CONDUCTING PHYLOGENETIC COMPARATIVE STUDIES WHEN THE PHYLOGENY IS NOT KNOWN

A method is proposed to conduct phylogenetic analyses of comparative or interspecific data when the true phylogeny is not known. Standard models of speciation and/or extinction or other methods are used to generate a sample from the set of all possible phylogenies for the measured species. The comparative data are then analyzed on each of the possible trees to obtain a distribution of possible evolutionary statistics for these data. The mean of this distribution is proposed as a reasonable estimate of the true evolutionary statistic of interest. Ways of obtaining confidence intervals and of developing hypothesis tests for this mean statistic are also proposed. The method can be used with any comparative method or phylogenetic analysis technique when phylogenetic relationships among species are not known or when branch lengths for a phylogeny in units of expected character change (as required by most methods) are not available. Computer programs to conduct the analyses are available on request.     

A mixed branch length model of heterotachy improves phylogenetic accuracy

Evolutionary relationships are typically inferred from molecular sequence data using a statistical model of the evolutionary process. When the model accurately reflects the underlying process, probabilistic phylogenetic methods recover the correct relationships with high accuracy. There is ample evidence, however, that models commonly used today do not adequately reflect real-world evolutionary dynamics. Virtually all contemporary models assume that relatively fast-evolving sites are fast across the entire tree, whereas slower sites always evolve at relatively slower rates. Many molecular sequences, however, exhibit site-specific changes in evolutionary rates, called "heterotachy." Here we examine the accuracy of 2 phylogenetic methods for incorporating heterotachy, the mixed branch length model--which incorporates site-specific rate changes by summing likelihoods over multiple sets of branch lengths on the same tree--and the covarion model, which uses a hidden Markov process to allow sites to switch between variable and invariable as they evolve. Under a variety of simple heterogeneous simulation conditions, the mixed model was dramatically more accurate than homotachous models, which were subject to topological biases as well as biases in branch length estimates. When data were simulated with strong versions of the types of heterotachy observed in real molecular sequences, the mixed branch length model was more accurate than homotachous techniques. Analyses of empirical data sets confirmed that the mixed branch length model can improve phylogenetic accuracy under conditions that cause homotachous models to fail. In contrast, the covarion model did not improve phylogenetic accuracy compared with homotachous models and was sometimes substantially less accurate. We conclude that a mixed branch length approach, although not the solution to all phylogenetic errors, is a valuable strategy for improving the accuracy of inferred trees.     

Life history affects the evolution of reproductive isolation among species of Coreopsis (Asteraceae)

The evolution of reproductive isolation within Coreopsis is investigated by integrating phylogenetic data with estimates of pollen viability of plants from inter- and intraspecific crosses. Three different models that predict F1 fitness are compared. The first uses ITS pairwise distances, the second is based on phylogenetic branch lengths derived from DNA sequences, and the third elaborates on the second model by dividing branch length according to reconstructions of the evolution of life history. This is the first study to use phylogenetic branch-length estimates for predicting levels of reproductive isolation. Estimated branch lengths (model 2) predict hybrid fitness more accurately than simply genetic distance (model 1) but only very slightly. This is probably because the two variables are strongly correlated in Coreopsis. Prediction is substantially improved by allowing evolutionary rates to differ between annual and perennial branches (model 3). A bootstrapping procedure indicates that the life-history effect is statistically significant. The more rapid evolution of reproductive isolation within annual species of Coreopsis may be due to differing mechanisms of reproductive isolation, that is, chromosomal rearrangements rather than genetic incompatibilities.     

Properties of Markov Chain Monte Carlo Performance across Many Empirical Alignments

