THE QUANTITATIVE ASSESSMENT OF PHYLOGENETIC CONSTRAINTS IN COMPARATIVE ANALYSES: SEXUAL DIMORPHISM IN BODY WEIGHT AMONG PRIMATES

We have presented a formal model for the quantitative analysis of phylogenetic and specific effects on the distribution of trait values among species. Total trait values are divided into phylogenetic values, inherited from an ancestral species, and specific values, the result of independent evolution. This allows a quantitative assessment of the strength of the phylogenetic inertia, or burden, displayed by a character in a lineage, so that questions concerning the relative importance of phylogenetic constraints in evolution can be answered. The separation of phylogenetic from specific effects proposed here also allows phylogenetic factors to be explicitly included in cross-species comparative analyses of adaptation. This solves a long-standing problem in evolutionary comparative studies. Only species' specific values can provide information concerning the independent evolution of characters in a set of related species. Therefore, only correlations among specific values for traits may be used as evidence for adaptation in cross-species comparative analyses. The phylogenetic autocorrelation model was applied to a comparative analysis of the determinants of sexual dimorphism in weight among 44 primate species. In addition to sexual dimorphism in weight, mating system, habitat, diet, and size (weight itself) were included in the analysis. All of the traits, except diet, were substantially influenced by phylogenetic inertia. The comparative analysis of the determinants of sexual dimorphism in weight indicates that 50% of the variation among primate species is due to phylogeny. Size, or scaling, could account for a total of 36% of the variance, making it almost as important as phylogeny in determining the level of dimorphism displayed by a species. Habitat, mating system, and diet follow, accounting for minor amounts of variation. Thus, in attempting to explain why a particular modern primate species is very dimorphic compared to other primates, we would say first because its ancestor was more dimorphic than average, second because it is a relatively large species, and third because it is terrestrial, polygynous, and folivorous.     

A comparative method for studying adaptation to a randomly evolving environment

Most phylogenetic comparative methods used for testing adaptive hypotheses make evolutionary assumptions that are not compatible with evolution toward an optimal state. As a consequence they do not correct for maladaptation. The "evolutionary regression" that is returned is more shallow than the optimal relationship between the trait and environment. We show how both evolutionary and optimal regressions, as well as phylogenetic inertia, can be estimated jointly by a comparative method built around an Ornstein-Uhlenbeck model of adaptive evolution. The method considers a single trait adapting to an optimum that is influenced by one or more continuous, randomly changing predictor variables.     

AN EIGENVECTOR METHOD FOR ESTIMATING PHYLOGENETIC INERTIA

We propose a new method to estimate and correct for phylogenetic inertia in comparative data analysis. The method, called phylogenetic eigenvector regression (PVR) starts by performing a principal coordinate analysis on a pairwise phylogenetic distance matrix between species. Traits under analysis are regressed on eigenvectors retained by a broken-stick model in such a way that estimated values express phylogenetic trends in data and residuals express independent evolution of each species. This partitioning is similar to that realized by the spatial autoregressive method, but the method proposed here overcomes the problem of low statistical performance that occurs with autoregressive method when phylogenetic correlation is low or when sample size is too small to detect it. Also, PVR is easier to perform with large samples because it is based on well-known techniques of multivariate and regression analyses. We evaluated the performance of PVR and compared it with the autoregressive method using real datasets and simulations. A detailed worked example using body size evolution of Carnivora mammals indicated that phylogenetic inertia in this trait is elevated and similarly estimated by both methods. In this example, Type I error at α = 0.05 of PVR was equal to 0.048, but an increase in the number of eigenvectors used in the regression increases the error. Also, similarity between PVR and the autoregressive method, defined by correlation between their residuals, decreased by overestimating the number of eigenvalues necessary to express the phylogenetic distance matrix. To evaluate the influence of cladogram topology on the distribution of eigenvalues extracted from the double-centered phylogenetic distance matrix, we analyzed 100 randomly generated cladograms (up to 100 species). Multiple linear regression of log transformed variables indicated that the number of eigenvalues extracted by the broken-stick model can be fully explained by cladogram topology. Therefore, the broken-stick model is an adequate criterion for determining the correct number of eigenvectors to be used by PVR. We also simulated distinct levels of phylogenetic inertia by producing a trend across 10, 25, and 50 species arranged in “comblike” cladograms and then adding random vectors with increased residual variances around this trend. In doing so, we provide an evaluation of the performance of both methods with data generated under different evolutionary models than tested previously. The results showed that both PVR and autoregressive method are efficient in detecting inertia in data when sample size is relatively high (more than 25 species) and when phylogenetic inertia is high. However, PVR is more efficient at smaller sample sizes and when level of phylogenetic inertia is low. These conclusions were also supported by the analysis of 10 real datasets regarding body size evolution in different animal clades. We concluded that PVR can be a useful alternative to an autoregressive method in comparative data analysis.     

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.     

