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Accurate phylogenies are fundamental to our understanding of the pattern and process of evolution. Yet, phylogenies at deep evolutionary timescales, with correspondingly long branches, have been fraught with controversy resulting from conflicting estimates from models with varying complexity and goodness of fit. Analyses of historical as well as current empirical datasets, such as alignments including Microsporidia, Nematoda, or Platyhelminthes, have demonstrated that inadequate modeling of across-site compositional heterogeneity, which is the result of biochemical constraints that lead to varying patterns of accepted amino acids along sequences, can lead to erroneous topologies that are strongly supported. Unfortunately, models that adequately account for across-site compositional heterogeneity remain computationally challenging or intractable for an increasing fraction of contemporary datasets. Here, we introduce "compositional constraint analysis," a method to investigate the effect of site-specific constraints on amino acid composition on phylogenetic inference. We show that more constrained sites with lower diversity and less constrained sites with higher diversity exhibit ostensibly conflicting signals under models ignoring across-site compositional heterogeneity that lead to long-branch attraction artifacts and demonstrate that more complex models accounting for across-site compositional heterogeneity can ameliorate this bias. We present CAT-posterior mean site frequencies (PMSF), a pipeline for diagnosing and resolving phylogenetic bias resulting from inadequate modeling of across-site compositional heterogeneity based on the CAT model. CAT-PMSF is robust against long-branch attraction in all alignments we have examined. We suggest using CAT-PMSF when convergence of the CAT model cannot be assured. We find evidence that compositionally constrained sites are driving long-branch attraction in two metazoan datasets and recover evidence for Porifera as the sister group to all other animals. [Animal phylogeny; cross-site heterogeneity; long-branch attraction; phylogenomics.]., (© The Author(s) 2023. Published by Oxford University Press on behalf of the Society of Systematic Biologists.)

There is still no consensus as to how to select models in Bayesian phylogenetics, and more generally in applied Bayesian statistics. Bayes factors are often presented as the method of choice, yet other approaches have been proposed, such as cross-validation or information criteria. Each of these paradigms raises specific computational challenges, but they also differ in their statistical meaning, being motivated by different objectives: either testing hypotheses or finding the best-approximating model. These alternative goals entail different compromises, and as a result, Bayes factors, cross-validation, and information criteria may be valid for addressing different questions. Here, the question of Bayesian model selection is revisited, with a focus on the problem of finding the best-approximating model. Several model selection approaches were re-implemented, numerically assessed and compared: Bayes factors, cross-validation (CV), in its different forms (k-fold or leave-one-out), and the widely applicable information criterion (wAIC), which is asymptotically equivalent to leave-one-out cross-validation (LOO-CV). Using a combination of analytical results and empirical and simulation analyses, it is shown that Bayes factors are unduly conservative. In contrast, CV represents a more adequate formalism for selecting the model returning the best approximation of the data-generating process and the most accurate estimates of the parameters of interest. Among alternative CV schemes, LOO-CV and its asymptotic equivalent represented by the wAIC, stand out as the best choices, conceptually and computationally, given that both can be simultaneously computed based on standard Markov chain Monte Carlo runs under the posterior distribution. [Bayes factor; cross-validation; marginal likelihood; model comparison; wAIC.]., (© The Author(s) 2023. Published by Oxford University Press on behalf of the Society of Systematic Biologists.)

Programs for Bayesian inference of phylogeny currently implement a unique and fixed suite of models. Consequently, users of these software packages are simultaneously forced to use a number of programs for a given study, while also lacking the freedom to explore models that have not been implemented by the developers of those programs. We developed a new open-source software package, RevBayes, to address these problems. RevBayes is entirely based on probabilistic graphical models, a powerful generic framework for specifying and analyzing statistical models. Phylogenetic-graphical models can be specified interactively in RevBayes, piece by piece, using a new succinct and intuitive language called Rev. Rev is similar to the R language and the BUGS model-specification language, and should be easy to learn for most users. The strength of RevBayes is the simplicity with which one can design, specify, and implement new and complex models. Fortunately, this tremendous flexibility does not come at the cost of slower computation; as we demonstrate, RevBayes outperforms competing software for several standard analyses. Compared with other programs, RevBayes has fewer black-box elements. Users need to explicitly specify each part of the model and analysis. Although this explicitness may initially be unfamiliar, we are convinced that this transparency will improve understanding of phylogenetic models in our field. Moreover, it will motivate the search for improvements to existing methods by brazenly exposing the model choices that we make to critical scrutiny. RevBayes is freely available at http://www.RevBayes.com [Bayesian inference; Graphical models; MCMC; statistical phylogenetics.]., (© The Author(s) 2016. Published by Oxford University Press, on behalf of the Society of Systematic Biologists.)