Nearly all current Bayesian phylogenetic applications rely on Markov chain Monte Carlo (MCMC) methods to approximate the posterior distribution for trees and other parameters of the model. These approximations are only reliable if Markov chains adequately converge and sample from the joint posterior distribution. Although several studies of phylogenetic MCMC convergence exist, these have focused on simulated data sets or select empirical examples. Therefore, much that is considered common knowledge about MCMC in empirical systems derives from a relatively small family of analyses under ideal conditions. To address this, we present an overview of commonly applied phylogenetic MCMC diagnostics and an assessment of patterns of these diagnostics across more than 18,000 empirical analyses. Many analyses appeared to perform well and failures in convergence were most likely to be detected using the average standard deviation of split frequencies, a diagnostic that compares topologies among independent chains. Different diagnostics yielded different information about failed convergence, demonstrating that multiple diagnostics must be employed to reliably detect problems. The number of taxa and average branch lengths in analyses have clear impacts on MCMC performance, with more taxa and shorter branches leading to more difficult convergence. We show that the usage of models that include both Γ-distributed among-site rate variation and a proportion of invariable sites is not broadly problematic for MCMC convergence but is also unnecessary. Changes to heating and the usage of model-averaged substitution models can both offer improved convergence in some cases, but neither are a panacea.     

Combining multiple data sets in a likelihood analysis: which models are the best?

Until recently, phylogenetic analyses have been routinely based on homologous sequences of a single gene. Given the vast number of gene sequences now available, phylogenetic studies are now based on the analysis of multiple genes. Thus, it has become necessary to devise statistical methods to combine multiple molecular data sets. Here, we compare several models for combining different genes for the purpose of evaluating the likelihood of tree topologies. Three methods of branch length estimation were studied: assuming all genes have the same branch lengths (concatenate model), assuming that branch lengths are proportional among genes (proportional model), or assuming that each gene has a separate set of branch lengths (separate model). We also compared three models of among-site rate variation: the homogenous model, a model that assumes one gamma parameter for all genes, and a model that assumes one gamma parameter for each gene. On the basis of two nuclear and one mitochondrial amino acid data sets, our results suggest that, depending on the data set chosen, either the separate model or the proportional model represents the most appropriate method for branch length analysis. For all the data sets examined, one gamma parameter for each gene represents the best model for among-site rate variation. Using these models we analyzed alternative mammalian tree topologies, and we describe the effect of the assumed model on the maximum likelihood tree. We show that the choice of the model has an impact on the best phylogeny obtained.     

Directional biases in phylogenetic structure quantification: a Mediterranean case study

Recent years have seen an increasing effort to incorporate phylogenetic hypotheses to the study of community assembly processes. The incorporation of such evolutionary information has been eased by the emergence of specialized software for the automatic estimation of partially resolved supertrees based on published phylogenies. Despite this growing interest in the use of phylogenies in ecological research, very few studies have attempted to quantify the potential biases related to the use of partially resolved phylogenies and to branch length accuracy, and no work has examined how tree shape may affect inference of community phylogenetic metrics. In this study, we tested the influence of phylogenetic resolution and branch length information on the quantification of phylogenetic structure, and also explored the impact of tree shape (stemminess) on the loss of accuracy in phylogenetic structure quantification due to phylogenetic resolution. For this purpose, we used 9 sets of phylogenetic hypotheses of varying resolution and branch lengths to calculate three indices of phylogenetic structure: the mean phylogenetic distance (NRI), the mean nearest taxon distance (NTI) and phylogenetic diversity (stdPD) metrics. The NRI metric was the less sensitive to phylogenetic resolution, stdPD showed an intermediate sensitivity, and NTI was the most sensitive one; NRI was also less sensitive to branch length accuracy than NTI and stdPD, the degree of sensitivity being strongly dependent on the dating method and the sample size. Directional biases were generally towards type II errors. Interestingly, we detected that tree shape influenced the accuracy loss derived from the lack of phylogenetic resolution, particularly for NRI and stdPD. We conclude that well‐resolved molecular phylogenies with accurate branch length information are needed to identify the underlying phylogenetic structure of communities, and also that sensitivity of phylogenetic structure measures to low phylogenetic resolution can strongly vary depending on phylogenetic tree shape.     

