The identifiability of tree topology for phylogenetic models, including covarion and mixture models.

For a model of molecular evolution to be useful for phylogenetic inference, the topology of evolutionary trees must be identifiable. That is, from a joint distribution the model predicts, it must be possible to recover the tree parameter. We establish tree identifiability for a number of phylogenetic models, including a covarion model and a variety of mixture models with a limited number of classes. The proof is based on the introduction of a more general model, allowing more states at internal nodes of the tree than at leaves, and the study of the algebraic variety formed by the joint distributions to which it gives rise. Tree identifiability is first established for this general model through the use of certain phylogenetic invariants.     

A penalty of using anonymous dominant markers (AFLPs, ISSRs, and RAPDs) for phylogenetic inference

AFLPs (and to a lesser extent ISSRs and RAPDs) are increasingly being used for phylogenetic inference among closely related species. Presence/absence characters for each AFLP allele treat all absences as homologous to one another. With three or more alleles, terminals are grouped by their shared absence of alleles in character-based phylogenetic-inference methods in a manner that is not redundant with their shared presence of an alternative allele. We conducted simulations to quantify how severe the negative effect of using presence/absence characters of individual bands is for phylogenetic inference relative to standard multistate characters. We examined alternative tree topologies, relative branch lengths, numbers of characters, rates of evolution, and numbers of alternative alleles, using both parsimony and Nei-and-Li distance analyses. Multistate parsimony generally outperformed presence/absence parsimony, which in turn outperformed Nei-and-Li distance. Increasing the character-state space (i.e., the number of alternative character states available) was found to be advantageous for all three methods of analysis examined, but was most advantageous for multistate parsimony. However, the advantage of multistate parsimony relative to Nei-and-Li distance decreased when applied to more divergent characters. More parsimony-informative variation generally alleviated the problem associated with scoring multistate characters as presence/absence characters. The ensemble consistency index was lower for presence/absence characters relative to multistate characters.     

The Identifiability of Covarion Models in Phylogenetics

Covarion models of character evolution describe inhomogeneities in substitution processes through time. In phylogenetics, such models are used to describe changing functional constraints or selection regimes during the evolution of biological sequences. In this work the identifiability of such models for generic parameters on a known phylogenetic tree is established, provided the number of covarion classes does not exceed the size of the observable state space. `Generic parameters' as used here means all parameters except possibly those in a set of measure zero within the parameter space. Combined with earlier results, this implies both the tree and generic numerical parameters are identifiable if the number of classes is strictly smaller than the number of observable states.     

Sequencing of whole plastid genomes and nuclear ribosomal DNA of Diospyros species (Ebenaceae) endemic to New Caledonia: many species,little divergence

Background and Aims Some plant groups, especially on islands, have been shaped by strong ancestral bottlenecks and rapid, recent radiation of phenotypic characters. Single molecular markers are often not informative enough for phylogenetic reconstruction in such plant groups. Whole plastid genomes and nuclear ribosomal DNA (nrDNA) are viewed by many researchers as sources of information for phylogenetic reconstruction of groups in which expected levels of divergence in standard markers are low. Here we evaluate the usefulness of these data types to resolve phylogenetic relationships among closely related Diospyros species.Methods Twenty-two closely related Diospyros species from New Caledonia were investigated using whole plastid genomes and nrDNA data from low-coverage next-generation sequencing (NGS). Phylogenetic trees were inferred using maximum parsimony, maximum likelihood and Bayesian inference on separate plastid and nrDNA and combined matrices.Key Results The plastid and nrDNA sequences were, singly and together, unable to provide well supported phylogenetic relationships among the closely related New Caledonian Diospyros species. In the nrDNA, a 6-fold greater percentage of parsimony-informative characters compared with plastid DNA was found, but the total number of informative sites was greater for the much larger plastid DNA genomes. Combining the plastid and nuclear data improved resolution. Plastid results showed a trend towards geographical clustering of accessions rather than following taxonomic species.Conclusions In plant groups in which multiple plastid markers are not sufficiently informative, an investigation at the level of the entire plastid genome may also not be sufficient for detailed phylogenetic reconstruction. Sequencing of complete plastid genomes and nrDNA repeats seems to clarify some relationships among the New Caledonian Diospyros species, but the higher percentage of parsimony-informative characters in nrDNA compared with plastid DNA did not help to resolve the phylogenetic tree because the total number of variable sites was much lower than in the entire plastid genome. The geographical clustering of the individuals against a background of overall low sequence divergence could indicate transfer of plastid genomes due to hybridization and introgression following secondary contact.     

