Phylogenetic mixture models can reduce node-density artifacts

We investigate the performance of phylogenetic mixture models in reducing a well-known and pervasive artifact of phylogenetic inference known as the node-density effect, comparing them to partitioned analyses of the same data. The node-density effect refers to the tendency for the amount of evolutionary change in longer branches of phylogenies to be underestimated compared to that in regions of the tree where there are more nodes and thus branches are typically shorter. Mixture models allow more than one model of sequence evolution to describe the sites in an alignment without prior knowledge of the evolutionary processes that characterize the data or how they correspond to different sites. If multiple evolutionary patterns are common in sequence evolution, mixture models may be capable of reducing node-density effects by characterizing the evolutionary processes more accurately. In gene-sequence alignments simulated to have heterogeneous patterns of evolution, we find that mixture models can reduce node-density effects to negligible levels or remove them altogether, performing as well as partitioned analyses based on the known simulated patterns. The mixture models achieve this without knowledge of the patterns that generated the data and even in some cases without specifying the full or true model of sequence evolution known to underlie the data. The latter result is especially important in real applications, as the true model of evolution is seldom known. We find the same patterns of results for two real data sets with evidence of complex patterns of sequence evolution: mixture models substantially reduced node-density effects and returned better likelihoods compared to partitioning models specifically fitted to these data. We suggest that the presence of more than one pattern of evolution in the data is a common source of error in phylogenetic inference and that mixture models can often detect these patterns even without prior knowledge of their presence in the data. Routine use of mixture models alongside other approaches to phylogenetic inference may often reveal hidden or unexpected patterns of sequence evolution and can improve phylogenetic inference.     

Automatic selection of partitioning schemes for phylogenetic analyses using iterative k-means clustering of site rates

Background

Model selection is a vital part of most phylogenetic analyses, and accounting for the heterogeneity in evolutionary patterns across sites is particularly important. Mixture models and partitioning are commonly used to account for this variation, and partitioning is the most popular approach. Most current partitioning methods require some a priori partitioning scheme to be defined, typically guided by known structural features of the sequences, such as gene boundaries or codon positions. Recent evidence suggests that these a priori boundaries often fail to adequately account for variation in rates and patterns of evolution among sites. Furthermore, new phylogenomic datasets such as those assembled from ultra-conserved elements lack obvious structural features on which to define a priori partitioning schemes. The upshot is that, for many phylogenetic datasets, partitioned models of molecular evolution may be inadequate, thus limiting the accuracy of downstream phylogenetic analyses.

Results

We present a new algorithm that automatically selects a partitioning scheme via the iterative division of the alignment into subsets of similar sites based on their rates of evolution. We compare this method to existing approaches using a wide range of empirical datasets, and show that it consistently leads to large increases in the fit of partitioned models of molecular evolution when measured using AICc and BIC scores. In doing so, we demonstrate that some related approaches to solving this problem may have been associated with a small but important bias.

Conclusions

Our method provides an alternative to traditional approaches to partitioning, such as dividing alignments by gene and codon position. Because our method is data-driven, it can be used to estimate partitioned models for all types of alignments, including those that are not amenable to traditional approaches to partitioning.     

Optimal data partitioning and a test case for ray-finned fishes (Actinopterygii) based on ten nuclear loci

