Liam J. Revell

Size-Correction and Principal Components for Interspecific Comparative Studies

Phylogenetic methods for the analysis of species data are widely used in evolutionary studies. However, preliminary data transformations and data reduction procedures (such as a size-correction and principal components analysis, PCA) are often performed without first correcting for nonindependence among the observations for species. In the present short comment and attached R and MATLAB code, I provide an overview of statistically correct procedures for phylogenetic size-correction and PCA. I also show that ignoring phylogeny in preliminary transformations can result in significantly elevated variance and type I error in our statistical estimators, even if subsequent analysis of the transformed data is performed using phylogenetic methods. This means that ignoring phylogeny during preliminary data transformations can possibly lead to spurious results in phylogenetic statistical analyses of species data.

A PHYLOGENETIC TEST FOR ADAPTIVE CONVERGENCE IN ROCK-DWELLING LIZARDS

Abstract Phenotypic similarity of species occupying similar habitats has long been taken as strong evidence of adaptation, but this approach implicitly assumes that similarity is evolutionarily derived. However, even derived similarities may not represent convergent adaptation if the similarities did not evolve as a result of the same selection pressures; an alternative possibility is that the similar features evolved for different reasons, but subsequently allowed the species to occupy the same habitat, in which case the convergent evolution of the same feature by species occupying similar habitats would be the result of exaptation. Many lizard lineages have evolved to occupy vertical rock surfaces, a habitat that places strong functional and ecological demands on lizards. We examined four clades in which species that use vertical rock surfaces exhibit long hindlimbs and flattened bodies. Morphological change on the phylogenetic branches leading to the rock-dwelling species in the four clades differed from change on other branches of the phylogeny; evolutionary transitions to rock-dwelling generally were associated with increases in limb length and decreases in head depth. Examination of particular characters revealed several different patterns of evolutionary change. Rock-dwelling lizards exhibited similarities in head depth as a result of both adaptation and exaptation. Moreover, even though rock-dwelling species generally had longer limbs than their close relatives, clade-level differences in limb length led to an overall lack of difference between rock- and non-rock-dwelling lizards. These results indicate that evolutionary change in the same direction in independent lineages does not necessarily produce convergence, and that the existence of similar advantageous structures among species independently occupying the same environment may not indicate adaptation.

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.

BEHAVIORAL CONVERGENCE AND ADAPTIVE RADIATION: EFFECTS OF HABITAT USE ON TERRITORIAL BEHAVIOR IN ANOLIS LIZARDS

Most studies of adaptive radiations focus on morphological aspects of differentiation, yet behavior is also an important component of evolutionary diversification, often mediating the relationship between animal ecology and morphology. In species within radiations that are convergent in ecology and morphology, we then also expect convergence in behavior. Here, we examined 13 Anolis lizard species to determine whether territorial strategies have evolved convergently with morphology and habitat use. We evaluated two aspects of territoriality: behavioral defense of space via territorial displays, and territory overlap within and between sexes. Controlling for the phylogenetic relationships of the taxa in our study, we found that species similar in perch height and diameter convergently evolved patterns of territory overlap, whereas species similar in habitat visibility (the proportion of space that can be seen from a perch) convergently evolved display behavior. We also found that species with greater display time have more extensive male–male territory overlap. This study provides strong evidence for the role of habitat in the evolution of territoriality and suggests that the social structure of a species ultimately evolves in concert with habitat use and morphology.

