Phylogenetic Inference with Weighted Codon Evolutionary Distances

We develop a new approach to estimate a matrix of pairwise evolutionary distances from a codon-based alignment based on a codon evolutionary model. The method first computes a standard distance matrix for each of the three codon positions. Then these three distance matrices are weighted according to an estimate of the global evolutionary rate of each codon position and averaged into a unique distance matrix. Using a large set of both real and simulated codon-based alignments of nucleotide sequences, we show that this approach leads to distance matrices that have a significantly better treelikeness compared to those obtained by standard nucleotide evolutionary distances. We also propose an alternative weighting to eliminate the part of the noise often associated with some codon positions, particularly the third position, which is known to induce a fast evolutionary rate. Simulation results show that fast distance-based tree reconstruction algorithms on distance matrices based on this codon position weighting can lead to phylogenetic trees that are at least as accurate as, if not better, than those inferred by maximum likelihood. Finally, a well-known multigene dataset composed of eight yeast species and 106 codon-based alignments is reanalyzed and shows that our codon evolutionary distances allow building a phylogenetic tree which is similar to those obtained by non-distance-based methods (e.g., maximum parsimony and maximum likelihood) and also significantly improved compared to standard nucleotide evolutionary distance estimates.     

Rate matrices for analyzing large families of protein sequences.

We propose and study a new approach for the analysis of families of protein sequences. This method is related to the LogDet distances used in phylogenetic reconstructions; it can be viewed as an attempt to embed these distances into a multidimensional framework. The proposed method starts by associating a Markov matrix to each pairwise alignment deduced from a given multiple alignment. The central objects under consideration here are matrix-valued logarithms L of these Markov matrices, which exist under conditions that are compatible with fairly large divergence between the sequences. These logarithms allow us to compare data from a family of aligned proteins with simple models (in particular, continuous reversible Markov models) and to test the adequacy of such models. If one neglects fluctuations arising from the finite length of sequences, any continuous reversible Markov model with a single rate matrix Q over an arbitrary tree predicts that all the observed matrices L are multiples of Q. Our method exploits this fact, without relying on any tree estimation. We test this prediction on a family of proteins encoded by the mitochondrial genome of 26 multicellular animals, which include vertebrates, arthropods, echinoderms, molluscs, and nematodes. A principal component analysis of the observed matrices L shows that a single rate model can be used as a rough approximation to the data, but that systematic deviations from any such model are unmistakable and related to the evolutionary history of the species under consideration.     

A phylogenetic model for investigating correlated evolution of substitution rates and continuous phenotypic characters

The comparative approach is routinely used to test for possible correlations between phenotypic or life-history traits. To correct for phylogenetic inertia, the method of independent contrasts assumes that continuous characters evolve along the phylogeny according to a multivariate Brownian process. Brownian diffusion processes have also been used to describe time variations of the parameters of the substitution process, such as the rate of substitution or the ratio of synonymous to nonsynonymous substitutions. Here, we develop a probabilistic framework for testing the coupling between continuous characters and parameters of the molecular substitution process. Rates of substitution and continuous characters are jointly modeled as a multivariate Brownian diffusion process of unknown covariance matrix. The covariance matrix, the divergence times and the phylogenetic variations of substitution rates and continuous characters are all jointly estimated in a Bayesian Monte Carlo framework, imposing on the covariance matrix a prior conjugate to the Brownian process so as to achieve a greater computational efficiency. The coupling between rates and phenotypes is assessed by measuring the posterior probability of positive or negative covariances, whereas divergence dates and phenotypic variations are marginally reconstructed in the context of the joint analysis. As an illustration, we apply the model to a set of 410 mammalian cytochrome b sequences. We observe a negative correlation between the rate of substitution and mass and longevity, which was previously observed. We also find a positive correlation between ω = dN/dS and mass and longevity, which we interpret as an indirect effect of variations of effective population size, thus in partial agreement with the nearly neutral theory. The method can easily be extended to any parameter of the substitution process and to any continuous phenotypic or environmental character.     