Data partitioning, the combined phylogenetic analysis of homogeneous blocks of data, is a common strategy used to accommodate heterogeneities in complex multilocus data sets. Variation in evolutionary rates and substitution patterns among sites are typically addressed by partitioning data by gene, codon position, or both. Excessive partitioning of the data, however, could lead to overparameterization; therefore, it seems critical to define the minimum numbers of partitions necessary to improve the overall fit of the model. We propose a new method, based on cluster analysis, to find an optimal partitioning strategy for multilocus protein-coding data sets. A heuristic exploration of alternative partitioning schemes, based on Bayesian and maximum likelihood (ML) criteria, is shown here to produce an optimal number of partitions. We tested this method using sequence data of 10 nuclear genes collected from 52 ray-finned fish (Actinopterygii) and four tetrapods. The concatenated sequences included 7995 nucleotide sites maximally split into 30 partitions defined a priori based on gene and codon position. Our results show that a model based on only 10 partitions defined by cluster analysis performed better than partitioning by both gene and codon position. Alternative data partitioning schemes also are shown to affect the topologies resulting from phylogenetic analysis, especially when Bayesian methods are used, suggesting that overpartitioning may be of major concern. The phylogenetic relationships among the major clades of ray-finned fish were assessed using the best data-partitioning schemes under ML and Bayesian methods. Some significant results include the monophyly of "Holostei" (Amia and Lepisosteus), the sister-group relationships between (1) esociforms and salmoniforms and (2) osmeriforms and stomiiforms, the polyphyly of Perciformes, and a close relationship of cichlids and atherinomorphs.     

Partitionfinder: combined selection of partitioning schemes and substitution models for phylogenetic analyses

In phylogenetic analyses of molecular sequence data, partitioning involves estimating independent models of molecular evolution for different sets of sites in a sequence alignment. Choosing an appropriate partitioning scheme is an important step in most analyses because it can affect the accuracy of phylogenetic reconstruction. Despite this, partitioning schemes are often chosen without explicit statistical justification. Here, we describe two new objective methods for the combined selection of best-fit partitioning schemes and nucleotide substitution models. These methods allow millions of partitioning schemes to be compared in realistic time frames and so permit the objective selection of partitioning schemes even for large multilocus DNA data sets. We demonstrate that these methods significantly outperform previous approaches, including both the ad hoc selection of partitioning schemes (e.g., partitioning by gene or codon position) and a recently proposed hierarchical clustering method. We have implemented these methods in an open-source program, PartitionFinder. This program allows users to select partitioning schemes and substitution models using a range of information-theoretic metrics (e.g., the Bayesian information criterion, akaike information criterion [AIC], and corrected AIC). We hope that PartitionFinder will encourage the objective selection of partitioning schemes and thus lead to improvements in phylogenetic analyses. PartitionFinder is written in Python and runs under Mac OSX 10.4 and above. The program, source code, and a detailed manual are freely available from www.robertlanfear.com/partitionfinder.     

Modelling heterotachy in phylogenetic inference by reversible-jump Markov chain Monte Carlo

The rate at which a given site in a gene sequence alignment evolves over time may vary. This phenomenon--known as heterotachy--can bias or distort phylogenetic trees inferred from models of sequence evolution that assume rates of evolution are constant. Here, we describe a phylogenetic mixture model designed to accommodate heterotachy. The method sums the likelihood of the data at each site over more than one set of branch lengths on the same tree topology. A branch-length set that is best for one site may differ from the branch-length set that is best for some other site, thereby allowing different sites to have different rates of change throughout the tree. Because rate variation may not be present in all branches, we use a reversible-jump Markov chain Monte Carlo algorithm to identify those branches in which reliable amounts of heterotachy occur. We implement the method in combination with our 'pattern-heterogeneity' mixture model, applying it to simulated data and five published datasets. We find that complex evolutionary signals of heterotachy are routinely present over and above variation in the rate or pattern of evolution across sites, that the reversible-jump method requires far fewer parameters than conventional mixture models to describe it, and serves to identify the regions of the tree in which heterotachy is most pronounced. The reversible-jump procedure also removes the need for a posteriori tests of 'significance' such as the Akaike or Bayesian information criterion tests, or Bayes factors. Heterotachy has important consequences for the correct reconstruction of phylogenies as well as for tests of hypotheses that rely on accurate branch-length information. These include molecular clocks, analyses of tempo and mode of evolution, comparative studies and ancestral state reconstruction. The model is available from the authors' website, and can be used for the analysis of both nucleotide and morphological data.     