Identifying evolutionary trees and substitution parameters for the general Markov model with invariable sites

The general Markov plus invariable sites (GM+I) model of biological sequence evolution is a two-class model in which an unknown proportion of sites are not allowed to change, while the remainder undergo substitutions according to a Markov process on a tree. For statistical use it is important to know if the model is identifiable; can both the tree topology and the numerical parameters be determined from a joint distribution describing sequences only at the leaves of the tree? We establish that for generic parameters both the tree and all numerical parameter values can be recovered, up to clearly understood issues of 'label swapping'. The method of analysis is algebraic, using phylogenetic invariants to study the variety defined by the model. Simple rational formulas, expressed in terms of determinantal ratios, are found for recovering numerical parameters describing the invariable sites.     

Radical instability and spurious branch support by likelihood when applied to matrices with non-random distributions of missing data

Non-random distributions of missing data are a general problem for likelihood-based statistical analyses, including those in a phylogenetic context. Extensive non-randomly distributed missing data are particularly problematic in supermatrix analyses that include many terminals and/or loci. It has been widely reported that missing data can lead to loss of resolution, but only very rarely create misleading or otherwise unsupported results in a parsimony context. Yet this does not hold for all parametric-based analyses because of their assumption of homogeneity across characters and lineages, which can lead to both long-branch attraction and long-branch repulsion. Contrived examples were used to demonstrate that non-random distributions of missing data, even without rate heterogeneity among characters and a well fitting model, can provide misleading likelihood-based topologies and branch-support values that are radically unstable based on slight modifications to character sampling. The same can occur despite complete absence of parsimony-informative characters. Otherwise unsupported resolution and high branch support for these clades were found to occur frequently in 22 empirical examples derived from a published supermatrix. Partitioning characters based on the distribution of missing data helped to decrease, but did not eliminate, these artifacts. These artifacts were exacerbated by low quality tree searches, particularly when holding only a single optimal tree that must be fully resolved.     

Mitochondrial DNA as effective molecular markers for the genetic variation and phylogeny of the family Osteoglossidae

The present study examined the genetic variation of the family Osteoglossidae from different geographical locations based on the mitochondrial NADH dehydrogenase subunit 2 (ND2) and ATPase subunit 6 (ATPase6) genes; we then re-constructed the phylogenetic relationships using the two sequences in combination. The results showed that the partial sequences of mitochondrial ND2 and ATPase6 of the family Osteoglossidae were 813 bp and 669 bp, respectively. A total of 42 species-specific nucleotide positions of the family Osteoglossidae were found to be useful for molecular identification. The sequence variation showed greater differences (8.3% ~ 28.1% for the combined sequences, 8.3% ~ 26.7% for the ND2 gene, and 9.3% ~ 28.7% for the ATPase6 gene) among the different species of Osteoglossidae, and there was a significant association between the genetic difference and geographical location. Phylogenetic analyses using neighbor-joining, Bayesian inference, and maximum parsimony (MP) methods based on the combined sequences of the two genes were able to distinguish the different species and were in agreement with the existing taxonomy based on morphological characters and in association with the geographical distribution among seven species of the family Osteoglossidae.     