A Bayesian perspective on a non-parsimonious parsimony model

Several stochastic models of character change, when implemented in a maximum likelihood framework, are known to give a correspondence between the maximum parsimony method and the method of maximum likelihood. One such model has an independently estimated branch-length parameter for each site and each branch of the phylogenetic tree. This model--the no-common-mechanism model--has many parameters, and, in fact, the number of parameters increases as fast as the alignment is extended. We take a Bayesian approach to the no-common-mechanism model and place independent gamma prior probability distributions on the branch-length parameters. We are able to analytically integrate over the branch lengths, and this allowed us to implement an efficient Markov chain Monte Carlo method for exploring the space of phylogenetic trees. We were able to reliably estimate the posterior probabilities of clades for phylogenetic trees of up to 500 sequences. However, the Bayesian approach to the problem, at least as implemented here with an independent prior on the length of each branch, does not tame the behavior of the branch-length parameters. The integrated likelihood appears to be a simple rescaling of the parsimony score for a tree, and the marginal posterior probability distribution of the length of a branch is dependent upon how the maximum parsimony method reconstructs the characters at the interior nodes of the tree. The method we describe, however, is of potential importance in the analysis of morphological character data and also for improving the behavior of Markov chain Monte Carlo methods implemented for models in which sites share a common branch-length parameter.     

Statistical hypothesis testing in intraspecific phylogeography: nested clade phylogeographical analysis vs. approximate Bayesian computation

Nested clade phylogeographical analysis (NCPA) and approximate Bayesian computation (ABC) have been used to test phylogeographical hypotheses. Multilocus NCPA tests null hypotheses, whereas ABC discriminates among a finite set of alternatives. The interpretive criteria of NCPA are explicit and allow complex models to be built from simple components. The interpretive criteria of ABC are ad hoc and require the specification of a complete phylogeographical model. The conclusions from ABC are often influenced by implicit assumptions arising from the many parameters needed to specify a complex model. These complex models confound many assumptions so that biological interpretations are difficult. Sampling error is accounted for in NCPA, but ABC ignores important sources of sampling error that creates pseudo-statistical power. NCPA generates the full sampling distribution of its statistics, but ABC only yields local probabilities, which in turn make it impossible to distinguish between a good fitting model, a non-informative model, and an over-determined model. Both NCPA and ABC use approximations, but convergences of the approximations used in NCPA are well defined whereas those in ABC are not. NCPA can analyse a large number of locations, but ABC cannot. Finally, the dimensionality of tested hypothesis is known in NCPA, but not for ABC. As a consequence, the 'probabilities' generated by ABC are not true probabilities and are statistically non-interpretable. Accordingly, ABC should not be used for hypothesis testing, but simulation approaches are valuable when used in conjunction with NCPA or other methods that do not rely on highly parameterized models.     

Efficient approximations for learning phylogenetic HMM models from data

MOTIVATION: We consider models useful for learning an evolutionary or phylogenetic tree from data consisting of DNA sequences corresponding to the leaves of the tree. In particular, we consider a general probabilistic model described in Siepel and Haussler that we call the phylogenetic-HMM model which generalizes the classical probabilistic models of Neyman and Felsenstein. Unfortunately, computing the likelihood of phylogenetic-HMM models is intractable. We consider several approximations for computing the likelihood of such models including an approximation introduced in Siepel and Haussler, loopy belief propagation and several variational methods. RESULTS: We demonstrate that, unlike the other approximations, variational methods are accurate and are guaranteed to lower bound the likelihood. In addition, we identify a particular variational approximation to be best-one in which the posterior distribution is variationally approximated using the classic Neyman-Felsenstein model. The application of our best approximation to data from the cystic fibrosis transmembrane conductance regulator gene region across nine eutherian mammals reveals a CpG effect.     

Assessing among‐lineage variability in phylogenetic imputation of functional trait datasets

Phylogenetic imputation has recently emerged as a potentially powerful tool for predicting missing data in functional traits datasets. As such, understanding the limitations of phylogenetic modelling in predicting trait values is critical if we are to use them in subsequent analyses. Previous studies have focused on the relationship between phylogenetic signal and clade‐level prediction accuracy, yet variability in prediction accuracy among individual tips of phylogenies remains largely unexplored. Here, we used simulations of trait evolution along the branches of phylogenetic trees to show how the accuracy of phylogenetic imputations is influenced by the combined effects of 1) the amount of phylogenetic signal in the traits and 2) the branch length of the tips to be imputed. Specifically, we conducted cross‐validation trials to estimate the variability in prediction accuracy among individual tips on the phylogenies (hereafter ‘tip‐level accuracy’). We found that under a Brownian motion model of evolution (BM, Pagel't λ = 1), tip‐level accuracy rapidly decreased with increasing tip branch‐lengths, and only tips of approximately 10% or less of the total height of the trees showed consistently accurate predictions (i.e. cross‐validation R‐squared >0.75). When phylogenetic signal was weak, the effect of tip branch‐length was reduced, becoming negligible for traits simulated with λ < 0.7, where accuracy was in any case low. Our study shows that variability in prediction accuracy among individual tips of the phylogeny should be considered when evaluating the reliability of phylogenetically imputed trait values. To address this challenge, we describe a Monte Carlo‐based method that allows one to estimate the expected tip‐level accuracy of phylogenetic predictions for continuous traits. Our approach identifies gaps in functional trait datasets for which phylogenetic imputation performs poorly, and will help ecologists to design more efficient trait collection campaigns by focusing resources on lineages whose trait values are more uncertain.     

