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.     

A phylogenetic comparative method for evaluating trait coevolution across two phylogenies for sets of interacting species

Evaluating trait correlations across species within a lineage via phylogenetic regression is fundamental to comparative evolutionary biology, but when traits of interest are derived from two sets of lineages that coevolve with one another, methods for evaluating such patterns in a dual‐phylogenetic context remain underdeveloped. Here, we extend multivariate permutation‐based phylogenetic regression to evaluate trait correlations in two sets of interacting species while accounting for their respective phylogenies. This extension is appropriate for both univariate and multivariate response data, and may use one or more independent variables, including environmental covariates. Imperfect correspondence between species in the interacting lineages can also be accommodated, such as when species in one lineage associate with multiple species in the other, or when there are unmatched taxa in one or both lineages. For both univariate and multivariate data, the method displays appropriate type I error, and statistical power increases with the strength of the trait covariation and the number of species in the phylogeny. These properties are retained even when there is not a 1:1 correspondence between lineages. Finally, we demonstrate the approach by evaluating the evolutionary correlation between traits in fig species and traits in their agaonid wasp pollinators. R computer code is provided.     

Hypothesis testing in comparative and experimental studies of function-valued traits

Many traits of evolutionary interest, when placed in their developmental, physiological, or environmental contexts, are function-valued. For instance, gene expression during development is typically a function of the age of an organism and physiological processes are often a function of environment. In comparative and experimental studies, a fundamental question is whether the function-valued trait of one group is different from another. To address this question, evolutionary biologists have several statistical methods available. These methods can be classified into one of two types: multivariate and functional. Multivariate methods, including univariate repeated-measures analysis of variance (ANOVA), treat each trait as a finite list of data. Functional methods, such as repeated-measures regression, view the data as a sample of points drawn from an underlying function. A key difference between multivariate and functional methods is that functional methods retain information about the ordering and spacing of a set of data values, information that is discarded by multivariate methods. In this study, we evaluated the importance of that discarded information in statistical analyses of function-valued traits. Our results indicate that functional methods tend to have substantially greater statistical power than multivariate approaches to detect differences in a function-valued trait between groups.     

The comparative ecology and biogeography of parasites

Comparative ecology uses interspecific relationships among traits, while accounting for the phylogenetic non-independence of species, to uncover general evolutionary processes. Applied to biogeographic questions, it can be a powerful tool to explain the spatial distribution of organisms. Here, we review how comparative methods can elucidate biogeographic patterns and processes, using analyses of distributional data on parasites (fleas and helminths) as case studies. Methods exist to detect phylogenetic signals, i.e. the degree of phylogenetic dependence of a given character, and either to control for these signals in statistical analyses of interspecific data, or to measure their contribution to variance. Parasite–host interactions present a special case, as a given trait may be a parasite trait, a host trait or a property of the coevolved association rather than of one participant only. For some analyses, it is therefore necessary to correct simultaneously for both parasite phylogeny and host phylogeny, or to evaluate which has the greatest influence on trait expression. Using comparative approaches, we show that two fundamental properties of parasites, their niche breadth, i.e. host specificity, and the nature of their life cycle, can explain interspecific and latitudinal variation in the sizes of their geographical ranges, or rates of distance decay in the similarity of parasite communities. These findings illustrate the ways in which phylogenetically based comparative methods can contribute to biogeographic research.     

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.     

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.     

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.     

Inferring life history from ovipositor morphology in parasitoid wasps using phylogenetic regression and discriminant analysis

Our understanding of the critical shift in life history among insect parasitoids from ectoparasitism to endoparasitism is hindered by the fact that this particular life history trait is not known for many phylogenetically important taxa. One method of coping with this problem is to seek correlations between the ovipositor structure and this life history trait among taxa whose life history is known, and then to use this to infer the trait in species whose life history in unknown. In one group of parasitoid wasps, the Ichneumonoidea (Hymenoptera), we scored a total of 20 morphometric and morphological characters of the ovipositor for 41 species whose life histories are known – representing all the main clades in which there have been independent transitions to endoparasitism plus a broad range of the ectoparasitoid groups; we then used phylogenetic regression and discriminant analyses to infer the life history of four species whose life histories are unknown. To allow for the effect of phylogenetic non-independence in the discriminant analysis, we carried out analyses using different randomly chosen representatives of the endoparasitoid clades (phylogenetic regression controls for phylogeny). These two methods gave congruent results from which we conclude that Megalohelcon and Gnamptodon are endoparasitoids, and Aspilodemon and Allobracon are ectoparasitoids. We discuss the consequences of these inferences for our understanding of the evolution of endoparasitism in the Ichneumonoidea.  © 2003 The Linnean Society of London. Zoological Journal of the Linnean Society , 2003, 139 , 213–228.     