The enigmatic monotypic crab plover Dromas ardeola is closely related to pratincoles and coursers (Aves, Charadriiformes, Glareolidae)

The phylogenetic placement of the monotypic crab plover Dromasardeola (Aves, Charadriiformes) remains controversial. Phylogenetic analysis of anatomical and behavioral traits using phenetic and cladistic methods of tree inference have resulted in conflicting tree topologies, suggesting a close association of Dromas to members of different suborders and lineages within Charadriiformes. Here, we revisited the issue by applying Bayesian and parsimony methods of tree inference to 2,012 anatomical and 5,183 molecular characters to a set of 22 shorebird genera (including Turnix). Our results suggest that Bayesian analysis of anatomical characters does not resolve the phylogenetic relationship of shorebirds with strong statistical support. In contrast, Bayesian and parsimony tree inference from molecular data provided much stronger support for the phylogenetic relationships within shorebirds, and support a sister relationship of Dromas to Glareolidae (pratincoles and coursers), in agreement with previously published DNA-DNA hybridization studies.     

The probability of a gene tree topology within a phylogenetic network with applications to hybridization detection

Gene tree topologies have proven a powerful data source for various tasks, including species tree inference and species delimitation. Consequently, methods for computing probabilities of gene trees within species trees have been developed and widely used in probabilistic inference frameworks. All these methods assume an underlying multispecies coalescent model. However, when reticulate evolutionary events such as hybridization occur, these methods are inadequate, as they do not account for such events. Methods that account for both hybridization and deep coalescence in computing the probability of a gene tree topology currently exist for very limited cases. However, no such methods exist for general cases, owing primarily to the fact that it is currently unknown how to compute the probability of a gene tree topology within the branches of a phylogenetic network. Here we present a novel method for computing the probability of gene tree topologies on phylogenetic networks and demonstrate its application to the inference of hybridization in the presence of incomplete lineage sorting. We reanalyze a Saccharomyces species data set for which multiple analyses had converged on a species tree candidate. Using our method, though, we show that an evolutionary hypothesis involving hybridization in this group has better support than one of strict divergence. A similar reanalysis on a group of three Drosophila species shows that the data is consistent with hybridization. Further, using extensive simulation studies, we demonstrate the power of gene tree topologies at obtaining accurate estimates of branch lengths and hybridization probabilities of a given phylogenetic network. Finally, we discuss identifiability issues with detecting hybridization, particularly in cases that involve extinction or incomplete sampling of taxa.     

Pitfalls of heterogeneous processes for phylogenetic reconstruction

Different genes often have different phylogenetic histories. Even within regions having the same phylogenetic history, the mutation rates often vary. We investigate the prospects of phylogenetic reconstruction when all the characters are generated from the same tree topology, but the branch lengths vary (with possibly different tree shapes). Furthering work of Kolaczkowski and Thornton (2004, Nature 431: 980-984) and Chang (1996, Math. Biosci. 134: 189-216), we show examples where maximum likelihood (under a homogeneous model) is an inconsistent estimator of the tree. We then explore the prospects of phylogenetic inference under a heterogeneous model. In some models, there are examples where phylogenetic inference under any method is impossible - despite the fact that there is a common tree topology. In particular, there are nonidentifiable mixture distributions, i.e., multiple topologies generate identical mixture distributions. We address which evolutionary models have nonidentifiable mixture distributions and prove that the following duality theorem holds for most DNA substitution models. The model has either: (i) nonidentifiability - two different tree topologies can produce identical mixture distributions, and hence distinguishing between the two topologies is impossible; or (ii) linear tests - there exist linear tests which identify the common tree topology for character data generated by a mixture distribution. The theorem holds for models whose transition matrices can be parameterized by open sets, which includes most of the popular models, such as Tamura-Nei and Kimura's 2-parameter model. The duality theorem relies on our notion of linear tests, which are related to Lake's linear invariants.     

Global identifiability of latent class models with applications to diagnostic test accuracy studies: A Gröbner basis approach

Identifiability of statistical models is a fundamental regularity condition that is required for valid statistical inference. Investigation of model identifiability is mathematically challenging for complex models such as latent class models. Jones et al. used Goodman's technique to investigate the identifiability of latent class models with applications to diagnostic tests in the absence of a gold standard test. The tool they used was based on examining the singularity of the Jacobian or the Fisher information matrix, in order to obtain insights into local identifiability (ie, there exists a neighborhood of a parameter such that no other parameter in the neighborhood leads to the same probability distribution as the parameter). In this paper, we investigate a stronger condition: global identifiability (ie, no two parameters in the parameter space give rise to the same probability distribution), by introducing a powerful mathematical tool from computational algebra: the Gröbner basis. With several existing well-known examples, we argue that the Gröbner basis method is easy to implement and powerful to study global identifiability of latent class models, and is an attractive alternative to the information matrix analysis by Rothenberg and the Jacobian analysis by Goodman and Jones et al.     