A Molecular Genetic Timescale for the Diversification of Autotrophic Stramenopiles (Ochrophyta): Substantive Underestimation of Putative Fossil Ages

Background

Stramenopiles constitute a large and diverse eukaryotic clade that is currently poorly characterized from both phylogenetic and temporal perspectives at deeper taxonomic levels. To better understand this group, and in particular the photosynthetic stramenopiles (Ochrophyta), we analyzed sequence data from 135 taxa representing most major lineages. Our analytical approach utilized several recently developed methods that more realistically model the temporal evolutionary process.

Methodology/Principal Findings

Phylogenetic reconstruction employed a Bayesian joint rate- and pattern-heterogeneity model to reconstruct the evolutionary history of these taxa. Inferred phylogenetic resolution was generally high at all taxonomic levels, sister-class relationships in particular receiving good statistical support. A signal for heterotachy was detected in clustered portions of the tree, although this does not seem to have had a major influence on topological inference. Divergence time estimates, assuming a lognormally-distributed relaxed molecular clock while accommodating topological uncertainty, were broadly congruent over alternative temporal prior distributions. These data suggest that Ochrophyta originated near the Proterozoic-Phanerozoic boundary, diverging from their sister-taxon Oomycota. The evolution of the major ochrophyte lineages appears to have proceeded gradually thereafter, with most lineages coming into existence by ∼200 million years ago.

Conclusions/Significance

The evolutionary timescale of the autotrophic stramenopiles reconstructed here is generally older than previously inferred from molecular clocks. However, this more ancient timescale nevertheless casts serious doubt on the taxonomic validity of putative xanthophyte/phaeophyte fossils from the Proterozoic, which predate by as much as a half billion years or more the age suggested by our molecular genetic data. If these fossils truly represent crown stramenopile lineages, then this would imply that molecular rate evolution in this group proceeds in a fashion that is fundamentally incompatible with the relaxed molecular clock model employed here. A more likely scenario is that there is considerable convergent morphological evolution within Heterokonta, and that these fossils have been taxonomically misdiagnosed.     

Spectral partitioning of phylogenetic data sets based on compatibility

We describe two new methods to partition phylogenetic data sets of discrete characters based on pairwise compatibility. The partitioning methods make no assumptions regarding the phylogeny, model of evolution, or characteristics of the data. The methods first build a compatibility graph, in which each node represents a character in the data set. Edges in the compatibility graph may represent strict compatibility of characters or they may be weighted based on a fractional compatibility scoring procedure that measures how close the characters are to being compatible. Given the desired number of partitions, the partitioning methods then seek to cluster the characters with the highest average pairwise compatibility, so that characters in each cluster are more compatible with each other than they are with characters in the other cluster(s). Partitioning according to these criteria is computationally intractable (NP-hard); however, spectral methods can quickly provide high-quality solutions. We demonstrate that the spectral partitioning effectively identifies characters with different evolutionary histories in simulated data sets, and it is better at highlighting phylogenetic conflict within empirical data sets than previously used partitioning methods.     

Mosaicism, modules, and the evolution of birds: results from a Bayesian approach to the study of morphological evolution using discrete character data

