Assessing Trait Covariation and Morphological Integration on Phylogenies Using Evolutionary Covariance Matrices

Morphological integration describes the degree to which sets of organismal traits covary with one another. Morphological covariation may be evaluated at various levels of biological organization, but when characterizing such patterns across species at the macroevolutionary level, phylogeny must be taken into account. We outline an analytical procedure based on the evolutionary covariance matrix that allows species-level patterns of morphological integration among structures defined by sets of traits to be evaluated while accounting for the phylogenetic relationships among taxa, providing a flexible and robust complement to related phylogenetic independent contrasts based approaches. Using computer simulations under a Brownian motion model we show that statistical tests based on the approach display appropriate Type I error rates and high statistical power for detecting known levels of integration, and these trends remain consistent for simulations using different numbers of species, and for simulations that differ in the number of trait dimensions. Thus, our procedure provides a useful means of testing hypotheses of morphological integration in a phylogenetic context. We illustrate the utility of this approach by evaluating evolutionary patterns of morphological integration in head shape for a lineage of Plethodon salamanders, and find significant integration between cranial shape and mandible shape. Finally, computer code written in R for implementing the procedure is provided.     

Phylogenetic frameworks: towards a firmer foundation for the comparative approach

The growing interest in using phylogenies to test evolutionary hypotheses has focused attention on the need for robust estimates of phylogenetic history. Whether specific branching structures are correct summaries of evolutionary history can be estimated only through the examination of congruence of many sets of characters. After consideration of practical and philosophical aspects of congruence, I conclude that taxonomic congruence (analysis of congruence of topologies produced from independent datasets) is preferable to character congruence (analysis of congruence between individual characters) for estimating accuracy of phylogenetic hypotheses. Existing methods for examining taxonomic congruence are discussed and the combinable components approach, when preceded by application of rigorous statistical manipulations (e.g. jackknifing or bootstrapping), found most appropriate. Implementation of the method of combinable components is described, and is demonstrated using published data for Menidia and Rana. The robust branching structure resulting from this analysis (a phylogenetic framework) contains those nodes (phylogenetic hypotheses) that are strongly supported by at least one dataset and are consistent with all others. This approach is the most appropriate/conservative for testing hypotheses about evolutionary history.     

Factors influencing changes in trait correlations across species after using phylogenetic independent contrasts

Comparative interspecific data sets have been analyzed routinely by phylogenetic methods, generally using Felsenstein’s phylogenetic independent contrasts (PIC) method. However, some authors have suggested that it may not be always necessary to incorporate phylogenetic information into statistical analyses of comparative data due to the low influence of shared history on the distribution of␣character states. The main goal of this paper was to undertake a comparison of results from non-phylogenetic Pearson correlation of tip values (TIPs) and phylogenetic independent contrasts analyses (PICs), using 566 correlation coefficients derived from 65 published papers. From each study we collected the following data: taxonomic group, number of species, type of phylogeny, number of polytomies in the phylogenetic tree, if branch length was transformed or not, trait types, the original correlation coefficient between the traits (TIPs) and the correlation coefficient between the traits using the independent contrasts method (PICs). The slope estimated from a regression of PIC correlations on TIP correlations was lower than one, and a paired t-test showed that correlations from PIC are significantly smaller than those obtained by TIP. Thus, PIC analyses tend to decrease the correlation between traits and usually increases the P-value and, thus, favoring the acceptance of the null hypothesis. Multiple factors, including taxonomic group, trait type and use of branch length transformations affected the change in decision regarding the acceptance of the null hypotheses and differences between PIC and TIP results. Due to the variety of factors affecting the differences between results provided by these methods, we suggest that comparative methods should be applied as a conservative approach to cross-species studies. Despite difficulties in quantifying precisely why these factors affect the differences between PIC and TIP, we also suggest that a better evaluation of evolutionary models underlying trait evolution is still necessary in this context and might explain some of the observed patterns.     

A METHOD FOR ASSESSING PHYLOGENETIC LEAST SQUARES MODELS FOR SHAPE AND OTHER HIGH‐DIMENSIONAL MULTIVARIATE DATA

Studies of evolutionary correlations commonly use phylogenetic regression (i.e., independent contrasts and phylogenetic generalized least squares) to assess trait covariation in a phylogenetic context. However, while this approach is appropriate for evaluating trends in one or a few traits, it is incapable of assessing patterns in highly multivariate data, as the large number of variables relative to sample size prohibits parametric test statistics from being computed. This poses serious limitations for comparative biologists, who must either simplify how they quantify phenotypic traits, or alter the biological hypotheses they wish to examine. In this article, I propose a new statistical procedure for performing ANOVA and regression models in a phylogenetic context that can accommodate high‐dimensional datasets. The approach is derived from the statistical equivalency between parametric methods using covariance matrices and methods based on distance matrices. Using simulations under Brownian motion, I show that the method displays appropriate Type I error rates and statistical power, whereas standard parametric procedures have decreasing power as data dimensionality increases. As such, the new procedure provides a useful means of assessing trait covariation across a set of taxa related by a phylogeny, enabling macroevolutionary biologists to test hypotheses of adaptation, and phenotypic change in high‐dimensional datasets.     