Accuracy of estimated phylogenetic trees from molecular data

The accuracies and efficiencies of three different methods of making phylogenetic trees from gene frequency data were examined by using computer simulation. The methods examined are UPGMA, Farris' (1972) method, and Tateno et al.'s (1982) modified Farris method. In the computer simulation eight species (or populations) were assumed to evolve according to a given model tree, and the evolutionary changes of allele frequencies were followed by using the infinite-allele model. At the end of the simulated evolution five genetic distance measures (Nei's standard and minimum distances, Rogers' distance, Cavalli-Sforza's f theta, and the modified Cavalli-Sforza distance) were computed for all pairs of species, and the distance matrix obtained for each distance measure was used for reconstructing a phylogenetic tree. The phylogenetic tree obtained was then compared with the model tree. The results obtained indicate that in all tree-making methods examined the accuracies of both the topology and branch lengths of a reconstructed tree (rooted tree) are very low when the number of loci used is less than 20 but gradually increase with increasing number of loci. When the expected number of gene substitutions (M) for the shortest branch is 0.1 or more per locus and 30 or more loci are used, the topological error as measured by the distortion index (dT) is not great, but the probability of obtaining the correct topology (P) is less than 0.5 even with 60 loci. When M is as small as 0.004, P is substantially lower. In obtaining a good topology (small dT and high P) UPGMA and the modified Farris method generally show a better performance than the Farris method. The poor performance of the Farris method is observed even when Rogers' distance which obeys the triangle inequality is used. The main reason for this seems to be that the Farris method often gives overestimates of branch lengths. For estimating the expected branch lengths of the true tree UPGMA shows the best performance. For this purpose Nei's standard distance gives a better result than the others because of its linear relationship with the number of gene substitutions. Rogers' or Cavalli-Sforza's distance gives a phylogenetic tree in which the parts near the root are condensed and the other parts are elongated. It is recommended that more than 30 loci, including both polymorphic and monomorphic loci, be used for making phylogenetic trees. The conclusions from this study seem to apply also to data on nucleotide differences obtained by the restriction enzyme techniques.     

Phylogenetic analysis under reticulate evolution

The usual assumption that species have evolved from a common ancestor by a simple branching process--where each branch is genetically isolated--has been challenged by the observation of frequent hybridization between species in natural populations. In fact, most plant species are thought to have hybrid origins. This reticulate pattern of species evolution has posed problems in the definition of speciation and in phylogenetic reconstruction, especially when molecular data are used. As a result, hybridization has been largely treated as an evolutionary accident or statistical error in phylogenetic analysis. In this paper, I explicitly incorporate hybridization as an evolutionary occurrence and then conduct phylogenetic reconstruction. I first examine the reticulate evolution under a pure drift model, and then extend the theory to fit a mutation model. A least-squares method is developed for reconstructing a reticulate phylogeny using gene frequency data. The efficacy of the method under the pure drift model is verified via Monte Carlo simulations.     