The study of morphological evolution after the inferred origin of active flight homologous with that in Aves has historically been characterized by an emphasis on anatomically disjunct, mosaic patterns of change. Relatively few prior studies have used discrete morphological character data in a phylogenetic context to quantitatively investigate morphological evolution or mosaic evolution in particular. One such previously employed method, which used summed unambiguously optimized synapomorphies, has been the basis for proposing disassociated and sequential "modernizing" or "fine-tuning" of pectoral and then pelvic locomotor systems after the origin of flight ("pectoral early-pelvic late" hypothesis). We use one of the most inclusive phylogenetic data sets of basal birds to investigate properties of this method and to consider the application of a Bayesian phylogenetic approach. Bayes factor and statistical comparisons of branch length estimates were used to evaluate support for a mosaic pattern of character change and the specific pectoral early-pelvic late hypothesis. Partitions were defined a priori based on anatomical subregion (e.g., pelvic, pectoral) and were based on those hypothesized using the summed synapomorphy approach. We compare 80 models all implementing the M(k) model for morphological data but varying in the number of anatomical subregion partitions, the models for among-partition rate variation and among-character rate variation, as well as the branch length prior. Statistical analysis reveals that partitioning data by anatomical subregion, independently estimating branch lengths for partitioned data, and use of shared or per partition gamma-shaped among-character rate distribution significantly increases estimated model likelihoods. Simulation studies reveal that partitioned models where characters are randomly assigned perform significantly worse than both the observed model and the single-partition equal-rate model, suggesting that only partitioning by anatomical subregion increases model performance. The preference for models with partitions defined a priori by anatomical subregion is consistent with a disjunctive pattern of character change for the data set investigated and may have implications for parameterization of Bayesian analyses of morphological data more generally. Statistical tests of differences in estimated branch lengths from the pectoral and pelvic partitions do not support the specific pectoral early-pelvic late hypothesis proposed from the summed synapomorphy approach; however, results suggest limited support for some pectoral branch lengths being significantly longer only early at/after the origin of flight.     

Phylogenetic mixtures on a single tree can mimic a tree of another topology

Phylogenetic mixtures model the inhomogeneous molecular evolution commonly observed in data. The performance of phylogenetic reconstruction methods where the underlying data are generated by a mixture model has stimulated considerable recent debate. Much of the controversy stems from simulations of mixture model data on a given tree topology for which reconstruction algorithms output a tree of a different topology; these findings were held up to show the shortcomings of particular tree reconstruction methods. In so doing, the underlying assumption was that mixture model data on one topology can be distinguished from data evolved on an unmixed tree of another topology given enough data and the "correct" method. Here we show that this assumption can be false. For biologists, our results imply that, for example, the combined data from two genes whose phylogenetic trees differ only in terms of branch lengths can perfectly fit a tree of a different topology.     

A nonparametric method for accommodating and testing across-site rate variation

Substitution rates are one of the most fundamental parameters in a phylogenetic analysis and are represented in phylogenetic models as the branch lengths on a tree. Variation in substitution rates across an alignment of molecular sequences is well established and likely caused by variation in functional constraint across the genes encoded in the sequences. Rate variation across alignment sites is important to accommodate in a phylogenetic analysis; failure to account for across-site rate variation can cause biased estimates of phylogeny or other model parameters. Traditionally, rate variation across sites has been modeled by treating the rate for a site as a random variable drawn from some probability distribution (such as the gamma probability distribution) or by partitioning sites to different rate classes and estimating the rate for each class independently. We consider a different approach, related to site-specific models in which sites are partitioned to rate classes. However, instead of treating the partitioning scheme in which sites are assigned to rate classes as a fixed assumption of the analysis, we treat the rate partitioning as a random variable under a Dirichlet process prior. We find that the Dirichlet process prior model for across-site rate variation fits alignments of DNA sequence data better than commonly used models of across-site rate variation. The method appears to identify the underlying codon structure of protein-coding genes; rate partitions that were sampled by the Markov chain Monte Carlo procedure were closer to a partition in which sites are assigned to rate classes by codon position than to randomly permuted partitions but still allow for additional variability across sites.     

The importance of data partitioning and the utility of Bayes factors in Bayesian phylogenetics

As larger, more complex data sets are being used to infer phylogenies, accuracy of these phylogenies increasingly requires models of evolution that accommodate heterogeneity in the processes of molecular evolution. We investigated the effect of improper data partitioning on phylogenetic accuracy, as well as the type I error rate and sensitivity of Bayes factors, a commonly used method for choosing among different partitioning strategies in Bayesian analyses. We also used Bayes factors to test empirical data for the need to divide data in a manner that has no expected biological meaning. Posterior probability estimates are misleading when an incorrect partitioning strategy is assumed. The error was greatest when the assumed model was underpartitioned. These results suggest that model partitioning is important for large data sets. Bayes factors performed well, giving a 5% type I error rate, which is remarkably consistent with standard frequentist hypothesis tests. The sensitivity of Bayes factors was found to be quite high when the across-class model heterogeneity reflected that of empirical data. These results suggest that Bayes factors represent a robust method of choosing among partitioning strategies. Lastly, results of tests for the inclusion of unexpected divisions in empirical data mirrored the simulation results, although the outcome of such tests is highly dependent on accounting for rate variation among classes. We conclude by discussing other approaches for partitioning data, as well as other applications of Bayes factors.     