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.     

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.     

A comparison of metrics for estimating phylogenetic signal under alternative evolutionary models

Several metrics have been developed for estimating phylogenetic signal in comparative data. These may be important both in guiding future studies on correlated evolution and for inferring broad-scale evolutionary and ecological processes (e.g., phylogenetic niche conservatism). Notwithstanding, the validity of some of these metrics is under debate, especially after the development of more sophisticated model-based approaches that estimate departure from particular evolutionary models (i.e., Brownian motion). Here, two of these model-based metrics (Blomberg’s K-statistics and Pagel’s λ) are compared with three statistical approaches [Moran’s I autocorrelation coefficient, coefficients of determination from the autoregressive method (ARM), and phylogenetic eigenvector regression (PVR)]. Based on simulations of a trait evolving under Brownian motion for a phylogeny with 209 species, we showed that all metrics are strongly, although non-linearly, correlated to each other. Our analyses revealed that statistical approaches provide valid results and may be still particularly useful when detailed phylogenies are unavailable or when trait variation among species is difficult to describe by more standard Brownian or O-U evolutionary models.     

TESTING FOR PHYLOGENETIC SIGNAL IN BIOLOGICAL TRAITS: THE UBIQUITY OF CROSS‐PRODUCT STATISTICS

To evaluate rates of evolution, to establish tests of correlation between two traits, or to investigate to what degree the phylogeny of a species assemblage is predictive of a trait value so‐called tests for phylogenetic signal are used. Being based on different approaches, these tests are generally thought to possess quite different statistical performances. In this article, we show that the Blomberg et al. K and K*, the Abouheif index, the Moran's I, and the Mantel correlation are all based on a cross‐product statistic, and are thus all related to each other when they are associated to a permutation test of phylogenetic signal. What changes is only the way phylogenetic and trait similarities (or dissimilarities) among the tips of a phylogeny are computed. The definitions of the phylogenetic and trait‐based (dis)similarities among tips thus determines the performance of the tests. We shortly discuss the biological and statistical consequences (in terms of power and type I error of the tests) of the observed relatedness among the statistics that allow tests for phylogenetic signal. Blomberg et al. K* statistic appears as one on the most efficient approaches to test for phylogenetic signal. When branch lengths are not available or not accurate, Abouheif's C_mean statistic is a powerful alternative to K*.     

Association analysis of population-based quantitative trait data: an assessment of ANOVA

The classical analysis of variance (ANOVA) compares the means of different groups under the assumption that the variances within each of the groups are equal. However, for genetic studies of complex disorders, it is not reasonable to assume that variance of a quantitative trait within each genotype at the trait locus will be equal. Thus, the use of ANOVA may lead to misleading association inferences. In this article, we perform a simulation-based study to assess the rate of false positives and the power of ANOVA under various probability distributions of the quantitative trait and different genetic parameters such as allele frequencies and coefficient of linkage disequilibrium.     

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.     

Recent progress in reconstructing angiosperm phylogeny

In the past year, the study of angiosperm phylogeny has moved from tentative inferences based on relatively small data matrices into an era of sophisticated, multigene analyses and significantly greater confidence. Recent studies provide both strong statistical support and mutual corroboration for crucial aspects of angiosperm phylogeny. These include identifying the earliest extant lineages of angiosperms, confirming Amborella as the sister of all other angiosperms, confirming some previously proposed lineages and redefining other groups consistent with their phylogeny. This phylogenetic framework enables the exploration of both genotypic and phenotypic diversification among angiosperms.     

Putting phylogeny into the analysis of biological traits: A methodological approach

Phylogenetic comparative methods have long considered phylogenetic signal as a source of statistical bias in the correlative analysis of biological traits. However, the main life-history strategies existing in a set of taxa are often combinations of life history traits that are inherently phylogenetically structured. In this paper, we present a method for identifying evolutionary strategies from large sets of biological traits, using phylogeny as a source of meaningful historical and ecological information. Our methodology extends a multivariate method developed for the analysis of spatial patterns, and relies on finding combinations of traits that are phylogenetically autocorrelated. Using extensive simulations, we show that our method efficiently uncovers phylogenetic structures with respect to various tree topologies, and remains powerful in cases where a large majority of traits are not phylogenetically structured. Our methodology is illustrated using empirical data, and implemented in the adephylo package for the free software R.     