Effects of sample size and intraspecific variation in phylogenetic comparative studies: a meta‐analytic review

Comparative analyses aim to explain interspecific variation in phenotype among taxa. In this context, phylogenetic approaches are generally applied to control for similarity due to common descent, because such phylogenetic relationships can produce spurious similarity in phenotypes (known as phylogenetic inertia or bias). On the other hand, these analyses largely ignore potential biases due to within‐species variation. Phylogenetic comparative studies inherently assume that species‐specific means from intraspecific samples of modest sample size are biologically meaningful. However, within‐species variation is often significant, because measurement errors, within‐ and between‐individual variation, seasonal fluctuations, and differences among populations can all reduce the repeatability of a trait. Although simulations revealed that low repeatability can increase the type I error in a phylogenetic study, researchers only exercise great care in accounting for similarity in phenotype due to common phylogenetic descent, while problems posed by intraspecific variation are usually neglected. A meta‐analysis of 194 comparative analyses all adjusting for similarity due to common phylogenetic descent revealed that only a few studies reported intraspecific repeatabilities, and hardly any considered or partially dealt with errors arising from intraspecific variation. This is intriguing, because the meta‐analytic data suggest that the effect of heterogeneous sampling can be as important as phylogenetic bias, and thus they should be equally controlled in comparative studies. We provide recommendations about how to handle such effects of heterogeneous sampling.     

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.     

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.     

Using heterochrony plots to detect the dissociated coevolution of characters

The comparison of developmental sequences among species is notoriously difficult. Here, heterochrony plots are introduced as a new graphic method to detect temporal shifts in the development of characters in pair-wise species comparisons. Plotting the timing of character development in one species against the timing of character development in another species allows us to compare a principally unlimited number of characters simultaneously and can detect whether suites of characters are dissociated from one another or not. Such heterochrony plots can be embedded into a comparative phylogenetic analysis in order to establish whether observed patterns of character codissociation are indeed due to their dissociated coevolution. Comparative phylogenetic analysis may also reveal multiple independent events of dissociated coevolution of the same suite of characters in a certain lineage, suggesting that the characters of this suite reciprocally constrain their evolutionary modifiability, thereby forming a unit of evolution. This ability to identify units of evolution is a prerequisite for assessing the validity of recently proposed scenarios, suggesting that modules of development and/or function tend to act as units of evolution. Starting from a detailed heterochrony plot comparing development in the direct developing frog Eleutherodactylus coqui and in the biphasically developing frog Discoglossus pictus, this comparative approach is illustrated focusing on the evolution of development of limbs, the nervous system and the pharyngeal arches in amphibians.     

Macroevolution of life‐history traits in passerine birds: adaptation and phylogenetic inertia

We used a recent passerine phylogeny and comparative method to evaluate the macroevolution of body and egg mass, incubation and fledging periods, time to independence and time with parents of the main passerine lineages. We hypothesised that passerine reproductive traits are affected by adaptation to both past and present environmental factors and phenotypic attributes such as body mass. Our results suggest that the evolution of body and egg mass, time to independence, incubation and fledging times are affected by strong phylogenetic inertia and that these breeding traits are all affected by body mass. Time with parents, where major lineages exhibit their own fixed optima and body mass does not have an effect, and clutch size which is affected by body mass and additionally by climate regimes, do not exhibit any phylogenetic inertia.     

Getting in shape: adaptation and phylogenetic inertia in morphology of Australian anuran larvae

The external morphology of frog larvae is predicted to vary among habitats, for a variety of functional reasons. I performed a phylogenetic comparative study to test whether correlations between habitat and the shape of the tadpole and its oral disc are adaptive in 82 species from south‐eastern Australia in the families Hylidae and Myobatrachidae. Habitat distributions and phylogenetic relationships were compiled from the literature and shape was quantified using geometric morphometric analysis of published drawings. Results indicate that shape evolved towards different optima in different habitats while also showing appreciable levels of phylogenetic inertia. Within myobatrachids, evolution of terrestrial tadpoles was associated with a short and shallow head/body and a shallow tail. In aquatic species, the use of benthic microhabitats was correlated with a long shallow tail, dorsal eye position, shallow head/body and ventral mouth with robust jaw sheaths. Even traits with evidence for adaptation evolved slowly in response to habitat shifts, usually requiring ≥10 million years to evolve half‐way to a new optimum. Although these findings support adaptive evolution of tadpole body form, they also highlight a strong influence of ancestral character states and indicate that phenotypes in extant species are partly maladaptive.     

A phylogenetic approach to cultural evolution

There has been a rapid increase in the use of phylogenetic methods to study the evolution of languages and culture. Languages fit a tree model of evolution well, at least in their basic vocabulary, challenging the view that blending, or admixture among neighbouring groups, was predominant in cultural history. Here, we argue that we can use language trees to test hypotheses about not only cultural history and diversification, but also bio-cultural adaptation. Phylogenetic comparative methods take account of the non-independence of cultures (Galton's problem), which can cause spurious statistical associations in comparative analyses. Advances in phylogenetic methods offer new possibilities for the analysis of cultural evolution, including estimating the rate of evolution and the direction of coevolutionary change of traits on the tree. They also enable phylogenetic uncertainty to be incorporated into the analyses, so that one does not have to treat phylogenetic trees as if they were known without error.     