Analysis of comparative data using generalized estimating equations

It is widely acknowledged that the analysis of comparative data from related species should be performed taking into account their phylogenetic relationships. We introduce a new method, based on the use of generalized estimating equations (GEE), for the analysis of comparative data. The principle is to incorporate, in the modelling process, a correlation matrix that specifies the dependence among observations. This matrix is obtained from the phylogenetic tree of the studied species. Using this approach, a variety of distributions (discrete or continuous) can be analysed using a generalized linear modelling framework, phylogenies with multichotomies can be analysed, and there is no need to estimate ancestral character state. A simulation study showed that the proposed approach has good statistical properties with a type-I error rate close to the nominal 5%, and statistical power to detect correlated evolution between two characters which increases with the strength of the correlation. The proposed approach performs well for the analysis of discrete characters. We illustrate our approach with some data on macro-ecological correlates in birds. Some extensions of the use of GEE are discussed.     

Comparative methods with sampling error and within-species variation: contrasts revisited and revised

Comparative methods analyses have usually assumed that the species phenotypes are the true means for those species. In most analyses, the actual values used are means of samples of modest size. The covariances of contrasts then involve both the covariance of evolutionary changes and a fraction of the within-species phenotypic covariance, the fraction depending on the sample size for that species. Ives et al. have shown how to analyze data in this case when the within-species phenotypic covariances are known. The present model allows them to be unknown and to be estimated from the data. A multivariate normal statistical model is used for multiple characters in samples of finite size from species related by a known phylogeny, under the usual Brownian motion model of change and with equal within-species phenotypic covariances. Contrasts in each character can be obtained both between individuals within a species and between species. Each contrast can be taken for all of the characters. These sets of contrasts, each the same contrast taken for different characters, are independent. The within-set covariances are unequal and depend on the unknown true covariance matrices. An expectation-maximization algorithm is derived for making a reduced maximum likelihood estimate of the covariances of evolutionary change and the within-species phenotypic covariances. It is available in the Contrast program of the PHYLIP package. Computer simulations show that the covariances are biased when the finiteness of sample size is not taken into account and that using the present model corrects the bias. Sampling variation reduces the power of inference of covariation in evolution of different characters. An extension of this method to incorporate estimates of additive genetic covariances from a simple genetic experiment is also discussed.     

A method for inferring the rate of evolution of homologous characters that can potentially improve phylogenetic inference, resolve deep divergence and correct systematic biases

Current phylogenetic methods attempt to account for evolutionary rate variation across characters in a matrix. This is generally achieved by the use of sophisticated evolutionary models, combined with dense sampling of large numbers of characters. However, systematic biases and superimposed substitutions make this task very difficult. Model adequacy can sometimes be achieved at the cost of adding large numbers of free parameters, with each parameter being optimized according to some criterion, resulting in increased computation times and large variances in the model estimates. In this study, we develop a simple approach that estimates the relative evolutionary rate of each homologous character. The method that we describe uses the similarity between characters as a proxy for evolutionary rate. In this article, we work on the premise that if the character-state distribution of a homologous character is similar to many other characters, then this character is likely to be relatively slowly evolving. If the character-state distribution of a homologous character is not similar to many or any of the rest of the characters in a data set, then it is likely to be the result of rapid evolution. We show that in some test cases, at least, the premise can hold and the inferences are robust. Importantly, the method does not use a "starting tree" to make the inference and therefore is tree independent. We demonstrate that this approach can work as well as a maximum likelihood (ML) approach, though the ML method needs to have a known phylogeny, or at least a very good estimate of that phylogeny. We then demonstrate some uses for this method of analysis, including the improvement in phylogeny reconstruction for both deep-level and recent relationships and overcoming systematic biases such as base composition bias. Furthermore, we compare this approach to two well-established methods for reweighting or removing characters. These other methods are tree-based and we show that they can be systematically biased. We feel this method can be useful for phylogeny reconstruction, understanding evolutionary rate variation, and for understanding selection variation on different characters.     

