Maximum Parsimony for Tree Mixtures

BackgroundBranching events in phylogenetic trees reflect bifurcating and/or multifurcating speciation and splitting events. In the presence of gene flow, a phylogeny cannot be described by a tree but is instead a directed acyclic graph known as a phylogenetic network. Both phylogenetic trees and networks are typically reconstructed using computational analysis of multi-locus sequence data. The advent of high-throughput sequencing technologies has brought about two main scalability challenges: (1) dataset size in terms of the number of taxa and (2) the evolutionary divergence of the taxa in a study. The impact of both dimensions of scale on phylogenetic tree inference has been well characterized by recent studies; in contrast, the scalability limits of phylogenetic network inference methods are largely unknown.ResultsIn this study, we quantify the performance of state-of-the-art phylogenetic network inference methods on large-scale datasets using empirical data sampled from natural mouse populations and a range of simulations using model phylogenies with a single reticulation. We find that, as in the case of phylogenetic tree inference, the performance of leading network inference methods is negatively impacted by both dimensions of dataset scale. In general, we found that topological accuracy degrades as the number of taxa increases; a similar effect was observed with increased sequence mutation rate. The most accurate methods were probabilistic inference methods which maximize either likelihood under coalescent-based models or pseudo-likelihood approximations to the model likelihood. The improved accuracy obtained with probabilistic inference methods comes at a computational cost in terms of runtime and main memory usage, which become prohibitive as dataset size grows past twenty-five taxa. None of the probabilistic methods completed analyses of datasets with 30 taxa or more after many weeks of CPU runtime.ConclusionsWe conclude that the state of the art of phylogenetic network inference lags well behind the scope of current phylogenomic studies. New algorithmic development is critically needed to address this methodological gap.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-016-1277-1) contains supplementary material, which is available to authorized users.

We present a fast and flexible software package—SimPhy—for the simulation of multiple gene families evolving under incomplete lineage sorting, gene duplication and loss, horizontal gene transfer—all three potentially leading to species tree/gene tree discordance—and gene conversion. SimPhy implements a hierarchical phylogenetic model in which the evolution of species, locus, and gene trees is governed by global and local parameters (e.g., genome-wide, species-specific, locus-specific), that can be fixed or be sampled from a priori statistical distributions. SimPhy also incorporates comprehensive models of substitution rate variation among lineages (uncorrelated relaxed clocks) and the capability of simulating partitioned nucleotide, codon, and protein multilocus sequence alignments under a plethora of substitution models using the program INDELible. We validate SimPhy's output using theoretical expectations and other programs, and show that it scales extremely well with complex models and/or large trees, being an order of magnitude faster than the most similar program (DLCoal-Sim). In addition, we demonstrate how SimPhy can be useful to understand interactions among different evolutionary processes, conducting a simulation study to characterize the systematic overestimation of the duplication time when using standard reconciliation methods. SimPhy is available at https://github.com/adamallo/SimPhy, where users can find the source code, precompiled executables, a detailed manual and example cases.

Until recently, rigorously reconstructing the many hybrid speciation events in plants has not been practical because of the limited number of molecular markers available for plant phylogenetic reconstruction and the lack of good, biologically based methods for inferring reticulation (network) events. This situation should change rapidly with the development of multiple nuclear markers for phylogenetic reconstruction and new methods for reconstructing reticulate evolution. These developments will necessitate a much greater incorporation of population genetics into phylogenetic reconstruction than has been common. Population genetic events such as gene duplication coupled with lineage sorting and meiotic and sexual recombination have always had the potential to affect phylogenetic inference. For tree reconstruction, these problems are usually minimized by using uniparental markers and nuclear markers that undergo rapid concerted evolution. Because reconstruction of reticulate speciation events will require nuclear markers that lack these characteristics, effects of population genetics on phylogenetic inference will need to be addressed directly. Current models and methods that allow hybrid speciation to be detected and reconstructed are discussed, with a focus on how lineage sorting and meiotic and sexual recombination affect network reconstruction. Approaches that would allow inference of phylogenetic networks in their presence are suggested.

Adaptive evolutionary processes in plants may be accompanied by episodes of introgression, parallel evolution and incomplete lineage sorting that pose challenges in untangling species evolutionary history. Genus Pinus (pines) is one of the most abundant and most studied groups among gymnosperms, and a good example of a lineage where these phenomena have been observed. Pines are among the most ecologically and economically important plant species. Some, such as the pines of the southeastern USA (southern pines in subsection Australes), are subjects of intensive breeding programmes. Despite numerous published studies, the evolutionary history of Australes remains ambiguous and often controversial. We studied the phylogeny of four major southern pine species: shortleaf (Pinus echinata), slash (P. elliottii), longleaf (P. palustris) and loblolly (P. taeda), using sequences from 11 nuclear loci and maximum likelihood and Bayesian methods. Our analysis encountered resolution difficulties similar to earlier published studies. Although incomplete lineage sorting and introgression are two phenomena presumptively underlying our results, the phylogenetic inferences seem to be also influenced by the genes examined, with certain topologies supported by sets of genes sharing common putative functionalities. For example, genes involved in wood formation supported the clade echinata-taeda, genes linked to plant defence supported the clade echinata-elliottii and genes linked to water management properties supported the clade echinata-palustris The support for these clades was very high and consistent across methods. We discuss the potential factors that could underlie these observations, including incomplete lineage sorting, hybridization and parallel or adaptive evolution. Our results likely reflect the relatively short evolutionary history of the subsection that is thought to have begun during the middle Miocene and has been influenced by climate fluctuations.