Using quaternary structures to assess the evolutionary history of proteins: the case of the aspartate carbamoyltransferase

Many evolutionary scenarios describing the history of proteins are based solely on phylogenetic studies. We have designed a new approach that allows ascertainment of such questionable scenarios by taking into account quaternary structures: we used aspartate carbamoyltransferase (ATCase) as a case study. Prokaryotic ATCases correspond to different classes of quaternary structures according to the mode of association of the catalytic PyrB subunit with other polypeptides, either the PyrI regulatory subunit (class B) or a dihydroorotase (class A), which may be active (PyrC, subclass A1) or inactive (PyrC', subclass A2). Class C is uniquely made up of trimers of PyrB. The PyrB phylogenetic tree is not congruent with the tree of life, but it became coherent when we recognized the existence of two families of ATCases, ATC I and ATC II. Remarkably, a very strong correlation was found between the pattern of PyrB phylogenetic clustering and the different classes of quaternary structures of ATCases. All class B ATCases form a clade in family ATC II, which also contains all eukaryotic sequences. In contrast, family ATC I is made up of classes A and C. These results suggest unexpected common ancestry for prokaryotic B and eukaryotic ATCases on the one hand, and for A and C on the other. Thus, the emergence of specific quaternary structures appears to have been a more recent event than the separation into the ATC I and ATC II families. We propose that different evolutionary constraints, depending on the identity of the partners interacting in the different kinds of holoenzymes, operated in a concerted way on the ancestral pyrB genes and the respective associated genes pyrI or pyrC, so as to maintain appropriate inter-polypeptides interactions at the level of quaternary structure. The process of coevolution of genes encoding proteins interacting in various holoenzymes has been assessed by calculating the correlation coefficient between their respective phylogenetic trees. Our approach integrating data obtained from the separate fields of structural biology and molecular evolution could be useful in other cases where pure statistical data need to receive independent confirmation.     

PHYLOGENIES,SPATIAL AUTOREGRESSION,AND THE COMPARATIVE METHOD: A COMPUTER SIMULATION TEST

Brownian motion computer simulation was used to test the statistical properties of a spatial autoregressive method in estimating evolutionary correlations between two traits using interspecific comparative data. When applied with a phylogeny of 42 species, the method exhibited reasonable Type I and II error rates. Estimation abilities were comparable to those of independent contrasts and minimum evolution (parsimony) methods, and generally superior to a traditional nonphylogenetic approach (not taking phylogenies into account at all). However, the autoregressive method performed extremely poorly with a smaller phylogeny (15 species) and with nearly independent (“star”) phylogenies. In both of these situations, any phylogenetic autocorrelation present in the data was not detected by the method. Results show how diagnostic techniques (e.g., Moran's I) can be useful in detecting and avoiding such situations, but that such techniques should not be used as definitive evidence that phylogenetic correlation is not present in a set of comparative data. The correction factor (α) proposed by Gittleman and Kot (1990) for use in weighting phylogenetic information had little effect in most analyses of 15 or 42 species with incorrect phylogenetic information, and may require much larger sample sizes before significant improvement is shown. With the sample sizes tested in this study, however, the autoregressive method implemented with this correction factor and correct phylogenetic information led to downwardly biased estimates of the absolute magnitude of the evolutionary correlation between two traits. Cautions and recommendations for implemention of the spatial autoregressive method are given; computer programs to conduct the analyses are available on request.     

PHYLOGENETIC ANALYSIS OF THE EVOLUTIONARY CORRELATION USING LIKELIHOOD

Many evolutionary processes can lead to a change in the correlation between continuous characters over time or on different branches of a phylogenetic tree. Shifts in genetic or functional constraint, in the selective regime, or in some combination thereof can influence both the evolution of continuous traits and their relation to each other. These changes can often be mapped on a phylogenetic tree to examine their influence on multivariate phenotypic diversification. We propose a new likelihood method to fit multiple evolutionary rate matrices (also called evolutionary variance–covariance matrices) to species data for two or more continuous characters and a phylogeny. The evolutionary rate matrix is a matrix containing the evolutionary rates for individual characters on its diagonal, and the covariances between characters (of which the evolutionary correlations are a function) elsewhere. To illustrate our approach, we apply the method to an empirical dataset consisting of two features of feeding morphology sampled from 28 centrarchid fish species, as well as to data generated via phylogenetic numerical simulations. We find that the method has appropriate type I error, power, and parameter estimation. The approach presented herein is the first to allow for the explicit testing of how and when the evolutionary covariances between characters have changed in the history of a group.     