Phylogenetic analysis and intraspecific variation: performance of parsimony,likelihood, and distance methods

Intraspecific variation is abundant in all types of systematic characters but is rarely addressed in simulation studies of phylogenetic method performance. We compared the accuracy of 15 phylogenetic methods using simulations to (1) determine the most accurate method(s) for analyzing polymorphic data (under simplified conditions) and (2) test if generalizations about the performance of phylogenetic methods based on previous simulations of fixed (nonpolymorphic) characters are robust to a very different evolutionary model that explicitly includes intraspecific variation. Simulated data sets consisted of allele frequencies that evolved by genetic drift. The phylogenetic methods included eight parsimony coding methods, continuous maximum likelihood, and three distance methods (UPGMA, neighbor joining, and Fitch-Margoliash) applied to two genetic distance measures (Nei's and the modified Cavalli-Sforza and Edwards chord distance). Two sets of simulations were performed. The first examined the effects of different branch lengths, sample sizes (individuals sampled per species), numbers of characters, and numbers of alleles per locus in the eight-taxon case. The second examined more extensively the effects of branch length in the four-taxon, two-allele case. Overall, the most accurate methods were likelihood, the additive distance methods (neighbor joining and Fitch-Margoliash), and the frequency parsimony method. Despite the use of a very different evolutionary model in the present article, many of the results are similar to those from simulations of fixed characters. Similarities include the presence of the "Felsenstein zone," where methods often fail, which suggests that long-branch attraction may occur among closely related species through genetic drift. Differences between the results of fixed and polymorphic data simulations include the following: (1) UPGMA is as accurate or more accurate than nonfrequency parsimony methods across nearly all combinations of branch lengths, and (2) likelihood and the additive distance methods are not positively misled under any combination of branch lengths tested (even when the assumptions of the methods are violated and few characters are sampled). We found that sample size is an important determinant of accuracy and affects the relative success of methods (i.e., distance and likelihood methods outperform parsimony at small sample sizes). Attempts to generalize about the behavior of phylogenetic methods should consider the extreme examples offered by fixed-mutation models of DNA sequence data and genetic-drift models of allele frequencies.     

LD-SPatt: large deviations statistics for patterns on Markov chains.

Statistics on Markov chains are widely used for the study of patterns in biological sequences. Statistics on these models can be done through several approaches. Central limit theorem (CLT) producing Gaussian approximations are one of the most popular ones. Unfortunately, in order to find a pattern of interest, these methods have to deal with tail distribution events where CLT is especially bad. In this paper, we propose a new approach based on the large deviations theory to assess pattern statistics. We first recall theoretical results for empiric mean (level 1) as well as empiric distribution (level 2) large deviations on Markov chains. Then, we present the applications of these results focusing on numerical issues. LD-SPatt is the name of GPL software implementing these algorithms. We compare this approach to several existing ones in terms of complexity and reliability and show that the large deviations are more reliable than the Gaussian approximations in absolute values as well as in terms of ranking and are at least as reliable as compound Poisson approximations. We then finally discuss some further possible improvements and applications of this new method.     

Parsimony, likelihood, and simplicity

The latest charge against parsimony in phylogenetic inference is that it involves estimating too many parameters. The charge is derived from the fact that, when each character is allowed a branch length vector of its own (instead of the homogeneous branch lengths assumed in current likelihood models), the results for likelihood and parsimony are identical. Parsimony, however, can also be derived from simpler models, involving fewer parameters. Therefore, parsimony provides (as many authors had argued before) the simplest explanation of the data, or the most realistic, depending on one's views. If (as argued by likelihoodists) phylogenetic inference is to use the simplest model that provides sufficient explanation of the data, the starting point of phylogenetic analyses should be parsimony, not maximum likelihood. If the addition of new parameters (which increase the likelihood) to a parsimony estimation is seen as desirable, this may lead to a preference for results based on current likelihood models. If the addition of parameters is continued, however, the results will eventually come back to the same place where they had started, since allowing each character a branch length of its own also produces parsimony. Parsimony can be justified by very different types of models—either very complex or very simple. This suggests that parsimony does have a unique place among methods of phylogenetic estimation.     

Saddle-Point Approximations,Integrodifference Equations,and Invasions

Invasion, the growth in numbers and spatial spread of a population over time, is a fundamental process in ecology. Governments and businesses expend vast sums to prevent and control invasions of pests and pestilences and to promote invasions of endangered species and biological control agents. Many mathematical models of biological invasions use nonlinear integrodifference equations to describe the growth and dispersal processes and to predict the speed of invasion fronts. Linear models have received less attention, perhaps because they are difficult to simulate for large times. In this paper, we use the saddle-point method, alias the method of steepest descent, to derive asymptotic approximations for the solutions of linear integrodifference equations. We work through five examples, for Gaussian, Laplace, and uniform dispersal kernels in one dimension and for asymmetric Gaussian and radially symmetric Laplace kernels in two dimensions. Our approximations are extremely close to the exact solutions, even for intermediate times. We also employ an empirical saddle-point approximation to predict densities using dispersal data. We use our approximations to examine the effects of censored dispersal data on estimates of invasion speed and population density.     