Difficulties in testing for covarion-like properties of sequences under the confounding influence of changing proportions of variable sites

The covarion (COV)-like properties of sequences are poorly described and their impact on phylogenetic analyses poorly understood. We demonstrate using simulations that, under an evolutionary model where the proportion of variable sites changes in nonadjacent lineages, log likelihood values for rates across site (RAS) and COV models become similar, making models difficult to distinguish. Further, although COV and RAS models provide a great improvement in likelihood scores over a homogeneous model with these simulated data, reconstruction accuracy of tree building is low, suggesting caution when it is suspected that proportions of variable sites differ in different evolutionary lineages. We study the performance of a recently developed contingency test that detects the presence of COV-type evolution modified for protein data. We report that if proportions of variable sites (p(var)) change in a lineage-specific manner such that their distributions in different lineages become sufficiently nonoverlapping, then the contingency test can incorrectly suggest a homogeneous model. Also of concern is the possibility of different proportions of variable sites between the groups being studied. In a study of chloroplast proteins, interpretation of the test is found to be susceptible to different partitioning of taxon groups, making the test very subjective in its implementation. Extreme intergroup differences in the extent of divergence and difference in proportions of variable sites could be contributing to this effect.     

Trophic structure of frugivorous bats in the Neotropics: emergent patterns in evolutionary history

相似文献   

Modeling body size evolution in Felidae under alternative phylogenetic hypotheses

The use of phylogenetic comparative methods in ecological research has advanced during the last twenty years, mainly due to accurate phylogenetic reconstructions based on molecular data and computational and statistical advances. We used phylogenetic correlograms and phylogenetic eigenvector regression (PVR) to model body size evolution in 35 worldwide Felidae (Mammalia, Carnivora) species using two alternative phylogenies and published body size data. The purpose was not to contrast the phylogenetic hypotheses but to evaluate how analyses of body size evolution patterns can be affected by the phylogeny used for comparative analyses (CA). Both phylogenies produced a strong phylogenetic pattern, with closely related species having similar body sizes and the similarity decreasing with increasing distances in time. The PVR explained 65% to 67% of body size variation and all Moran's I values for the PVR residuals were non-significant, indicating that both these models explained phylogenetic structures in trait variation. Even though our results did not suggest that any phylogeny can be used for CA with the same power, or that "good" phylogenies are unnecessary for the correct interpretation of the evolutionary dynamics of ecological, biogeographical, physiological or behavioral patterns, it does suggest that developments in CA can, and indeed should, proceed without waiting for perfect and fully resolved phylogenies.     

A random effects branch-site model for detecting episodic diversifying selection

Adaptive evolution frequently occurs in episodic bursts, localized to a few sites in a gene, and to a small number of lineages in a phylogenetic tree. A popular class of "branch-site" evolutionary models provides a statistical framework to search for evidence of such episodic selection. For computational tractability, current branch-site models unrealistically assume that all branches in the tree can be partitioned a priori into two rigid classes--"foreground" branches that are allowed to undergo diversifying selective bursts and "background" branches that are negatively selected or neutral. We demonstrate that this assumption leads to unacceptably high rates of false positives or false negatives when the evolutionary process along background branches strongly deviates from modeling assumptions. To address this problem, we extend Felsenstein's pruning algorithm to allow efficient likelihood computations for models in which variation over branches (and not just sites) is described in the random effects likelihood framework. This enables us to model the process at every branch-site combination as a mixture of three Markov substitution models--our model treats the selective class of every branch at a particular site as an unobserved state that is chosen independently of that at any other branch. When benchmarked on a previously published set of simulated sequences, our method consistently matched or outperformed existing branch-site tests in terms of power and error rates. Using three empirical data sets, previously analyzed for episodic selection, we discuss how modeling assumptions can influence inference in practical situations.     