Meta-Analysis of Genome-wide Association Studies with Overlapping Subjects

Data from multiple genome-wide association studies are often analyzed together for the purposes of combining information from several studies of the same disease or comparing results across different disorders. We provide a valid and efficient approach to such meta-analysis, allowing for overlapping study subjects. The available data may contain individual participant records or only meta-analytic summary results. Simulation studies demonstrate that failure to account for overlapping subjects can greatly inflate type I error when combining results from multiple studies of the same disease and can drastically reduce power when comparing results across different disorders. In addition, the proposed approach can be substantially more powerful than the simple approach of splitting the overlapping subjects among studies, especially for comparing results across different disorders. The advantages of the new approach are illustrated with empirical data from two sets of genome-wide association studies.     

Phylogenetic information and experimental design in molecular systematics.

Despite the widespread perception that evolutionary inference from molecular sequences is a statistical problem, there has been very little attention paid to questions of experimental design. Previous consideration of this topic has led to little more than an empirical folklore regarding the choice of suitable genes for analysis, and to dispute over the best choice of taxa for inclusion in data sets. I introduce what I believe are new methods that permit the quantification of phylogenetic information in a sequence alignment. The methods use likelihood calculations based on Markov-process models of nucleotide substitution allied with phylogenetic trees, and allow a general approach to optimal experimental design. Two examples are given, illustrating realistic problems in experimental design in molecular phylogenetics and suggesting more general conclusions about the choice of genomic regions, sequence lengths and taxa for evolutionary studies.     

Phylogenetic uncertainty revisited: Implications for ecological analyses

Ecologists and biogeographers usually rely on a single phylogenetic tree to study evolutionary processes that affect macroecological patterns. This approach ignores the fact that each phylogenetic tree is a hypothesis about the evolutionary history of a clade, and cannot be directly observed in nature. Also, trees often leave out many extant species, or include missing species as polytomies because of a lack of information on the relationship among taxa. Still, researchers usually do not quantify the effects of phylogenetic uncertainty in ecological analyses. We propose here a novel analytical strategy to maximize the use of incomplete phylogenetic information, while simultaneously accounting for several sources of phylogenetic uncertainty that may distort statistical inferences about evolutionary processes. We illustrate the approach using a clade‐wide analysis of the hummingbirds, evaluating how different sources of uncertainty affect several phylogenetic comparative analyses of trait evolution and biogeographic patterns. Although no statistical approximation can fully substitute for a complete and robust phylogeny, the method we describe and illustrate enables researchers to broaden the number of clades for which studies informed by evolutionary relationships are possible, while allowing the estimation and control of statistical error that arises from phylogenetic uncertainty. Software tools to carry out the necessary computations are offered.     

Genome phylogeny based on short-range correlations in DNA sequences.

The surprising fact that global statistical properties computed on a genomewide scale may reveal species information has first been observed in studies of dinucleotide frequencies. Here we will look at the same phenomenon with a totally different statistical approach. We show that patterns in the short-range statistical correlations in DNA sequences serve as evolutionary fingerprints of eukaryotes. All chromosomes of a species display the same characteristic pattern, markedly different from those of other species. The chromosomes of a species are sorted onto the same branch of a phylogenetic tree due to this correlation pattern. The average correlation between nucleotides at a distance k is quantified in two independent ways: (i) by estimating it from a higher-order Markov process and (ii) by computing the mutual information function at a distance k. We show how the quality of phylogenetic reconstruction depends on the range of correlation strengths and on the length of the underlying sequence segment. This concept of the correlation pattern as a phylogenetic signature of eukaryote species combines two rather distant domains of research, namely phylogenetic analysis based on molecular observation and the study of the correlation structure of DNA sequences.     

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.     