Bayesian Inference of Reticulate Phylogenies under the Multispecies Network Coalescent

The multispecies coalescent (MSC) is a statistical framework that models how gene genealogies grow within the branches of a species tree. The field of computational phylogenetics has witnessed an explosion in the development of methods for species tree inference under MSC, owing mainly to the accumulating evidence of incomplete lineage sorting in phylogenomic analyses. However, the evolutionary history of a set of genomes, or species, could be reticulate due to the occurrence of evolutionary processes such as hybridization or horizontal gene transfer. We report on a novel method for Bayesian inference of genome and species phylogenies under the multispecies network coalescent (MSNC). This framework models gene evolution within the branches of a phylogenetic network, thus incorporating reticulate evolutionary processes, such as hybridization, in addition to incomplete lineage sorting. As phylogenetic networks with different numbers of reticulation events correspond to points of different dimensions in the space of models, we devise a reversible-jump Markov chain Monte Carlo (RJMCMC) technique for sampling the posterior distribution of phylogenetic networks under MSNC. We implemented the methods in the publicly available, open-source software package PhyloNet and studied their performance on simulated and biological data. The work extends the reach of Bayesian inference to phylogenetic networks and enables new evolutionary analyses that account for reticulation.     

ClipKIT: A multiple sequence alignment trimming software for accurate phylogenomic inference

Highly divergent sites in multiple sequence alignments (MSAs), which can stem from erroneous inference of homology and saturation of substitutions, are thought to negatively impact phylogenetic inference. Thus, several different trimming strategies have been developed for identifying and removing these sites prior to phylogenetic inference. However, a recent study reported that doing so can worsen inference, underscoring the need for alternative alignment trimming strategies. Here, we introduce ClipKIT, an alignment trimming software that, rather than identifying and removing putatively phylogenetically uninformative sites, instead aims to identify and retain parsimony-informative sites, which are known to be phylogenetically informative. To test the efficacy of ClipKIT, we examined the accuracy and support of phylogenies inferred from 14 different alignment trimming strategies, including those implemented in ClipKIT, across nearly 140,000 alignments from a broad sampling of evolutionary histories. Phylogenies inferred from ClipKIT-trimmed alignments are accurate, robust, and time saving. Furthermore, ClipKIT consistently outperformed other trimming methods across diverse datasets, suggesting that strategies based on identifying and retaining parsimony-informative sites provide a robust framework for alignment trimming.

Highly divergent sites in multiple sequence alignments are thought to negatively impact phylogenetic inference; trimming methods aim to remove these sites, but recent analysis suggests that doing so can worsen inference. This study introduces ClipKIT, a trimming method that instead aims to retain parsimony-informative sites; phylogenetic inference using ClipKIT-trimmed alignments is accurate, robust and time-saving.     

Incorporation of gap characters and lineage-specific regions into phylogenetic analyses of gene families from divergent clades: an example from the kinesin superfamily across eukaryotes

The kinesin superfamily across eukaryotes was used to examine how incorporation of gap characters scored from conserved regions shared by all members of a gene family and incorporation of amino acid and gap characters scored from lineage‐specific regions affect gene‐tree inference of the gene family as a whole. We addressed these two questions in the context of two different densities of sequence sampling, four alignment programs, and two methods of tree construction. Taken together, our findings suggest the following. First, gap characters should be incorporated into gene‐tree inference, even for divergent sequences. Second, gene regions that are not conserved among all or most sequences sampled should not be automatically discarded without evaluation of potential phylogenetic signal that may be contained in gap and/or sequence characters. Third, among the four alignment programs evaluated using their default alignment parameters, Clustal may be expected to output alignments that result in the greatest gene‐tree resolution and support. Yet, this high resolution and support should be regarded as optimistic, rather than conservative, estimates. Fourth, this same conclusion regarding resolution and support holds for Bayesian gene‐tree analyses relative to parsimony‐jackknife gene‐tree analyses. We suggest that a more conservative approach, such as aligning the sequences using DIALIGN‐T or MAFFT, analyzing the appropriate characters using parsimony, and assessing branch support using the jackknife, is more appropriate for inferring gene trees of divergent gene families. © The Willi Hennig Society 2007.     

