Assessing phylogenetic signal with measurement error: a comparison of mantel tests, blomberg et Al.'s k, and phylogenetic distograms

In macroevolutionary studies, different approaches are commonly used to measure phylogenetic signal-the tendency of related taxa to resemble one another-including the K statistic and the Mantel test. The latter was recently criticized for lacking statistical power. Using new simulations, we show that the power of the Mantel test depends on the metrics used to define trait distances and phylogenetic distances between species. Increasing power is obtained by lowering variance and increasing negative skewness in interspecific distances, as obtained using Euclidean trait distances and the complement of Abouheif proximity as a phylogenetic distance. We show realistic situations involving "measurement error" due to intraspecific variability where the Mantel test is more powerful to detect a phylogenetic signal than a permutation test based on the K statistic. We highlight limitations of the K-statistic (univariate measure) and show that its application should take into account measurement errors using repeated measures per species to avoid estimation bias. Finally, we argue that phylogenetic distograms representing Euclidean trait distance as a function of the square root of patristic distance provide an insightful representation of the phylogenetic signal that can be used to assess both the impact of measurement error and the departure from a Brownian evolution model.     

Adaptation and the comparative method

Over the past two decades, it has become widely accepted that phylogenies need to be incorporated into statistical analyses of interspecific data. However, recent debate has focused on whether it is appropriate to apply phylogenetic comparative methods (PCMs) to the study of adaptation. Although some of the criticisms are serious, it is premature to stop applying PCMs altogether. New statistical methods designed explicitly for the comparative study of adaptation overcome these criticisms and offer fresh insights into the evolution of phenotypes.     

Adaptive constraints and the phylogenetic comparative method: a computer simulation test

Recently, the utility of modern phylogenetic comparative methods (PCMs) has been questioned because of the seemingly restrictive assumptions required by these methods. Although most comparative analyses involve traits thought to be undergoing natural or sexual selection, most PCMs require an assumption that the traits be evolving by less directed random processes, such as Brownian motion (BM). In this study, we use computer simulation to generate data under more realistic evolutionary scenarios and consider the statistical abilities of a variety of PCMs to estimate correlation coefficients from these data. We found that correlations estimated without taking phylogeny into account were often quite poor and never substantially better than those produced by the other tested methods. In contrast, most PCMs performed quite well even when their assumptions were violated. Felsenstein's independent contrasts (FIC) method gave the best performance in many cases, even when weak constraints had been acting throughout phenotypic evolution. When strong constraints acted in opposition to variance-generating (i.e., BM) forces, however, FIC correlation coefficients were biased in the direction of those BM forces. In most cases, all other PCMs tested (phylogenetic generalized least squares, phylogenetic mixed model, spatial autoregression, and phylogenetic eigenvector regression) yielded good statistical performance, regardless of the details of the evolutionary model used to generate the data. Actual parameter estimates given by different PCMs for each dataset, however, were occasionally very different from one another, suggesting that the choice among them should depend on the types of traits and evolutionary processes being considered.     

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.     

Phylogeny shape and the phylogenetic comparative method

We explored the impact of phylogeny shape on the results of interspecific statistical analyses incorporating phylogenetic information. In most phylogenetic comparative methods (PCMs), the phylogeny can be represented as a relationship matrix, and the hierarchical nature of interspecific phylogenies translates into a distinctive blocklike matrix that can be described by its eigenvectors (topology) and eigenvalues (branch lengths). Thus, differences in the eigenvectors and eigenvalues of different relationship matrices can be used to gauge the impact of possible phylogeny errors by comparing the actual phylogeny used in a PCM analysis with a second phylogenetic hypothesis that may be more accurate. For example, we can use the sum of inverse eigenvalues as a rough index to compare the impact of phylogenies with different branch lengths. Topological differences are better described by the eigenvectors. In general, phylogeny errors that involve deep splits in the phylogeny (e.g., moving a taxon across the base of the phylogeny) are likely to have much greater impact than will those involving small perturbations in the fine structure near the tips. Small perturbations, however, may have more of an impact if the phylogeny structure is highly dependent (with many recent splits near the tips of the tree). Unfortunately, the impact of any phylogeny difference on the results of a PCM depends on the details of the data being considered. Recommendations regarding the choice, design, and statistical power of interspecific analyses are also made.     