The mouse skull as a source of morphometric data for phylogeny inference

Brownian motion has been a model widely used for describing phenotypic evolution of continuous characters under random drift. Evolution of traits evolving under weak stabilizing selection, together with drift, can also be modeled by the Ornstein-Uhlenbeck process, in which a population moves at random on an adaptive peak under the influence of drift with selection returning the population towards the optimum. Obviously, reliability of an evolutionary model stands or falls with the extent to which the underlying assumptions are supported or violated. Another potential problem of continuous characters as a source of data for phylogeny inference is the correlation between them. To assess whether the Brownian motion model or the Ornstein-Uhlenbeck model are suitable for modeling the evolution of continuous cranial and dental characters and to what extent these characters are correlated with one another, 11 measurements encompassing various aspects of the mouse skull morphology were collected and subjected to a comparative analysis using the generalized least squares method. It could be shown that only about one-half of the characters evolved according to the Brownian motion model or the Ornstein-Uhlenbeck model. Moreover, about 44% of the correlation coefficients exceeded 0.8, suggesting a need for removing at least phenotypic covariances from the data prior to a phylogenetic analysis. Finally, ancestral states of the characters under study were estimated with the generalized least square method. There has been a general trend towards enlarging the overall size of the skull and increasing the braincase volume in the species of the genus Mus.     

Phylogenetic analysis of correlation structure in stalk-eyed flies (Diasemopsis,Diopsidae)

Morphological divergence among species may be constrained by the pattern of genetic variances and covariances among traits within species. Assessing the existence of such a relationship in nature requires information on the stability of intraspecific correlation and covariance structure and the correspondence of this structure to the pattern of evolutionary divergence within a lineage. Here, we investigate these issues for nine morphological traits and 15 species of stalk-eyed flies in the genus Diasemopsis. Within-species matrices for these traits were generated from phenotypic data for all the Diasemopsis species and from genetic data for a single Diasemopsis species, D. dubia. The among-species pattern of divergence was assessed by calculating the evolutionary correlations for all pairwise combinations of the morphological traits along the phylogeny of these species. Comparisons of intraspecific matrices reveal significant similarity among all species in the phenotypic correlations matrices but not the covariance matrices. In addition, the differences in correlation structure that do exist among species are not related to their phylogenetic placement or change in the means of the traits. Comparisons of the phenotypic and phylogenetic matrices suggest a strong relationship between the pattern of evolutionary change among species and both the intraspecific correlation structure and the stability of this structure among species. The phenotypic and the phylogenetic matrices are significantly similar, and pairs of traits whose intraspecific correlations are more stable across taxa exhibit stronger coevolution on the phylogeny. These results suggest either the existence of strong constraints on the pattern of evolutionary change or a consistent pattern of correlated selection shaping both the phenotypic and phylogenetic matrices. The genetic correlation structure for D. dubia, however, does not correspond with patterns found in the phenotypic and phylogenetic data. Possible reasons for this disagreement are discussed.     

Automated Masking of AFLP Markers Improves Reliability of Phylogenetic Analyses

The amplified fragment length polymorphisms (AFLP) method has become an attractive tool in phylogenetics due to the ease with which large numbers of characters can be generated. In contrast to sequence-based phylogenetic approaches, AFLP data consist of anonymous multilocus markers. However, potential artificial amplifications or amplification failures of fragments contained in the AFLP data set will reduce AFLP reliability especially in phylogenetic inferences. In the present study, we introduce a new automated scoring approach, called “AMARE” (AFLP MAtrix REduction). The approach is based on replicates and makes marker selection dependent on marker reproducibility to control for scoring errors. To demonstrate the effectiveness of our approach we record error rate estimations, resolution scores, PCoA and stemminess calculations. As in general the true tree (i.e. the species phylogeny) is not known, we tested AMARE with empirical, already published AFLP data sets, and compared tree topologies of different AMARE generated character matrices to existing phylogenetic trees and/or other independent sources such as morphological and geographical data. It turns out that the selection of masked character matrices with highest resolution scores gave similar or even better phylogenetic results than the original AFLP data sets.     

A new phylogenetic method for identifying exceptional phenotypic diversification

Currently available phylogenetic methods for studying the rate of evolution in a continuously valued character assume that the rate is constant throughout the tree or that it changes along specific branches according to an a priori hypothesis of rate variation provided by the user. Herein, we describe a new method for studying evolutionary rate variation in continuously valued characters given an estimate of the phylogenetic history of the species in our study. According to this method, we propose no specific prior hypothesis for how the variation in evolutionary rate is structured throughout the history of the species in our study. Instead, we use a Bayesian Markov Chain Monte Carlo approach to estimate evolutionary rates and the shift point between rates on the tree. We do this by simultaneously sampling rates and shift points in proportion to their posterior probability, and then collapsing the posterior sample into an estimate of the parameters of interest. We use simulation to show that the method is quite successful at identifying the phylogenetic position of a shift in the rate of evolution, and that estimated rates are asymptotically unbiased. We also provide an empirical example of the method using data for Anolis lizards. [This article was published online on September 20, 2011. An error in a co‐author's name was subsequently identified. This notice is included in the online and print versions to indicate that both have been corrected September 21, 2011.]     

