have been developed that accurately handle ILS in allopolyploids, but they are thus far restricted to networks of diploids and tetraploids. We propose a procedure that improves on this limitation by designing a workflow that assigns homoeologs to hypothetical diploid ancestral genomes prior to genome tree construction. Conflicting assignment hypotheses are evaluated against substitution model error and coalescent stochasticity. Incongruence that cannot be explained by stochastic mechanisms needs to be explained by other processes (e.g., homoploid hybridization or paralogy). The data can then be filtered to build multilabeled genome phylogenies using inference methods that can recover species trees, either in the face of substitution model error and coalescent stochasticity alone, or while simultaneously accounting for hybridization. Methods are already available for folding the resulting multilabeled genome phylogeny into a network. We apply the workflow to the reconstruction of the reticulate phylogeny of the plant genus Fumaria (Papaveraceae) with ploidal levels ranging from 2[Formula: see text] to 14[Formula: see text]. We describe the challenges in recovering nuclear NRPB2 homoeologs in high ploidy species while combining in vivo cloning and direct sequencing techniques. Using parametric bootstrapping simulations we assign nuclear homoeologs and chloroplast sequences (four concatenated loci) to their common hypothetical diploid ancestral genomes. As these assignments hinge on effective population size assumptions, we investigate how varying these assumptions impacts the recovered multilabeled genome phylogeny.

Concatenation Analyses in the Presence of Incomplete Lineage Sorting.

Incomplete lineage sorting (ILS), modelled by the multi-species coalescent, is a process that results in a gene tree being different from the species tree. Because ILS is expected to occur for at least some loci within genome-scale analyses, the evaluation of species tree estimation methods in the presence of ILS is of great interest. Performance on simulated and biological data have suggested that concatenation analyses can result in the wrong tree with high support under some conditions, and a recent theoretical result by Roch and Steel proved that concatenation using unpartitioned maximum likelihood analysis can be statistically inconsistent in the presence of ILS. In this study, we survey the major species tree estimation methods, including the newly proposed “statistical binning” methods, and discuss their theoretical properties. We also note that there are two interpretations of the term “statistical consistency”, and discuss the theoretical results proven under both interpretations.

Concatenation Analyses in the Presence of Incomplete Lineage Sorting

Concatenation Analyses in the Presence of Incomplete Lineage Sorting

Statistical binning enables an accurate coalescent-based estimation of the avian tree.

Gene tree incongruence arising from incomplete lineage sorting (ILS) can reduce the accuracy of concatenation-based estimations of species trees. Although coalescent-based species tree estimation methods can have good accuracy in the presence of ILS, they are sensitive to gene tree estimation error. We propose a pipeline that uses bootstrapping to evaluate whether two genes are likely to have the same tree, then it groups genes into sets using a graph-theoretic optimization and estimates a tree on each subset using concatenation, and finally produces an estimated species tree from these trees using the preferred coalescent-based method. Statistical binning improves the accuracy of MP-EST, a popular coalescent-based method, and we use it to produce the first genome-scale coalescent-based avian tree of life.

Coalescent methods are robust to the simultaneous effects of long branches and incomplete lineage sorting.

It is well known that species with elevated substitution rates can give rise to disproportionately long branches in the species tree. This combination of long and short branches can contribute to long-branch artifacts (LBA). Despite efforts to remedy LBA via increased taxon sampling and methodological improvements in gene tree estimation, it remains unclear how long and short branches affect species tree estimation in the presence of incomplete lineage sorting (ILS). Here, we examine the combined influence of long external and short internal branches on concatenation and coalescent methods using both simulated and empirical data. Our results demonstrate that the presence of long and short branches alone does not obviously confound the consistency of concatenation and coalescent methods. However, when long external and short internal branches occur simultaneously with high ILS, concatenation methods can be misled, especially when two of these long branches are sister lineages. In contrast, coalescent methods are more robust under these circumstances. This is particularly relevant because this topological pattern also characterizes numerous ancient rapid radiations across the tree of life. Because short internal branches can increase the potential for ILS and gene tree discordance, our results collectively suggest that coalescent methods are more likely to infer the correct species tree in cases of ancient rapid radiations where long external and short internal branches are in close phylogenetic proximity.

BBCA: Improving the scalability of *BEAST using random binning.

BackgroundSpecies tree estimation can be challenging in the presence of gene tree conflict due to incomplete lineage sorting (ILS), which can occur when the time between speciation events is short relative to the population size. Of the many methods that have been developed to estimate species trees in the presence of ILS, *BEAST, a Bayesian method that co-estimates the species tree and gene trees given sequence alignments on multiple loci, has generally been shown to have the best accuracy. However, *BEAST is extremely computationally intensive so that it cannot be used with large numbers of loci; hence, *BEAST is not suitable for genome-scale analyses.ResultsWe present BBCA (boosted binned coalescent-based analysis), a method that can be used with *BEAST (and other such co-estimation methods) to improve scalability. BBCA partitions the loci randomly into subsets, uses *BEAST on each subset to co-estimate the gene trees and species tree for the subset, and then combines the newly estimated gene trees together using MP-EST, a popular coalescent-based summary method. We compare time-restricted versions of BBCA and *BEAST on simulated datasets, and show that BBCA is at least as accurate as *BEAST, and achieves better convergence rates for large numbers of loci.ConclusionsPhylogenomic analysis using *BEAST is currently limited to datasets with a small number of loci, and analyses with even just 100 loci can be computationally challenging. BBCA uses a very simple divide-and-conquer approach that makes it possible to use *BEAST on datasets containing hundreds of loci. This study shows that BBCA provides excellent accuracy and is highly scalable.