Sequence ordinations: a multivariate analysis approach to analysing large sequence data sets

Ordination is a powerful method for analysing complex data setsbut has been largely ignored in sequence analysis. This papershows how to use principal coordinates analysis to find low–dimensionalrepresentations of distance matrices derived from aligned setsof sequences. The method takes a matrix of Euclidean distancesbetween all pairs of sequence and finds a coordinate space wherethe distances are exactly preserved The main problem is to finda measure of distance between aligned sequences that is Euclidean.The simplest distance function is the square root of the percentagedifference (as measured by identities) between two sequences,where one ignores any positions in the alignment where thereis a gap in any sequence. If one does not ignore positions witha gap, the distances cannot be guaranteed to be Euclidean butthe deleterious effects are trivial. Two examples of using themethod are shown. A set of 226 aligned globins were analysedand the resulting ordination very successfully represents theknown patterns of relationship between the sequences. In theother example, a set of 610 aligned 5S rRNA sequences were analysed.Sequence ordinations complement phylogenetic analyses. Theyshould not be viewed as a complete alternative.     

The degree and pattern of phylogenetic signal in primate long-bone structure

Interspecific scaling is a fundamental tool for comparative studies of primate long-bone structure and adaptation. However, scaling analyses based on conventional statistical methods can lead to false positives regarding adaptive relationships when traits exhibit strong phylogenetic signal. This problem can be addressed through the use of phylogenetic comparative methods (PCMs). To date, PCMs have not been incorporated into comparative studies of primate long-bone structure because it has been assumed that long-bone structure is free of phylogenetic signal once appropriately scaled. To test this assumption, we evaluated the degree of phylogenetic signal in three types of long-bone structural traits (bone length, articular surface areas, and cross-sectional geometric properties) from 17 quadrupedal primate species. We compared the pattern of phylogenetic signal in raw trait values and residual trait values after regression against body mass, bone length, and the product of body mass x bone length. Our results show that significant phylogenetic signal is present in all traits before scaling, due in part to their strong covariance with body mass. After scaling, bone length still exhibits strong phylogenetic signal, but articular surface areas do not, and cross-sectional properties exhibit different levels of signal depending on the variable used to scale the data. These results suggest that PCMs should be incorporated into interspecific studies of bone length and perhaps cross-sectional geometric properties. Our results also demonstrate that tests for phylogenetic signal prior to implementing a PCM should focus on residual variance, not individual traits.     

Is horizontal transmission really a problem for phylogenetic comparative methods? A simulation study using continuous cultural traits

Phylogenetic comparative methods (PCMs) provide a potentially powerful toolkit for testing hypotheses about cultural evolution. Here, we build on previous simulation work to assess the effect horizontal transmission between cultures has on the ability of both phylogenetic and non-phylogenetic methods to make inferences about trait evolution. We found that the mode of horizontal transmission of traits has important consequences for both methods. Where traits were horizontally transmitted separately, PCMs accurately reported when trait evolution was not correlated even at the highest levels of horizontal transmission. By contrast, linear regression analyses often incorrectly concluded that traits were correlated. Where simulated trait evolution was not correlated and traits were horizontally transmitted as a pair, both methods inferred increased levels of positive correlation with increasing horizontal transmission. Where simulated trait evolution was correlated, increasing rates of separate horizontal transmission led to decreasing levels of inferred correlation for both methods, but increasing rates of paired horizontal transmission did not. Furthermore, the PCM was also able to make accurate inferences about the ancestral state of traits. These results suggest that under certain conditions, PCMs can be robust to the effects of horizontal transmission. We discuss ways that future work can investigate the mode and tempo of horizontal transmission of cultural traits.     

Correlated evolution in fig pollination

This is the first comparative study of correlated evolution between figs (Ficus species, Moraceae) and their pollinators (Hymenoptera: Agaoninae) based on molecular phylogenies of both lineages. Fig relationships based on the internal transcribed spacer region (ITS) of nuclear ribosomal DNA and pollinator relationships inferred from mitochondrial cytochrome oxidase I (COI) sequences enabled the study of correlated evolution based on molecular phylogenies for the largest set of interacting species ever compared. Comparative methods have been applied to tests of adaptation, but the application of these methods in tests of coadaptation, defined as reciprocal evolutionary change in interacting lineages, has received less attention. I have extended tests of correlated evolution between two traits along a phylogeny to the case of interacting lineages, where two traits may or may not share a common phylogenetic history. Independent contrasts and phylogenetic autocorrelation rejected the null hypothesis that trait correlations within lineages are stronger than trait correlations between interacting lineages. Fig style lengths and pollinator ovipositor lengths, for example, were more highly correlated than were pollinator body size and ovipositor length. Mutualistic interactions between figs and their pollinators illustrate the novel ways in which phylogenies and comparative methods can detect patterns of correlated evolution. The most outstanding evidence of correlated evolution between these obligate mutualists is that interacting trait correlations are stronger than within-lineage allometric relationships.     