Dynamically heterogenous partitions and phylogenetic inference: an evaluation of analytical strategies with cytochrome b and ND6 gene sequences in cranes

ki ctes over whether molecular sequence data should be partitioned for phylogenetic analysis often confound two types of heterogeneity among partitions. We distinguish historical heterogeneity (i.e., different partitions have different evolutionary relationships) from dynamic heterogeneity (i.e., different partitions show different patterns of sequence evolution) and explore the impact of the latter on phylogenetic accuracy and precision with a two-gene, mitochondrial data set for cranes. The well-established phylogeny of cranes allows us to contrast tree-based estimates of relevant parameter values with estimates based on pairwise comparisons and to ascertain the effects of incorporating different amounts of process information into phylogenetic estimates. We show that codon positions in the cytochrome b and NADH dehydrogenase subunit 6 genes are dynamically heterogenous under both Poisson and invariable-sites + gamma-rates versions of the F84 model and that heterogeneity includes variation in base composition and transition bias as well as substitution rate. Estimates of transition-bias and relative-rate parameters from pairwise sequence comparisons were comparable to those obtained as tree-based maximum likelihood estimates. Neither rate-category nor mixed-model partitioning strategies resulted in a loss of phylogenetic precision relative to unpartitioned analyses. We suggest that weighted-average distances provide a computationally feasible alternative to direct maximum likelihood estimates of phylogeny for mixed-model analyses of large, dynamically heterogenous data sets.     

Phylogenetic relationships among the phrynosomatid sand lizards inferred from mitochondrial DNA sequences generated by heterogeneous evolutionary processes

Nucleotide sequences of the mitochondrial protein coding cytochrome b (cyt b; 650 bp) and small-subunit 12S ribosomal RNA (approximately 350 bp) genes were used in analyses of phylogenetic relationships among extant phrynosomatid sand lizards, including an examination of competing hypotheses regarding the evolution of "earlessness." Sequences were obtained from all currently recognized species of sand lizards as well as representatives of the first and second outgroups and analyzed using both parsimony and likelihood methods. The cyt b data offer strong support for relationships that correspond with relatively recent divergences and moderate to low support for relationships reflecting more ancient divergences within the clade. These data support monophyly of the "earless" taxa, the placement of Uma as the sister taxon to the other sand lizards, and monophyly of all four taxa traditionally ranked as genera. All well-supported relationships in the 12S phylogeny are completely congruent with well-supported relationships in the cyt b phylogeny; however, the 12S data alone provide very little support for deeper divergences. Phylogenetic relationships within species are concordant with geography and suggest patterns of phylogeographic differentiation, including the conclusion that at least one currently recognized species (Holbrookia maculata) actually consists of more than one species. By independently optimizing likelihood model parameters for various subsets of the data, we found that nucleotide substitution processes vary widely between genes and among the structural and functional regions or classes of sites within each gene. Therefore, we compared competing phylogenetic hypotheses, using parameter estimates specific to those subsets, analyzing the subsets separately and in various combinations. The hypothesis supported by the cyt b data was favored over rival hypotheses in all but one of the five comparisons made with the entire data set, including the set of partitions that best explained the data, although we were unable to confidently reject (P < 0.05) alternative hypotheses. Our results highlight the importance of optimizing models and parameter estimates for different genes or parts thereof--a strategy that takes advantages of the strengths of both combining and partitioning data.     