A comparative method for both discrete and continuous characters using the threshold model

The threshold model developed by Sewall Wright in 1934 can be used to model the evolution of two-state discrete characters along a phylogeny. The model assumes that there is a quantitative character, called liability, that is unobserved and that determines the discrete character according to whether the liability exceeds a threshold value. A Markov chain Monte Carlo algorithm is used to infer the evolutionary covariances of the liabilities for discrete characters, sampling liability values consistent with the phylogeny and with the observed data. The same approach can also be used for continuous characters by assuming that the tip species have values that have been observed. In this way, one can make a comparative-methods analysis that combines both discrete and continuous characters. Simulations are presented showing that the covariances of the liabilities are successfully estimated, although precision can be achieved only by using a large number of species, and we must always worry whether the covariances and the model apply throughout the group. An advantage of the threshold model is that the model can be straightforwardly extended to accommodate within-species phenotypic variation and allows an interface with quantitative-genetics models.     

Phylogenetic signal, evolutionary process, and rate

A recent advance in the phylogenetic comparative analysis of continuous traits has been explicit, model-based measurement of "phylogenetic signal" in data sets composed of observations collected from species related by a phylogenetic tree. Phylogenetic signal is a measure of the statistical dependence among species' trait values due to their phylogenetic relationships. Although phylogenetic signal is a measure of pattern (statistical dependence), there has nonetheless been a widespread propensity in the literature to attribute this pattern to aspects of the evolutionary process or rate. This may be due, in part, to the perception that high evolutionary rate necessarily results in low phylogenetic signal; and, conversely, that low evolutionary rate or stabilizing selection results in high phylogenetic signal (due to the resulting high resemblance between related species). In this study, we use individual-based numerical simulations on stochastic phylogenetic trees to clarify the relationship between phylogenetic signal, rate, and evolutionary process. Under the simplest model for quantitative trait evolution, homogeneous rate genetic drift, there is no relation between evolutionary rate and phylogenetic signal. For other circumstances, such as functional constraint, fluctuating selection, niche conservatism, and evolutionary heterogeneity, the relationship between process, rate, and phylogenetic signal is complex. For these reasons, we recommend against interpretations of evolutionary process or rate based on estimates of phylogenetic signal.     

From micro- to macroevolution through quantitative genetic variation: positive evidence from field crickets

Quantitative genetics has been introduced to evolutionary biologists with the suggestion that microevolution could be directly linked to macroevolutionary patterns using, among other parameters, the additive genetic variance/ covariance matrix (G) which is a statistical representation of genetic constraints to evolution. However, little is known concerning the rate and pattern of evolution of G in nature, and it is uncertain whether the constraining effect of G is important over evolutionary time scales. To address these issues, seven species of field crickets from the genera Gryllus and Teleogryllus were reared in the laboratory, and quantitative genetic parameters for morphological traits were estimated from each of them using a nested full-sibling family design. We used three statistical approaches (T method, Flury hierarchy, and Mantel test) to compare G matrices or genetic correlation matrices in a phylogenetic framework. Results showed that G matrices were generally similar across species, with occasional differences between some species. We suggest that G has evolved at a low rate, a conclusion strengthened by the consideration that part of the observed across-species variation in G can be explained by the effect of a genotype by environment interaction. The observed pattern of G matrix variation between species could not be predicted by either morphological trait values or phylogeny. The constraint hypothesis was tested by comparing the multivariate orientation of the reconstructed ancestral G matrix to the orientation of the across-species divergence matrix (D matrix, based on mean trait values). The D matrix mainly revealed divergence in size and, to a much smaller extent, in a shape component related to the ovipositor length. This pattern of species divergence was found to be predictable from the ancestral G matrix in agreement with the expectation of the constraint hypothesis. Overall, these results suggest that the G matrix seems to have an influence on species divergence, and that macroevolution can be predicted, at least qualitatively, from quantitative genetic theory. Alternative explanations are discussed.     