INTEGRATING FOSSILS WITH MOLECULAR PHYLOGENIES IMPROVES INFERENCE OF TRAIT EVOLUTION

Comparative biologists often attempt to draw inferences about tempo and mode in evolution by comparing the fit of evolutionary models to phylogenetic comparative data consisting of a molecular phylogeny with branch lengths and trait measurements from extant taxa. These kinds of approaches ignore historical evidence for evolutionary pattern and process contained in the fossil record. In this article, we show through simulation that incorporation of fossil information dramatically improves our ability to distinguish among models of quantitative trait evolution using comparative data. We further suggest a novel Bayesian approach that allows fossil information to be integrated even when explicit phylogenetic hypotheses are lacking for extinct representatives of extant clades. By applying this approach to a comparative dataset comprising body sizes for caniform carnivorans, we show that incorporation of fossil information not only improves ancestral state estimates relative to those derived from extant taxa alone, but also results in preference of a model of evolution with trend toward large body size over alternative models such as Brownian motion or Ornstein–Uhlenbeck processes. Our approach highlights the importance of considering fossil information when making macroevolutionary inference, and provides a way to integrate the kind of sparse fossil information that is available to most evolutionary biologists.     

An expectation-maximization-likelihood-ratio test for handling missing data: application in experimental crosses

The mapping of quantitative trait loci (QTL) is an important research question in animal and human studies. Missing data are common in such study settings, and ignoring such missing data may result in biased estimates of the genotypic effect and thus may eventually lead to errant results and incorrect inferences. In this article, we developed an expectation-maximization (EM)-likelihood-ratio test (LRT) in QTL mapping. Simulation studies based on two different types of phylogenetic models revealed that the EM-LRT, a statistical technique that uses EM-based parameter estimates in the presence of missing data, offers a greater statistical power compared with the ordinary analysis-of-variance (ANOVA)-based test, which discards incomplete data. We applied both the EM-LRT and the ANOVA-based test in a real data set collected from F2 intercross studies of inbred mouse strains. It was found that the EM-LRT makes an optimal use of the observed data and its advantages over the ANOVA F-test are more pronounced when more missing data are present. The EM-LRT method may have important implications in QTL mapping in experimental crosses.     

Comparative bioacoustics: a roadmap for quantifying and comparing animal sounds across diverse taxa

Animals produce a wide array of sounds with highly variable acoustic structures. It is possible to understand the causes and consequences of this variation across taxa with phylogenetic comparative analyses. Acoustic and evolutionary analyses are rapidly increasing in sophistication such that choosing appropriate acoustic and evolutionary approaches is increasingly difficult. However, the correct choice of analysis can have profound effects on output and evolutionary inferences. Here, we identify and address some of the challenges for this growing field by providing a roadmap for quantifying and comparing sound in a phylogenetic context for researchers with a broad range of scientific backgrounds. Sound, as a continuous, multidimensional trait can be particularly challenging to measure because it can be hard to identify variables that can be compared across taxa and it is also no small feat to process and analyse the resulting high-dimensional acoustic data using approaches that are appropriate for subsequent evolutionary analysis. Additionally, terminological inconsistencies and the role of learning in the development of acoustic traits need to be considered. Phylogenetic comparative analyses also have their own sets of caveats to consider. We provide a set of recommendations for delimiting acoustic signals into discrete, comparable acoustic units. We also present a three-stage workflow for extracting relevant acoustic data, including options for multivariate analyses and dimensionality reduction that is compatible with phylogenetic comparative analysis. We then summarize available phylogenetic comparative approaches and how they have been used in comparative bioacoustics, and address the limitations of comparative analyses with behavioural data. Lastly, we recommend how to apply these methods to acoustic data across a range of study systems. In this way, we provide an integrated framework to aid in quantitative analysis of cross-taxa variation in animal sounds for comparative phylogenetic analysis. In addition, we advocate the standardization of acoustic terminology across disciplines and taxa, adoption of automated methods for acoustic feature extraction, and establishment of strong data archival practices for acoustic recordings and data analyses. Combining such practices with our proposed workflow will greatly advance the reproducibility, biological interpretation, and longevity of comparative bioacoustic studies.     

Orthonormal transform to decompose the variance of a life-history trait across a phylogenetic tree

In recent years, there has been an increased interest in studying the variability of a quantitative life-history trait across a set of species sharing a common phylogeny. However, such studies have suffered from an insufficient development of statistical methods aimed at decomposing the trait variance with respect to the topological structure of the tree. Here we propose a new and generic approach that expresses the topological properties of the phylogenetic tree via an orthonormal basis, which is further used to decompose the trait variance. Such a decomposition provides a structure function, referred to as an "orthogram," which is relevant to characterize in both graphical and statistical aspects the dependence of trait values on the topology of the tree ("phylogenetic dependence"). We also propose four complementary test statistics to be computed from orthogram values that help to diagnose both the intensity and the nature of phylogenetic dependence. The relevance of the method is illustrated by the analysis of three phylogenetic data sets, drawn from the literature and typifying contrasted levels and aspects of phylogenetic dependence. Freely available routines which have been programmed in the R framework are also proposed.