The relative performance of Bayesian and parsimony approaches when sampling characters evolving under homogeneous and heterogeneous sets of parameters

We tested whether it is beneficial for the accuracy of phylogenetic inference to sample characters that are evolving under different sets of parameters, using both Bayesian MCMC (Markov chain Monte Carlo) and parsimony approaches. We examined differential rates of evolution among characters, differential character-state frequencies and character-state space, and differential relative branch lengths among characters. We also compared the relative performance of parsimony and Bayesian analyses by progressively incorporating more of these heterogeneous parameters and progressively increasing the severity of this heterogeneity. Bayesian analyses performed better than parsimony when heterogeneous simulation parameters were incorporated into the substitution model. However, parsimony outperformed Bayesian MCMC when heterogeneous simulation parameters were not incorporated into the Bayesian substitution model. The higher the rate of evolution simulated, the better parsimony performed relative to Bayesian analyses. Bayesian and parsimony analyses converged in their performance as the number of simulated heterogeneous model parameters increased. Up to a point, rate heterogeneity among sites was generally advantageous for phylogenetic inference using both approaches. In contrast, branch-length heterogeneity was generally disadvantageous for phylogenetic inference using both parsimony and Bayesian approaches. Parsimony was found to be more conservative than Bayesian analyses, in that it resolved fewer incorrect clades.
© The Willi Hennig Society 2006.     

Likelihood-based clustering (LiBaC) for codon models, a method for grouping sites according to similarities in the underlying process of evolution

Models of codon evolution are useful for investigating the strength and direction of natural selection via a parameter for the nonsynonymous/synonymous rate ratio (omega = d(N)/d(S)). Different codon models are available to account for diversity of the evolutionary patterns among sites. Codon models that specify data partitions as fixed effects allow the most evolutionary diversity among sites but require that site partitions are a priori identifiable. Models that use a parametric distribution to express the variability in the omega ratio across site do not require a priori partitioning of sites, but they permit less among-site diversity in the evolutionary process. Simulation studies presented in this paper indicate that differences among sites in estimates of omega under an overly simplistic analytical model can reflect more than just natural selection pressure. We also find that the classic likelihood ratio tests for positive selection have a high false-positive rate in some situations. In this paper, we developed a new method for assigning codon sites into groups where each group has a different model, and the likelihood over all sites is maximized. The method, called likelihood-based clustering (LiBaC), can be viewed as a generalization of the family of model-based clustering approaches to models of codon evolution. We report the performance of several LiBaC-based methods, and selected alternative methods, over a wide variety of scenarios. We find that LiBaC, under an appropriate model, can provide reliable parameter estimates when the process of evolution is very heterogeneous among groups of sites. Certain types of proteins, such as transmembrane proteins, are expected to exhibit such heterogeneity. A survey of genes encoding transmembrane proteins suggests that overly simplistic models could be leading to false signal for positive selection among such genes. In these cases, LiBaC-based methods offer an important addition to a "toolbox" of methods thereby helping to uncover robust evidence for the action of positive selection.     

SPIn: model selection for phylogenetic mixtures via linear invariants

In phylogenetic inference, an evolutionary model describes the substitution processes along each edge of a phylogenetic tree. Misspecification of the model has important implications for the analysis of phylogenetic data. Conventionally, however, the selection of a suitable evolutionary model is based on heuristics or relies on the choice of an approximate input tree. We introduce a method for model Selection in Phylogenetics based on linear INvariants (SPIn), which uses recent insights on linear invariants to characterize a model of nucleotide evolution for phylogenetic mixtures on any number of components. Linear invariants are constraints among the joint probabilities of the bases in the operational taxonomic units that hold irrespective of the tree topologies appearing in the mixtures. SPIn therefore requires no input tree and is designed to deal with nonhomogeneous phylogenetic data consisting of multiple sequence alignments showing different patterns of evolution, for example, concatenated genes, exons, and/or introns. Here, we report on the results of the proposed method evaluated on multiple sequence alignments simulated under a variety of single-tree and mixture settings for both continuous- and discrete-time models. In the simulations, SPIn successfully recovers the underlying evolutionary model and is shown to perform better than existing approaches.