REEXAMINING THE RELATIONSHIP BETWEEN BODY SIZE AND TONAL SIGNALS FREQUENCY IN WHALES: A COMPARATIVE APPROACH USING A NOVEL PHYLOGENY

A negative relationship between cetacean body size and tonal sound minimum and maximum frequencies has been demonstrated in several studies using standard statistical approaches where species are considered independent data points. Such studies, however, fail to account for known dependencies among related species—shared similarity due to common ancestry. Here we test these hypotheses by generating the most complete species level cetacean phylogeny to date, which we then use to reconstruct the evolutionary history of body size and standard tonal sounds parameters (minimum, maximum, and center frequency). Our results show that when phylogenetic relationships are considered the correlation between body size (length or mass) and minimum frequency is corroborated with approximately 27% of the variation in tonal sound frequency being explained by body size compared to 86% to 93% explained when phylogenetic relationships are not considered. Central frequency also correlates with body size in toothed whales, but for other tonal sound frequency parameters, including maximum frequency, this hypothesized correlation disappears. Therefore, constraints imposed by body size seem to have played a role in the evolution of minimum frequency but alternative hypotheses are required to explain variation in maximum frequency.     

Ecological and evolutionary genetics of Arabidopsis

The crucifer Arabidopsis thaliana has been the subject of intense research into molecular and developmental genetics. One of the consequences of having this wealth of physiological and molecular data available, is that ecologists and evolutionary biologists have begun to incorporate this model system into their studies. Current research on A. thaliana and its close relatives ably illustrates the potential for synergy between mechanistic and organismal biology. On the one hand, mechanistically oriented research can be placed in an historical context, which takes into account the particular phylogenetic history and ecology of these species. This helps us to make sense of redundancies, anomalies and sub-optimalities that would otherwise be difficult to interpret. On the other hand, ecologists and evolutionary biologists now have the opportunity to investigate the physiological and molecular basis for the phenotypic changes they observe. This provides new insight into the mechanisms that influence evolutionary change.     

Evolutionary Models and Phylogenetic Signal Assessment via Mantel Test

Phylogenetically closely related species tend to be more similar to each other than to more distantly related ones, a pattern called phylogenetic signal. Appropriate tests to evaluate the association between phylogenetic relatedness and trait variation among species are employed in a myriad of eco-evolutionary studies. However, most tests available to date are only suitable for datasets describing continuous traits, and are most often applicable only for single trait analysis. The Mantel test is a useful method to measure phylogenetic signal for multiple (continuous, binary and/or categorical) traits. However, the classical Mantel test does not incorporate any evolutionary model (EM) in the analysis. Here, we describe a new analytical procedure, which incorporates explicitly an evolutionary model in the standard Mantel test (EM-Mantel). We run numerical simulations to evaluate its statistical properties, under different combinations of species pool size, trait type and number. Our results showed that EM-Mantel test has appropriate type I error and acceptable power, which increases with the strength of phylogenetic signal and with species pool size but depended on trait type. EM-Mantel test is a good alternative for measuring phylogenetic signal in binary and categorical traits and for datasets with multiple traits.     

A new bayesian method for fitting evolutionary models to comparative data with intraspecific variation

Phylogenetic comparative methods that incorporate intraspecific variability are relatively new and, so far, not especially widely used in empirical studies. In the present short article we will describe a new Bayesian method for fitting evolutionary models to comparative data that incorporates intraspecific variability. This method differs from an existing likelihood-based approach in that it requires no a priori inference about species means and variances; rather it takes phenotypic values from individuals and a phylogenetic tree as input, and then samples species means and variances, along with the parameters of the evolutionary model, from their joint posterior probability distribution. One of the most novel and intriguing attributes of this approach is that jointly sampling the species means with the evolutionary model parameters means that the model and tree can influence our estimates of species mean trait values, not just the reverse. In the present implementation, we first apply this method to the most widely used evolutionary model for continuously valued phenotypic trait data (Brownian motion). However, the general approach has broad applicability, which we illustrate by also fitting the λ model, another simple model for quantitative trait evolution on a phylogeny. We test our approach via simulation and by analyzing two empirical datasets obtained from the literature. Finally, we have implemented the methods described herein in a new function for the R statistical computing environment, and this function will be distributed as part of the 'phytools' R library.     