Euclidean nature of phylogenetic distance matrices

Phylogenies are fundamental to comparative biology as they help to identify independent events on which statistical tests rely. Two groups of phylogenetic comparative methods (PCMs) can be distinguished: those that take phylogenies into account by introducing explicit models of evolution and those that only consider phylogenies as a statistical constraint and aim at partitioning trait values into a phylogenetic component (phylogenetic inertia) and one or multiple specific components related to adaptive evolution. The way phylogenetic information is incorporated into the PCMs depends on the method used. For the first group of methods, phylogenies are converted into variance-covariance matrices of traits following a given model of evolution such as Brownian motion (BM). For the second group of methods, phylogenies are converted into distance matrices that are subsequently transformed into Euclidean distances to perform principal coordinate analyses. Here, we show that simply taking the elementwise square root of a distance matrix extracted from a phylogenetic tree ensures having a Euclidean distance matrix. This is true for any type of distances between species (patristic or nodal) and also for trees harboring multifurcating nodes. Moreover, we illustrate that this simple transformation using the square root imposes less geometric distortion than more complex transformations classically used in the literature such as the Cailliez method. Given the Euclidean nature of the elementwise square root of phylogenetic distance matrices, the positive semidefinitiveness of the phylogenetic variance-covariance matrix of a trait following a BM model, or related models of trait evolution, can be established. In that way, we build a bridge between the two groups of statistical methods widely used in comparative analysis. These results should be of great interest for ecologists and evolutionary biologists performing statistical analyses incorporating phylogenies.     

Rapid maximum likelihood ancestral state reconstruction of continuous characters: A rerooting‐free algorithm

Ancestral state reconstruction is a method used to study the evolutionary trajectories of quantitative characters on phylogenies. Although efficient methods for univariate ancestral state reconstruction under a Brownian motion model have been described for at least 25 years, to date no generalization has been described to allow more complex evolutionary models, such as multivariate trait evolution, non‐Brownian models, missing data, and within‐species variation. Furthermore, even for simple univariate Brownian motion models, most phylogenetic comparative R packages compute ancestral states via inefficient tree rerooting and full tree traversals at each tree node, making ancestral state reconstruction extremely time‐consuming for large phylogenies. Here, a computationally efficient method for fast maximum likelihood ancestral state reconstruction of continuous characters is described. The algorithm has linear complexity relative to the number of species and outperforms the fastest existing R implementations by several orders of magnitude. The described algorithm is capable of performing ancestral state reconstruction on a 1,000,000‐species phylogeny in fewer than 2 s using a standard laptop, whereas the next fastest R implementation would take several days to complete. The method is generalizable to more complex evolutionary models, such as phylogenetic regression, within‐species variation, non‐Brownian evolutionary models, and multivariate trait evolution. Because this method enables fast repeated computations on phylogenies of virtually any size, implementation of the described algorithm can drastically alleviate the computational burden of many otherwise prohibitively time‐consuming tasks requiring reconstruction of ancestral states, such as phylogenetic imputation of missing data, bootstrapping procedures, Expectation‐Maximization algorithms, and Bayesian estimation. The described ancestral state reconstruction algorithm is implemented in the Rphylopars functions anc.recon and phylopars.     

MORPHOMETRICS AND CLADISTICS: MEASURING PHYLOGENY IN THE SEA URCHIN ECHINOCARDIUM

A phylogenetic approach to the study of evolutionary patterns is based on taxic homologies (synapomorphies). In contrast, the recognition of evolutionary processes (namely heterochronies) involves analysis of the entire morphology. Recent developments in geometric morphometry permit analysis of morphological similarities grounded in operational homologies. Such morphometric techniques are explored (1) at the level of evolutionary processes, and (2) as a complement in exploration of phylogenetic relationships. To examplify this, we perform a two-part study of the ontogeny and phylogeny of the spatangoid sea urchin Echinocardium. First, a phylogenetic analysis of ten Recent species in the genus is performed on 18 informative characters of the test. Second, morphological divergences among the species are analyzed using procrustean (superimposition) methods based on 49 homologous points. An additive distance tree is built from a matrix of morphometric distances among adult specimens. This tree is fully congruent with the phyletic results. Ontogenetic processes are explored by inserting ontogenetic series into the analysis. A distance tree including the juvenile stages shows that the general evolutionary trend of the genus is peramorphic, but species-to-species comparisons attest that no general clinal trend exists. Our analysis emphasizes the importance of morphometric approaches in evolutionary studies (1) for the understanding of heterochronies; (2) to trace the morphological implications of phylogenetic patterns; and (3) to estimate the impact of homoplasies.     