Modeling across site variation of the substitution process is increasingly recognized as important for obtaining more accurate phylogenetic reconstructions. Both finite and infinite mixture models have been proposed and have been shown to significantly improve on classical single-matrix models. Compared with their finite counterparts, infinite mixtures have a greater expressivity. However, they are computationally more challenging. This has resulted in practical compromises in the design of infinite mixture models. In particular, a fast but simplified version of a Dirichlet process model over equilibrium frequency profiles implemented in PhyloBayes has often been used in recent phylogenomics studies, while more refined model structures, more realistic and empirically more fit, have been practically out of reach. We introduce a message passing interface version of PhyloBayes, implementing the Dirichlet process mixture models as well as more classical empirical matrices and finite mixtures. The parallelization is made efficient thanks to the combination of two algorithmic strategies: a partial Gibbs sampling update of the tree topology and the use of a truncated stick-breaking representation for the Dirichlet process prior. The implementation shows close to linear gains in computational speed for up to 64 cores, thus allowing faster phylogenetic reconstruction under complex mixture models. PhyloBayes MPI is freely available from our website www.phylobayes.org.

In phylogenetic studies, the evolution of molecular sequences is assumed to have taken place along the phylogeny traced by the ancestors of extant species. In the presence of lateral gene transfer, however, this may not be the case, because the species lineage from which a gene was transferred may have gone extinct or not have been sampled. Because it is not feasible to specify or reconstruct the complete phylogeny of all species, we must describe the evolution of genes outside the represented phylogeny by modeling the speciation dynamics that gave rise to the complete phylogeny. We demonstrate that if the number of sampled species is small compared with the total number of existing species, the overwhelming majority of gene transfers involve speciation to and evolution along extinct or unsampled lineages. We show that the evolution of genes along extinct or unsampled lineages can to good approximation be treated as those of independently evolving lineages described by a few global parameters. Using this result, we derive an algorithm to calculate the probability of a gene tree and recover the maximum-likelihood reconciliation given the phylogeny of the sampled species. Examining 473 near-universal gene families from 36 cyanobacteria, we find that nearly a third of transfer events (28%) appear to have topological signatures of evolution along extinct species, but only approximately 6% of transfers trace their ancestry to before the common ancestor of the sampled cyanobacteria.

Phylogenomic analyses of ancient relationships are usually performed using amino acid data, but it is unclear whether amino acids or nucleotides should be preferred. With the 2-fold aim of addressing this problem and clarifying pancrustacean relationships, we explored the signals in the 62 protein-coding genes carefully assembled by Regier et al. in 2010. With reference to the pancrustaceans, this data set infers a highly supported nucleotide tree that is substantially different to the corresponding, but poorly supported, amino acid one. We show that the discrepancy between the nucleotide-based and the amino acids-based trees is caused by substitutions within synonymous codon families (especially those of serine-TCN and AGY). We show that different arthropod lineages are differentially biased in their usage of serine, arginine, and leucine synonymous codons, and that the serine bias is correlated with the topology derived from the nucleotides, but not the amino acids. We suggest that a parallel, partially compositionally driven, synonymous codon-usage bias affects the nucleotide topology. As substitutions between serine codon families can proceed through threonine or cysteine intermediates, amino acid data sets might also be affected by the serine codon-usage bias. We suggest that a Dayhoff recoding strategy would partially ameliorate the effects of such bias. Although amino acids provide an alternative hypothesis of pancrustacean relationships, neither the nucleotides nor the amino acids version of this data set seems to bring enough genuine phylogenetic information to robustly resolve the relationships within group, which should still be considered unresolved.

Although most of the important evolutionary events in the history of biology can only be studied via interspecific comparisons, it is challenging to apply the rich body of population genetic theory to the study of interspecific genetic variation. Probabilistic modeling of the substitution process would ideally be derived from first principles of population genetics, allowing a quantitative connection to be made between the parameters describing mutation, selection, drift, and the patterns of interspecific variation. There has been progress in reconciling population genetics and interspecific evolution for the case where mutation rates are sufficiently low, but when mutation rates are higher, reconciliation has been hampered due to complications from how the loss or fixation of new mutations can be influenced by linked nonneutral polymorphisms (i.e., the Hill-Robertson effect). To investigate the generation of interspecific genetic variation when concurrent fitness-affecting polymorphisms are common and the Hill-Robertson effect is thereby potentially strong, we used the Wright-Fisher model of population genetics to simulate very many generations of mutation, natural selection, and genetic drift. This was done so that the chronological history of advantageous, deleterious, and neutral substitutions could be traced over time along the ancestral lineage. Our simulations show that the process by which a nonrecombining sequence changes over time can markedly deviate from the Markov assumption that is ubiquitous in molecular phylogenetics. In particular, we find tendencies for advantageous substitutions to be followed by deleterious ones and for deleterious substitutions to be followed by advantageous ones. Such non-Markovian patterns reflect the fact that the fate of the ancestral lineage depends not only on its current allelic state but also on gene copies not belonging to the ancestral lineage. Although our simulations describe nonrecombining sequences, we conclude by discussing how non-Markovian behavior of the ancestral lineage is plausible even when recombination rates are not low. As a result, we believe that increased attention needs to be devoted to the robustness of evolutionary inference procedures that rely upon the Markov assumption.