Inferring and testing hypotheses of cladistic character dependence by using character compatibility

The notion that two characters evolve independently is of interest for two reasons. First, theories of biological integration often predict that change in one character requires complementary change in another. Second, character independence is a basic assumption of most phylogenetic inference methods, and dependent characters might confound attempts at phylogenetic inference. Previously proposed tests of correlated character evolution require a model phylogeny and therefore assume that nonphylogenetic correlation has a negligible effect on initial tree construction. This paper develops "tree-free" methods for testing the independence of cladistic characters. These methods can test the character independence model as a hypothesis before phylogeny reconstruction, or can be used simply to test for correlated evolution. We first develop an approach for visualizing suites of correlated characters by using character compatibility. Two characters are compatible if they can be used to construct a tree without homoplasy. The approach is based on the examination of mutual compatibilities between characters. The number of times two characters i and j share compatibility with a third character is calculated, and a pairwise shared compatibility matrix is constructed. From this matrix, an association matrix analogous to a dissimilarity matrix is derived. Eigenvector analyses of this association matrix reveal suites of characters with similar compatibility patterns. A priori character subsets can be tested for significant correlation on these axes. Monte Carlo tests are performed to determine the expected distribution of mutual compatibilities, given various criteria from the original data set. These simulated distributions are then used to test whether the observed amounts of nonphylogenetic correlation in character suites can be attributed to chance alone. We have applied these methods to published morphological data for caecilian amphibians. The analyses corroborate instances of dependent evolution hypothesized by previous workers and also identify novel partitions. Phylogenetic analysis is performed after reducing correlated suites to single characters. The resulting cladogram has greater topological resolution and implies appreciably less change among the remaining characters than does a tree derived from the raw data matrix.     

Phylogenetic study of Class Armophorea (Alveolata,Ciliophora) based on 18S-rDNA data

The 18S rDNA phylogeny of Class Armophorea, a group of anaerobic ciliates, is proposed based on an analysis of 44 sequences (out of 195) retrieved from the NCBI/GenBank database. Emphasis was placed on the use of two nucleotide alignment criteria that involved variation in the gap-opening and gap-extension parameters and the use of rRNA secondary structure to orientate multiple-alignment. A sensitivity analysis of 76 data sets was run to assess the effect of variations in indel parameters on tree topologies. Bayesian inference, maximum likelihood and maximum parsimony phylogenetic analyses were used to explore how different analytic frameworks influenced the resulting hypotheses. A sensitivity analysis revealed that the relationships among higher taxa of the Intramacronucleata were dependent upon how indels were determined during multiple-alignment of nucleotides. The phylogenetic analyses rejected the monophyly of the Armophorea most of the time and consistently indicated that the Metopidae and Nyctotheridae were related to the Litostomatea. There was no consensus on the placement of the Caenomorphidae, which could be a sister group of the Metopidae + Nyctorheridae, or could have diverged at the base of the Spirotrichea branch or the Intramacronucleata tree.     