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.     

STABILIZING SELECTION AND THE COMPARATIVE ANALYSIS OF ADAPTATION

Comparative studies tend to differ from optimality and functionality studies in how they treat adaptation. While the comparative approach focuses on the origin and change of traits, optimality studies assume that adaptations are maintained at an optimum by stabilizing selection. This paper presents a model of adaptive evolution on a macroevolutionary time scale that includes the maintenance of traits at adaptive optima by stabilizing selection as the dominant evolutionary force. Interspecific variation is treated as variation in the position of adaptive optima. The model illustrates how phylogenetic constraints not only lead to correlations between phylogenetically related species, but also to imperfect adaptations. From this model, a statistical comparative method is derived that can be used to estimate the effect of a selective factor on adaptive optima in a way that would be consistent with an optimality study of adaptation to this factor. The method is illustrated with an analysis of dental evolution in fossil horses. The use of comparative methods to study evolutionary trends is also discussed.     

General quantitative genetic methods for comparative biology: phylogenies,taxonomies and multi‐trait models for continuous and categorical characters

Although many of the statistical techniques used in comparative biology were originally developed in quantitative genetics, subsequent development of comparative techniques has progressed in relative isolation. Consequently, many of the new and planned developments in comparative analysis already have well‐tested solutions in quantitative genetics. In this paper, we take three recent publications that develop phylogenetic meta‐analysis, either implicitly or explicitly, and show how they can be considered as quantitative genetic models. We highlight some of the difficulties with the proposed solutions, and demonstrate that standard quantitative genetic theory and software offer solutions. We also show how results from Bayesian quantitative genetics can be used to create efficient Markov chain Monte Carlo algorithms for phylogenetic mixed models, thereby extending their generality to non‐Gaussian data. Of particular utility is the development of multinomial models for analysing the evolution of discrete traits, and the development of multi‐trait models in which traits can follow different distributions. Meta‐analyses often include a nonrandom collection of species for which the full phylogenetic tree has only been partly resolved. Using missing data theory, we show how the presented models can be used to correct for nonrandom sampling and show how taxonomies and phylogenies can be combined to give a flexible framework with which to model dependence.     

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.     

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.     

Recent developments in the analysis of comparative data

Comparative methods can be used to test ideas about adaptation by identifying cases of either parallel or convergent evolutionary change across taxa. Phylogenetic relationships must be known or inferred if comparative methods are to separate the cross-taxonomic covariation among traits associated with evolutionary change from that attributable to common ancestry. Only the former can be used to test ideas linking convergent or parallel evolutionary change to some aspect of the environment. The comparative methods that are currently available differ in how they manage the effects brought about by phylogenetic relationships. One method is applicable only to discrete data, and uses cladistic techniques to identify evolutionary events that depart from phylogenetic trends. Techniques for continuous variables attempt to control for phylogenetic effects in a variety of ways. One method examines the taxonomic distribution of variance to identify the taxa within which character variation is small. The method assumes that taxa with small amounts of variation are those in which little evolutionary change has occurred, and thus variation is unlikely to be independent of ancestral trends. Analyses are then concentrated among taxa that show more variation, on the assumption that greater evolutionary change in the character has taken place. Several methods estimate directly the extent to which ancestry can predict the observed variation of a character, and subtract the ancestral effect to reveal variation of phylogeny. Yet another can remove phylogenetic effects if the true phylogeny is known. One class of comparative methods controls for phylogenetic effects by searching for comparative trends within rather than across taxa. With current knowledge of phylogenies, there is a trade-off in the choice of a comparative method: those that control phylogenetic effects with greater certainty are either less applicable to real data, or they make restrictive or untestable assumptions. Those that rely on statistical patterns to infer phylogenetic effects may not control phylogeny as efficiently but are more readily applied to existing data sets.     

Primate comparative genomics: lemur biology and evolution

Comparative genome sequencing projects are providing insight into aspects of genome biology that raise new questions and challenge existing paradigms. Placement in the phylogenetic tree can often be a major determinant of which organism to choose for study. Lemurs hold a key position at the base of the primate evolutionary tree and will be highly informative for the genomics community by offering comparisons of primate-specific characteristics and processes. Combining research in chromosome evolution, genome evolution and behavior with lemur comparative genomic sequencing will offer insights into many levels of primate evolution. We discuss the current state of lemur cytogenetic and phylogenetic analyses, and suggest how focusing more genomic efforts on lemurs will be beneficial to understanding human and primate evolution, as well as disease, and will contribute to conservation efforts.