BackgroundPhylogenetic reconstruction is one of the paramount challenges of contemporary bioinformatics. A subtask of existing tree reconstruction algorithms is modeled by the Small Parsimony problem: given a tree T and an assignment of character-states to its leaves, assign states to the internal nodes of T such as to minimize the parsimony score, that is, the number of edges of T connecting nodes with different states. While this problem is polynomial-time solvable on trees, the matter is more complicated if T contains reticulate events such as hybridizations or recombinations, i.e. when T is a network. Indeed, three different versions of the parsimony score on networks have been proposed and each of them is NP-hard to decide. Existing parameterized algorithms focus on combining the number c of possible character-states with the number of reticulate events (per biconnected component).ResultsWe consider the parameter treewidth t of the underlying undirected graph of the input network, presenting dynamic programming algorithms for (slight generalizations of) all three versions of the parsimony problem on size-n networks running in times c^t {n^{O(1)}}, (3c)^t {n^{O(1)}}, and 6^{tc}n^{O(1)}, respectively. Our algorithms use a formulation of the treewidth that may facilitate formalizing treewidth-based dynamic programming algorithms on phylogenetic networks for other problems.ConclusionsOur algorithms allow the computation of the three popular parsimony scores, modeling the evolutionary development of a (multistate) character on a given phylogenetic network of low treewidth. Our results subsume and improve previously known algorithm for all three variants. While our results rely on being given a “good” tree-decomposition of the input, encouraging theoretical results as well as practical implementations producing them are publicly available. We present a reformulation of tree decompositions in terms of “agreeing trees” on the same set of nodes. As this formulation may come more natural to researchers and engineers developing algorithms for phylogenetic networks, we hope to render exploiting the input network’s treewidth as parameter more accessible to this audience.

Phylogenetic analyses of gene expression have great potential for addressing a wide range of questions. These analyses will, for example, identify genes that have evolutionary shifts in expression that are correlated with evolutionary changes in morphological, physiological, and developmental characters of interest. This will provide entirely new opportunities to identify genes related to particular phenotypes. There are, however, 3 key challenges that must be addressed for such studies to realize their potential. First, data on gene expression must be measured from multiple species, some of which may be field-collected, and parameterized in such a way that they can be compared across species. Second, it will be necessary to develop comparative phylogenetic methods suitable for large multidimensional datasets. In most phylogenetic comparative studies to date, the number n of independent observations (independent contrasts) has been greater than the number p of variables (characters). The behavior of comparative methods for these classic problems is now well understood under a wide variety of conditions. In studies of gene expression, and in studies based on other high-throughput tools, the number n of samples is dwarfed by the number p of variables. The estimated covariance matrices will be singular, complicating their analysis and interpretation, and prone to spurious results. Third, new approaches are needed to investigate the expression of the many genes whose phylogenies are not congruent with species phylogenies due to gene loss, gene duplication, and incomplete lineage sorting. Here we outline general considerations of project design for phylogenetic analyses of gene expression and suggest solutions to these three categories of challenges. These topics are relevant to high-throughput phenotypic data well beyond gene expression.

Impact of gene family evolutionary histories on phylogenetic species tree inference by gene tree parsimony

Detecting hybrid speciation in the presence of incomplete lineage sorting using gene tree incongruence: A model

BackgroundSpecies phylogenies are not estimated directly, but rather through phylogenetic analyses of different gene datasets. However, true gene trees can differ from the true species tree (and hence from one another) due to biological processes such as horizontal gene transfer, incomplete lineage sorting, and gene duplication and loss, so that no single gene tree is a reliable estimate of the species tree. Several methods have been developed to estimate species trees from estimated gene trees, differing according to the specific algorithmic technique used and the biological model used to explain differences between species and gene trees. Relatively little is known about the relative performance of these methods.ResultsWe report on a study evaluating several different methods for estimating species trees from sequence datasets, simulating sequence evolution under a complex model including indels (insertions and deletions), substitutions, and incomplete lineage sorting. The most important finding of our study is that some fast and simple methods are nearly as accurate as the most accurate methods, which employ sophisticated statistical methods and are computationally quite intensive. We also observe that methods that explicitly consider errors in the estimated gene trees produce more accurate trees than methods that assume the estimated gene trees are correct.ConclusionsOur study shows that highly accurate estimations of species trees are achievable, even when gene trees differ from each other and from the species tree, and that these estimations can be obtained using fairly simple and computationally tractable methods.