Phenotypic characters of static homology increase phylogenetic stability under direct optimization of otherwise dynamic homology characters

Direct optimization of unaligned sequence characters provides a natural framework to explore the sensitivity of phylogenetic hypotheses to variation in analytical parameters. Phenotypic data, when combined into such analyses, are typically analyzed with static homology correspondences unlike the dynamic homology sequence data. Static homology characters may be expected to constrain the direct optimization and thus, potentially increase the similarity of phylogenetic hypotheses under different cost sets. However, whether a total-evidence approach increases the phylogenetic stability or not remains empirically largely unexplored. Here, I studied the impact of static homology data on sensitivity using six empirical data sets composed of several molecular markers and phenotypic data. The inclusion of static homology phenotypic data increased the average stability of phylogenetic hypothesis in five out of the six data sets. To investigate if any static homology characters would have similar effect, the analyses were repeated with randomized phenotypic data, and with one of the molecular markers fixed as static homology characters. These analyses had, on average, almost no effect on the phylogenetic stability, although the randomized phenotypic data sometimes resulted in even higher stability than empirical phenotypic data. The impact was related to the strength of the phylogenetic signal in the phenotypic data: higher average jackknife support of the phenotypic tree correlated with stronger stabilizing effect in the total-evidence analysis. Phenotypic data with a strong signal made the total-evidence trees topologically more similar to the phenotypic trees, thus, they constrained the dynamic homology correspondences of the sequence data. Characters that increase phylogenetic stability are particularly valuable for phylogenetic inference. These results indicate an important role and additive value of phenotypic data in increasing the stability of phylogenetic hypotheses in total-evidence analyses.     

A Primer to Molecular Phylogenetic Analysis in Plants

Reconstructing a tree of life by inferring evolutionary history is an important focus of evolutionary biology. Phylogenetic reconstructions also provide useful information for a range of scientific disciplines such as botany, zoology, phylogeography, archaeology and biological anthropology. Until the development of protein and DNA sequencing techniques in the 1960s and 1970s, phylogenetic reconstructions were based on fossil records and comparative morphological/physiological analyses. Since then, progress in molecular phylogenetics has compensated for some of the shortcomings of phenotype-based comparisons. Comparisons at the molecular level increase the accuracy of phylogenetic inference because there is no environmental influence on DNA/peptide sequences and evaluation of sequence similarity is not subjective. While the number of morphological/physiological characters that are sufficiently conserved for phylogenetic inference is limited, molecular data provide a large number of datapoints and enable comparisons from diverse taxa. Over the last 20 years, developments in molecular phylogenetics have greatly contributed to our understanding of plant evolutionary relationships. Regions in the plant nuclear and organellar genomes that are optimal for phylogenetic inference have been determined and recent advances in DNA sequencing techniques have enabled comparisons at the whole genome level. Sequences from the nuclear and organellar genomes of thousands of plant species are readily available in public databases, enabling researchers without access to molecular biology tools to investigate phylogenetic relationships by sequence comparisons using the appropriate nucleotide substitution models and tree building algorithms. In the present review, the statistical models and algorithms used to reconstruct phylogenetic trees are introduced and advances in the exploration and utilization of plant genomes for molecular phylogenetic analyses are discussed.     

Robustness of compound Dirichlet priors for Bayesian inference of branch lengths

We modified the phylogenetic program MrBayes 3.1.2 to incorporate the compound Dirichlet priors for branch lengths proposed recently by Rannala, Zhu, and Yang (2012. Tail paradox, partial identifiability and influential priors in Bayesian branch length inference. Mol. Biol. Evol. 29:325-335.) as a solution to the problem of branch-length overestimation in Bayesian phylogenetic inference. The compound Dirichlet prior specifies a fairly diffuse prior on the tree length (the sum of branch lengths) and uses a Dirichlet distribution to partition the tree length into branch lengths. Six problematic data sets originally analyzed by Brown, Hedtke, Lemmon, and Lemmon (2010. When trees grow too long: investigating the causes of highly inaccurate Bayesian branch-length estimates. Syst. Biol. 59:145-161) are reanalyzed using the modified version of MrBayes to investigate properties of Bayesian branch-length estimation using the new priors. While the default exponential priors for branch lengths produced extremely long trees, the compound Dirichlet priors produced posterior estimates that are much closer to the maximum likelihood estimates. Furthermore, the posterior tree lengths were quite robust to changes in the parameter values in the compound Dirichlet priors, for example, when the prior mean of tree length changed over several orders of magnitude. Our results suggest that the compound Dirichlet priors may be useful for correcting branch-length overestimation in phylogenetic analyses of empirical data sets.