In recent years, the advent of Markov chain Monte Carlo (MCMC) techniques, coupled with modern computational capabilities, has enabled the study of evolutionary models without a closed form solution of the likelihood function. However, current Bayesian MCMC applications can incur significant computational costs, as they are based on a full sampling from the posterior probability distribution of the parameters of interest. Here, we draw attention as to how MCMC techniques can be embedded within normal approximation strategies for more economical statistical computation. The overall procedure is based on an estimate of the first and second moments of the likelihood function, as well as a maximum likelihood estimate. Through examples, we review several MCMC-based methods used in the statistical literature for such estimation, applying the approaches to constructing posterior distributions under non-analytical evolutionary models relaxing the assumptions of rate homogeneity, and of independence between sites. Finally, we use the procedures for conducting Bayesian model selection, based on Laplace approximations of Bayes factors, which we find to be accurate and computationally advantageous. Altogether, the methods we expound here, as well as other related approaches from the statistical literature, should prove useful when investigating increasingly complex descriptions of molecular evolution, alleviating some of the difficulties associated with nonanalytical models.

Genome-scale data sets result in an enhanced resolution of the phylogenetic inference by reducing stochastic errors. However, there is also an increase of systematic errors due to model violations, which can lead to erroneous phylogenies. Here, we explore the impact of systematic errors on the resolution of the eukaryotic phylogeny using a data set of 143 nuclear-encoded proteins from 37 species. The initial observation was that, despite the impressive amount of data, some branches had no significant statistical support. To demonstrate that this lack of resolution is due to a mutual annihilation of phylogenetic and nonphylogenetic signals, we created a series of data sets with slightly different taxon sampling. As expected, these data sets yielded strongly supported but mutually exclusive trees, thus confirming the presence of conflicting phylogenetic and nonphylogenetic signals in the original data set. To decide on the correct tree, we applied several methods expected to reduce the impact of some kinds of systematic error. Briefly, we show that (i) removing fast-evolving positions, (ii) recoding amino acids into functional categories, and (iii) using a site-heterogeneous mixture model (CAT) are three effective means of increasing the ratio of phylogenetic to nonphylogenetic signal. Finally, our results allow us to formulate guidelines for detecting and overcoming phylogenetic artefacts in genome-scale phylogenetic analyses.

Collections of phylogenetic trees are usually summarized using consensus methods. These methods build a single tree, supposed to be representative of the collection. However, in the case of heterogeneous collections of trees, the resulting consensus may be poorly resolved (strict consensus, majority-rule consensus, ...), or may perform arbitrary choices among mutually incompatible clades, or splits (greedy consensus). Here, we propose an alternative method, which we call the multipolar consensus (MPC). Its aim is to display all the splits having a support above a predefined threshold, in a minimum number of consensus trees, or poles. We show that the problem is equivalent to a graph-coloring problem, and propose an implementation of the method. Finally, we apply the MPC to real data sets. Our results indicate that, typically, all the splits down to a weight of 10% can be displayed in no more than 4 trees. In addition, in some cases, biologically relevant secondary signals, which would not have been present in any of the classical consensus trees, are indeed captured by our method, indicating that the MPC provides a convenient exploratory method for phylogenetic analysis. The method was implemented in a package freely available at http://www.lirmm.fr/~cbonnard/MPC.html

In the Bayesian paradigm, a common method for comparing two models is to compute the Bayes factor, defined as the ratio of their respective marginal likelihoods. In recent phylogenetic works, the numerical evaluation of marginal likelihoods has often been performed using the harmonic mean estimation procedure. In the present article, we propose to employ another method, based on an analogy with statistical physics, called thermodynamic integration. We describe the method, propose an implementation, and show on two analytical examples that this numerical method yields reliable estimates. In contrast, the harmonic mean estimator leads to a strong overestimation of the marginal likelihood, which is all the more pronounced as the model is higher dimensional. As a result, the harmonic mean estimator systematically favors more parameter-rich models, an artefact that might explain some recent puzzling observations, based on harmonic mean estimates, suggesting that Bayes factors tend to overscore complex models. Finally, we apply our method to the comparison of several alternative models of amino-acid replacement. We confirm our previous observations, indicating that modeling pattern heterogeneity across sites tends to yield better models than standard empirical matrices.