Phylogeny reconstruction in the neogene bryozoan metrarabdotos: A paleontologic evaluation of methodology

An adequate stratigraphic record can not only aid in both cladistic and stratophenetic reconstruction of phytogenies, but can also serve in estimating the temporal consistency of the resulting phylogenetic trees. For hypothetical data sets, cladistically constructed trees can be as consistent with the temporal distribution of sampled populations or species as those constructed stratophenetically. Empirical testing in taxonomic groups with sufficiently dense fossil records is needed to show whether, and under what conditions, this potential can be realized. A stratophenetic tree and cladistic trees based on several approaches to character weighting were constructed for Caribbean Neogene species of the bryozoan Metrarabdotos with multiple‐character data from closely spaced sequential populations. The modular morphology and highly punctuated evolutionary pattern of these species blur the distinction between continuous and discrete characters, so that all available characters are potentially of equal significance in establishing phytogenies, rather than just those with discrete states conventionally used in cladistic analysis. However, only the cladistic trees generated with all characters weighted to emphasize contribution to species discrimination have temporal consistencies that are clearly significant statistically and approach that of the stratophenetic tree in magnitude. These results provide a start toward establishing general guidelines for cladistic analysis of taxa with stratigraphie records too sparse for stratophenetic reconstruction.     

Selective extinction and rapid loss of evolutionary history in the bird fauna

The extinction of species results in a permanent loss of evolutionary history. Recent theoretical studies show that this loss may be proportionally much smaller than the loss of species, but under some conditions can exceed it. Such conditions occur when the phylogenetic tree that describes the evolutionary relationships among species is highly imbalanced due to differences between lineages in past speciation and/or extinction rates. I used the taxonomy by C. G. Sibley and B. L. Monroe Jr to estimate the global loss of bird evolutionary history from historical and predicted extinctions, and to quantify the ensuing changes in balance of the bird phylogenetic tree. In the global bird fauna, evolutionary history is being lost at a high rate, similar to the rate of species extinction. The bird phylogenetic tree is highly imbalanced, and the imbalance is increased significantly by anthropogenic extinction. Historically, the elevated loss of bird evolutionary history has been fuelled mostly by phylogenetic non-randomness in the extinction of species, but the direct effect of tree imbalance is substantial and could dominate in the future.     

TRANSLATING BETWEEN MICROEVOLUTIONARY PROCESS AND MACROEVOLUTIONARY PATTERNS: THE CORRELATION STRUCTURE OF INTERSPECIFIC DATA

As species evolve along a phylogenetic tree, we expect closely related species to retain some phenotypic similarities due to their shared evolutionary histories. The amount of expected similarity depends both on the hierarchical phylogenetic structure, and on the specific magnitude and types of evolutionary changes that accumulate during each generation. In this study, we show how models of microevolutionary change can be translated into the resulting macroevolutionary patterns. We illustrate how the structure of phenotypic covariances expected in interspecific measurements can be derived, and how this structure depends on the microevolutionary forces guiding phenotypic change at each generation. We then explore the covariance structure expected from several simple microevolutionary models of phenotypic evolution, including various combinations of random genetic drift, directional selection, stabilizing selection, and environmental change, as well as models of punctuated or burst-like evolution. We find that stabilizing selection leads to patterns of exponential decrease of between species covariance with phylogenetic distance. This is different from the usual linear patterns of decrease assumed in most comparative and systematic methods. Nevertheless, linear patterns of decrease can result from many processes in addition to random genetic drift, such as directional and fluctuating selection as well as modes of punctuated change. Our framework can be used to develop methods for (1) phylogenetic reconstruction; (2) inference of the evolutionary process from comparative data; and (3) conducting or evaluating statistical analyses of comparative data while taking phylogenetic history into account.