Incomplete distance matrices,supertrees and bat phylogeny

In this paper, we evaluate the relative performance of competing approaches for estimating phylogenies from incomplete distance matrices. The direct approach proceeds with phylogenetic reconstruction while ignoring missing cells, whereas the indirect approach proceeds by estimating the missing distances prior to phylogenetic analysis. Two distinct indirect procedures based on the ultrametric inequality and the four-point condition are further compared. Using simulations, we show that more reliable results are obtained when such indirect methods are used. Expectedly, the phylogenies become less accurate as the percentage of missing cells increases, but combining different estimation methods greatly improves the accuracy. An application to bat phylogeny confirms the results obtained in the simulation study and illustrates the effect of missing distances in the construction of supertrees.     

No substitute for real data: A cautionary note on the use of phylogenies from birth–death polytomy resolvers for downstream comparative analyses

The statistical estimation of phylogenies is always associated with uncertainty, and accommodating this uncertainty is an important component of modern phylogenetic comparative analysis. The birth–death polytomy resolver is a method of accounting for phylogenetic uncertainty that places missing (unsampled) taxa onto phylogenetic trees, using taxonomic information alone. Recent studies of birds and mammals have used this approach to generate pseudoposterior distributions of phylogenetic trees that are complete at the species level, even in the absence of genetic data for many species. Many researchers have used these distributions of phylogenies for downstream evolutionary analyses that involve inferences on phenotypic evolution, geography, and community assembly. I demonstrate that the use of phylogenies constructed in this fashion is inappropriate for many questions involving traits. Because species are placed on trees at random with respect to trait values, the birth–death polytomy resolver breaks down natural patterns of trait phylogenetic structure. Inferences based on these trees are predictably and often drastically biased in a direction that depends on the underlying (true) pattern of phylogenetic structure in traits. I illustrate the severity of the phenomenon for both continuous and discrete traits using examples from a global bird phylogeny.     

The ancestral distance test: what relatedness can reveal about correlated evolution in large lineages with missing character data and incomplete phylogenies

The ancestral distance test is introduced to detect correlated evolution between two binary traits in large phylogenies that may lack resolved subclades, branch lengths, and/or comparative data. We define the ancestral distance as the time separating a randomly sampled taxon from its most recent ancestor (MRA) with extant descendants that have an independent trait. The sampled taxon either has (target sample) or lacks (nontarget sample) a dependent trait. Modeled as a Markov process, we show that the distribution of ancestral distances for the target sample is identical to that of the nontarget sample when characters are uncorrelated, whereas ancestral distances are smaller on average for the target sample when characters are correlated. Simulations suggest that the ancestral distance can be estimated using the time, total branch length, taxonomic rank, or number of speciation events between a sampled taxon and the MRA. These results are shown to be robust to deviations from Markov assumptions. A Monte Carlo technique estimates P-values when fully resolved phylogenies with branch lengths are available, and we evaluate the Monte Carlo approach using a data set with known correlation. Measures of relatedness were found to provide a robust means to test hypotheses of correlated character evolution.     

DISTANCE METHODS: A REPLY TO FARRIS

Abstract— Farris (1985) claimed that my assertions about unbiasedness and consistency of estimates of a phylogeny obtained by least squares fitting are in error. The counterexample he constructed violates the assumptions of additivity and independence of distances which were clearly stated in my earlier paper. As such it is not a valid counterexample. It is argued, contrary to Farris's claims, that one need not avoid nonmetric distances, and that one should avoid negative branch lengths in estimates of phylogenies from distance data. Statistical tests of clockness, and, to a limited extent, of alternative phylogenies can be constructed, and these are demonstrated by example. A computer program to infer phylogenies from distance matrices has been in free distribution by me for several years; it seems as effective as the program recently announced by Farris. Information on phylogenies is present in distance data, as in other kinds of data, and statistical methods can be developed to extract it.     

Bayesian estimation of ancestral character states on phylogenies

Biologists frequently attempt to infer the character states at ancestral nodes of a phylogeny from the distribution of traits observed in contemporary organisms. Because phylogenies are normally inferences from data, it is desirable to account for the uncertainty in estimates of the tree and its branch lengths when making inferences about ancestral states or other comparative parameters. Here we present a general Bayesian approach for testing comparative hypotheses across statistically justified samples of phylogenies, focusing on the specific issue of reconstructing ancestral states. The method uses Markov chain Monte Carlo techniques for sampling phylogenetic trees and for investigating the parameters of a statistical model of trait evolution. We describe how to combine information about the uncertainty of the phylogeny with uncertainty in the estimate of the ancestral state. Our approach does not constrain the sample of trees only to those that contain the ancestral node or nodes of interest, and we show how to reconstruct ancestral states of uncertain nodes using a most-recent-common-ancestor approach. We illustrate the methods with data on ribonuclease evolution in the Artiodactyla. Software implementing the methods (BayesMultiState) is available from the authors.     