Phylogenetic inference and reconstruction methods generate hypotheses on evolutionary history. Competing inference methods are frequently used, and the evaluation of the generated hypotheses is achieved using tree comparison costs. The Robinson–Foulds (RF) distance is a widely used cost to compare the topology of two trees, but this cost is sensitive to tree error and can overestimate tree differences. To overcome this limitation, a refined version of the RF distance called the Cluster Affinity (CA) distance was introduced. However, CA distances are symmetric and cannot compare different types of trees. These asymmetric comparisons occur when gene trees are compared with species trees, when disparate datasets are integrated into a supertree, or when tree comparison measures are used to infer a phylogenetic network. In this study, we introduce a relaxation of the original Affinity distance to compare heterogeneous trees called the asymmetric CA cost. We also develop a biologically interpretable cost, the Cluster Support cost that normalizes by cluster size across gene trees. The characteristics of these costs are similar to the symmetric CA cost. We describe efficient algorithms, derive the exact diameters, and use these to standardize the cost to be applicable in practice. These costs provide objective, fine-scale, and biologically interpretable values that can assess differences and similarities between phylogenetic trees.

Incomplete lineage sorting and phenotypic evolution in marsupials

Accurate gene tree-species tree reconciliation is fundamental to inferring the evolutionary history of a gene family. However, although it has long been appreciated that population-related effects such as incomplete lineage sorting (ILS) can dramatically affect the gene tree, many of the most popular reconciliation methods consider discordance only due to gene duplication and loss (and sometimes horizontal gene transfer). Methods that do model ILS are either highly parameterized or consider a restricted set of histories, thus limiting their applicability and accuracy. To address these challenges, we present a novel algorithm DLCpar for inferring a most parsimonious (MP) history of a gene family in the presence of duplications, losses, and ILS. Our algorithm relies on a new reconciliation structure, the labeled coalescent tree (LCT), that simultaneously describes coalescent and duplication-loss history. We show that the LCT representation enables an exhaustive and efficient search over the space of reconciliations, and, for most gene families, the least common ancestor (LCA) mapping is an optimal solution for the species mapping between the gene tree and species tree in an MP LCT. Applying our algorithm to a variety of clades, including flies, fungi, and primates, as well as to simulated phylogenies, we achieve high accuracy, comparable to sophisticated probabilistic reconciliation methods, at reduced run time and with far fewer parameters. These properties enable inferences of the complex evolution of gene families across a broad range of species and large data sets.

The amount of completely sequenced chloroplast genomes increases rapidly every day, leading to the possibility to build large-scale phylogenetic trees of plant species. Considering a subset of close plant species defined according to their chloroplasts, the phylogenetic tree that can be inferred by their core genes is not necessarily well supported, due to the possible occurrence of “problematic” genes (i.e., homoplasy, incomplete lineage sorting, horizontal gene transfers, etc.) which may blur the phylogenetic signal. However, a trustworthy phylogenetic tree can still be obtained provided such a number of blurring genes is reduced. The problem is thus to determine the largest subset of core genes that produces the best-supported tree. To discard problematic genes and due to the overwhelming number of possible combinations, this article focuses on how to extract the largest subset of sequences in order to obtain the most supported species tree. Due to computational complexity, a distributed Binary Particle Swarm Optimization (BPSO) is proposed in sequential and distributed fashions. Obtained results from both versions of the BPSO are compared with those computed using an hybrid approach embedding both genetic algorithms and statistical tests. The proposal has been applied to different cases of plant families, leading to encouraging results for these families.

An evolutionary algorithm based on parsimony for the multiobjective phylogenetic network inference problem

The plant-specific expansin proteins constitute an ancient and major gene family known to have roles in regulating diverse biological processes in plants. Although the functions of many expansin genes have been identified in wheat and other species, little is known about the evolution and genomic locations of the expansin genes in wheat (Triticum aestivum). In this study, a total of 87 expansin genes were identified in the wheat genome, including 52 EXPAs, 42 EXPBs and 4 EXLAs. The EXLB gene was not found in the wheat genome. Phylogenetic tree and comparative analysis revealed amplification of the EXPBs in rice, maize and wheat. The predicted wheat expansins were distributed across 14 of 21 chromosomes with different densities, 3 tightly co-located clusters and 15 paralogous pairs, indicating that tandem duplication and segmental duplication events also played roles in the evolution of expansins in wheat. In addition, the gene structures and conserved protein domains of wheat expansins suggest high levels of conservation within the phylogenetic subgroups. Analysis of a published microarray database showed that most wheat expansin genes exhibit different expression levels in different tissues and developmental stages. To our knowledge, this is the first report of a genome-wide analysis of the wheat expansin gene family, which should provide valuable information for further elucidating the classification and putative functions of the entire gene family.