Taxon sampling, correlated evolution, and independent contrasts

Independent contrasts are widely used to incorporate phylogenetic information into studies of continuous traits, particularly analyses of evolutionary trait correlations, but the effects of taxon sampling on these analyses have received little attention. In this paper, simulations were used to investigate the effects of taxon sampling patterns and alternative branch length assignments on the statistical performance of correlation coefficients and sign tests; "full-tree" analyses based on contrasts at all nodes and "paired-comparisons" based only on contrasts of terminal taxon pairs were also compared. The simulations showed that random samples, with respect to the traits under consideration, provide statistically robust estimates of trait correlations. However, exact significance tests are highly dependent on appropriate branch length information; equal branch lengths maintain lower Type I error than alternative topological approaches, and adjusted critical values of the independent contrast correlation coefficient are provided for use with equal branch lengths. Nonrandom samples, with respect to univariate or bivariate trait distributions, introduce discrepancies between interspecific and phylogenetically structured analyses and bias estimates of underlying evolutionary correlations. Examples of nonrandom sampling processes may include community assembly processes, convergent evolution under local adaptive pressures, selection of a nonrandom sample of species from a habitat or life-history group, or investigator bias. Correlation analyses based on species pairs comparisons, while ignoring deeper relationships, entail significant loss of statistical power and as a result provide a conservative test of trait associations. Paired comparisons in which species differ by a large amount in one trait, a method introduced in comparative plant ecology, have appropriate Type I error rates and high statistical power, but do not correctly estimate the magnitude of trait correlations. Sign tests, based on full-tree or paired-comparison approaches, are highly reliable across a wide range of sampling scenarios, in terms of Type I error rates, but have very low power. These results provide guidance for selecting species and applying comparative methods to optimize the performance of statistical tests of trait associations.     

Does phylogeny matter? Assessing the impact of phylogenetic information in ecological meta‐analysis

Meta-analysis is increasingly used in ecology and evolutionary biology. Yet, in these fields this technique has an important limitation: phylogenetic non-independence exists among taxa, violating the statistical assumptions underlying traditional meta-analytic models. Recently, meta-analytical techniques incorporating phylogenetic information have been developed to address this issue. However, no syntheses have evaluated how often including phylogenetic information changes meta-analytic results. To address this gap, we built phylogenies for and re-analysed 30 published meta-analyses, comparing results for traditional vs. phylogenetic approaches and assessing which characteristics of phylogenies best explained changes in meta-analytic results and relative model fit. Accounting for phylogeny significantly changed estimates of the overall pooled effect size in 47% of datasets for fixed-effects analyses and 7% of datasets for random-effects analyses. Accounting for phylogeny also changed whether those effect sizes were significantly different from zero in 23 and 40% of our datasets (for fixed- and random-effects models, respectively). Across datasets, decreases in pooled effect size magnitudes after incorporating phylogenetic information were associated with larger phylogenies and those with stronger phylogenetic signal. We conclude that incorporating phylogenetic information in ecological meta-analyses is important, and we provide practical recommendations for doing so.     

Bridging meta-analysis and the comparative method: a test of seed size effect on germination after frugivores’ gut passage

Most studies using meta-analysis try to establish relationships between traits across taxa from interspecific databases and, thus, the phylogenetic relatedness among these taxa should be taken into account to avoid pseudoreplication derived from common ancestry. This paper illustrates, with a representative example of the relationship between seed size and the effect of frugivores gut on seed germination, that meta-analytic procedures can also be phylogenetically corrected by means of the comparative method. The conclusions obtained in the meta-analytical and phylogenetical approaches are very different. The meta-analysis revealed that the positive effects that gut passage had on seed germination increased with seed size in the case of gut passage through birds whereas decreased in the case of gut passage through non-flying mammals. However, once the phylogenetic relatedness among plant species was taken into account, the effects of gut passage on seed germination did not depend on seed size and were similar between birds and non-flying mammals. Some methodological considerations are given to improve the bridge between the meta-analysis and the comparative method.     

Testing Bergmann's rule and the resource seasonality hypothesis in Malagasy primates using GIS-based climate data

We tested four major hypotheses on the ecological aspects of body mass variation in extant Malagasy strepsirrhines: thermoregulation, resource seasonality/scarcity, resource quality, and primary productivity. These biogeographic hypotheses focus on the ecological aspects of body mass variation, largely ignoring the role of phylogeny for explaining body mass variation within lineages. We tested the independent effects of climate and resource-related variables on variation in body mass among Malagasy primates using recently developed comparative methods that account for phylogenetic history and spatial autocorrelation. We extracted data on lemur body mass and climate variables for a total of 43 species from 39 sites. Climatic data were obtained from the WorldClim database, which is based on climate data from weather stations compiled around the world. Using generalized linear models that incorporate parameters to account for phylogenetic and spatial autocorrelation, we found that diet and climate variables were weak predictors of lemur body mass. Moreover, there was a strong phylogenetic effect relative to the effects of space on lemur body mass in all models. Thus, we failed to find support for any of the four hypotheses on patterns of geography and body mass in extant strepsirrhines. Our results indicate that body mass has been conserved since early in the evolutionary history of each genus, while species diversified into different environmental niches. Our findings are in contrast to some previous studies that have suggested resource and climate related effects on body mass, though these studies have examined this question at different taxonomic and/or geographic scales.