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.     

Fitting models of continuous trait evolution to incompletely sampled comparative data using approximate Bayesian computation

In recent years, a suite of methods has been developed to fit multiple rate models to phylogenetic comparative data. However, most methods have limited utility at broad phylogenetic scales because they typically require complete sampling of both the tree and the associated phenotypic data. Here, we develop and implement a new, tree-based method called MECCA (Modeling Evolution of Continuous Characters using ABC) that uses a hybrid likelihood/approximate Bayesian computation (ABC)-Markov-Chain Monte Carlo approach to simultaneously infer rates of diversification and trait evolution from incompletely sampled phylogenies and trait data. We demonstrate via simulation that MECCA has considerable power to choose among single versus multiple evolutionary rate models, and thus can be used to test hypotheses about changes in the rate of trait evolution across an incomplete tree of life. We finally apply MECCA to an empirical example of body size evolution in carnivores, and show that there is no evidence for an elevated rate of body size evolution in the pinnipeds relative to terrestrial carnivores. ABC approaches can provide a useful alternative set of tools for future macroevolutionary studies where likelihood-dependent approaches are lacking.     

POOR STATISTICAL PERFORMANCE OF THE MANTEL TEST IN PHYLOGENETIC COMPARATIVE ANALYSES

The Mantel test, based on comparisons of distance matrices, is commonly employed in comparative biology, but its statistical properties in this context are unknown. Here, we evaluate the performance of the Mantel test for two applications in comparative biology: testing for phylogenetic signal, and testing for an evolutionary correlation between two characters. We find that the Mantel test has poor performance compared to alternative methods, including low power and, under some circumstances, inflated type‐I error. We identify a remedy for the inflated type‐I error of three‐way Mantel tests using phylogenetic permutations; however, this test still has considerably lower power than independent contrasts. We recommend that use of the Mantel test should be restricted to cases in which data can only be expressed as pairwise distances among taxa.     

Relating traits to diversification: a simple test

We describe a simple comparative method for determining whether rates of diversification are correlated with continuous traits in species-level phylogenies. This involves comparing traits of species with net speciation rate (number of nodes linking extant species with the root divided by the root to tip evolutionary distance), using a phylogenetically corrected correlation. We use simulations to examine the power of this test. We find that the approach has acceptable power to uncover relationships between speciation and a continuous trait and is robust to background random extinction; however, the power of the approach is reduced when the rate of trait evolution is decreased. The test has low power to relate diversification to traits when extinction rate is correlated with the trait. Clearly, there are inherent limitations in using only data on extant species to infer correlates of extinction; however, this approach is potentially a powerful tool in analyzing correlates of speciation.     

A phylogeny of the Platyhelminthes: towards a total-evidence solution

We advocate a total-evidence approach for the reconstruction of working phylogenies for the Turbellaria and the phylum Platyhelminthes. Few morphology-based character matrices are available in the systematic literature concerning flatworms, and molecular-based phylogenies are rapidly providing the only means by which we can estimate phylogenies cladistically. Character matrices based on gross morphology and ultrastructure are required and should be internally consistent, i.e. character coding should follow a set of a priori guidelines and character duplication and contradiction is avoided. In order to test our molecular phylogenies we need complementary data sets from morphology. To understand morphological homology we need phylogenetic evidence from independent (e.g. molecular) data. Fully complementary morphological and molecular data sets enable us to validate phylogenetic hypotheses and the combination of these sets in phylogenetic reconstruction utilises all statements of homology. Working phylogenies which include all phylogenetic information not only shed light on individual character evolution, but form a strong basis for comparative studies investigating the origin and evolutionary radiation of the taxonomic group under scrutiny. This revised version was published online in July 2006 with corrections to the Cover Date.     

Phylogenetic imputation of plant functional trait databases

Continental‐scale maps of plant functional diversity are a fundamental piece of data of interest to ecosystem modelers and ecologists, yet such maps have been exceedingly hard to generate. The large effort to compile global plant functional trait databases largely for the purpose of mapping and analyzing the spatial distribution of function has resulted in very sparse data matrices thereby limiting progress. Identifying robust methodologies to gap fill or impute trait values in these databases is an important objective. Here I argue that existing statistical tools from phylogenetic comparative methods can be used to rapidly impute values into global plant functional trait databases due to the large amount of phylogenetic signal often in trait data. In particular, statistical models of phylogenetic signal in traits can be generated from existing data and used to predict missing values of closely related species often with a high degree of accuracy thereby facilitating the continental‐scale mapping of plant function. Despite the promise of this approach, I also discuss potential pitfalls and future challenges that will need to be addressed.