The Applicability of Ordinary Least Squares to Consistently Short Distances between Taxa in Phylogenetic Tree Construction and the Normal Distribution Test Consequences

Short phylogenetic distances between taxa occur, for example, in studies on ribosomal RNA-genes with slow substitution rates. For consistently short distances, it is proved that in the completely singular limit of the covariance matrix ordinary least squares (OLS) estimates are minimum variance or best linear unbiased (BLU) estimates of phylogenetic tree branch lengths. Although OLS estimates are in this situation equal to generalized least squares (GLS) estimates, the GLS chi-square likelihood ratio test will be inapplicable as it is associated with zero degrees of freedom. Consequently, an OLS normal distribution test or an analogous bootstrap approach will provide optimal branch length tests of significance for consistently short phylogenetic distances. As the asymptotic covariances between branch lengths will be equal to zero, it follows that the product rule can be used in tree evaluation to calculate an approximate simultaneous confidence probability that all interior branches are positive.     

On the maintenance of genetic variation: global analysis of Kimura's continuum-of-alleles model

Methods of functional analysis are applied to provide an exact mathematical analysis of Kimura's continuum-of-alleles model. By an approximate analysis, Kimura obtained the result that the equilibrium distribution of allelic effects determining a quantitative character is Gaussian if fitness decreases quadratically from the optimum and if production of new mutants follows a Gaussian density. Lande extended this model considerably and proposed that high levels of genetic variation can be maintained by mutation even when there is strong stabilizing selection. This hypothesis has been questioned recently by Turelli, who published analyses and computer simulations of some multiallele models, approximating the continuum-of-alleles model, and reviewed relevant data. He found that the Kimura and Lande predictions overestimate the amount of equilibrium variance considerably if selection is not extremely weak or mutation rate not extremely high. The present analysis provides the first proof that in Kimura's model an equilibrium in fact exists and, moreover, that it is globally stable. Finally, using methods from quantum mechanics, estimates of the exact equilibrium variance are derived which are in best accordance with Turelli's results. This shows that continuum-of-alleles models may be excellent approximations to multiallele models, if analysed appropriately.     

Kakusan4 and Aminosan: two programs for comparing nonpartitioned, proportional and separate models for combined molecular phylogenetic analyses of multilocus sequence data

Proportional and separate models able to apply different combination of substitution rate matrix (SRM) and among-site rate variation model (ASRVM) to each locus are frequently used in phylogenetic studies of multilocus data. A proportional model assumes that branch lengths are proportional among partitions and a separate model assumes that each partition has an independent set of branch lengths. However, the selection from among nonpartitioned (i.e., a common combination of models is applied to all-loci concatenated sequences), proportional and separate models is usually based on the researcher's preference rather than on any information criteria. This study describes two programs, 'Kakusan4' (for DNA sequences) and 'Aminosan' (for amino-acid sequences), which allow the selection of evolutionary models based on several types of information criteria. The programs can handle both multilocus and single-locus data, in addition to providing an easy-to-use wizard interface and a noninteractive command line interface. In the case of multilocus data, SRMs and ASRVMs are compared at each locus and at all-loci concatenated sequences, after which nonpartitioned, proportional and separate models are compared based on information criteria. The programs also provide model configuration files for mrbayes, paup*, phyml, raxml and Treefinder to support further phylogenetic analysis using a selected model. When likelihoods are optimized by Treefinder, the best-fit models were found to differ depending on the data set. Furthermore, differences in the information criteria among nonpartitioned, proportional and separate models were much larger than those among the nonpartitioned models. These findings suggest that selecting from nonpartitioned, proportional and separate models results in a better phylogenetic tree. Kakusan4 and Aminosan are available at http://www.fifthdimension.jp/. They are licensed under gnugpl Ver.2, and are able to run on Windows, MacOS X and Linux.