THE G MATRIX UNDER FLUCTUATING CORRELATIONAL MUTATION AND SELECTION

Abstract Theoretical quantitative genetics provides a framework for reconstructing past selection and predicting future patterns of phenotypic differentiation. However, the usefulness of the equations of quantitative genetics for evolutionary inference relies on the evolutionary stability of the additive genetic variance–covariance matrix (G matrix). A fruitful new approach for exploring the evolutionary dynamics of G involves the use of individual-based computer simulations. Previous studies have focused on the evolution of the eigenstructure of G. An alternative approach employed in this paper uses the multivariate response-to-selection equation to evaluate the stability of G. In this approach, I measure similarity by the correlation between response-to-selection vectors due to random selection gradients. I analyze the dynamics of G under several conditions of correlational mutation and selection. As found in a previous study, the eigenstructure of G is stabilized by correlational mutation and selection. However, over broad conditions, instability of G did not result in a decreased consistency of the response to selection. I also analyze the stability of G when the correlation coefficients of correlational mutation and selection and the effective population size change through time. To my knowledge, no prior study has used computer simulations to investigate the stability of G when correlational mutation and selection fluctuate. Under these conditions, the eigenstructure of G is unstable under some simulation conditions. Different results are obtained if G matrix stability is assessed by eigenanalysis or by the response to random selection gradients. In this case, the response to selection is most consistent when certain aspects of the eigenstructure of G are least stable and vice versa.

PCCA: a program for phylogenetic canonical correlation analysis

UNLABELLED PCCA (phylogenetic canonical correlation analysis) is a new program for canonical correlation analysis of multivariate, continuously valued data from biological species. Canonical correlation analysis is a technique in which derived variables are obtained from two sets of original variables whereby the correlations between corresponding derived variables are maximized. It is a very useful multivariate statistical method for the calculation and analysis of correlations between character sets. The program controls for species non-independence due to phylogenetic history and computes canonical coefficients, correlations and scores; and conducts hypothesis tests on the canonical correlations. It can also compute a multivariate version of Pagels lambda, which can then be used in the phylogenetic transformation. AVAILABILITY PCCA is distributed as DOS/Windows, Mac OS X and Linux/Unix executables with a detailed program manual and is freely available on the World Wide Web at: http://anolis.oeb.harvard.edu/~liam/programs/.

On the Analysis of Evolutionary Change along Single Branches in a Phylogeny

Comparative biologists are sometimes interested in estimating the evolutionary rate along single branches in a phylogeny. I evaluate two methods by which the evolutionary rate along single branches can be compared with the evolutionary rate throughout the rest of the tree. The first is McPeek’s contrasts method, and the second is a likelihood method presented independently in two recently published studies. Although the latter method was developed primarily for the comparison of rates among clades, the approach is equally suited for the analysis of evolutionary rate along single or isolated branches. I find that Type I error is acceptable in both methods but that power and parameter estimation are relatively poor in McPeek’s method as it is typically applied.

A phylogenetic perspective on foraging mode evolution and habitat use in West Indian Anolis lizards

Although many descriptive studies of foraging mode have been performed, the factors that underlie the evolution of foraging mode remain poorly understood. To test the hypothesis that foraging mode evolution is affected by habitat use, we analysed two data sets including 31 species of West Indian Anolis lizards. In this genus, the same suite of habitat specialists (or ecomorphs) has evolved on four islands, providing the replication necessary to evaluate the generality of the relationship between foraging mode and habitat use. Using habitat and behavioural data, we conducted phylogenetic comparative analyses to determine whether species of the same ecomorph have evolved similar foraging behaviour and whether differences in foraging mode are associated with differences in habitat use. We found that Anolis species show substantial variation in foraging behaviour, including differences in movement and eating rates. Furthermore, variation among ecomorphs indicates that foraging behaviour is related to habitat use, although the specific environmental factors driving foraging divergence are unclear. Our results show that foraging mode is an evolutionarily labile trait that is influenced by evolution of habitat use.

TESTING THE GENETIC CONSTRAINT HYPOTHESIS IN A PHYLOGENETIC CONTEXT: A SIMULATION STUDY

Abstract Quantitative genetic theory predicts that when populations diverge by drift the interspecific divergence (D matrix), calculated from species means, will be proportional to the average value of the additive genetic variance–covariance matrix, or G matrix. Most empirical studies in which this hypothesis has been investigated have ignored phylogenetic nonindependence among included taxa. Baker and Wilkinson (2003; also Revell et al. 2007) used a test for constraint in which the D matrix is calculated from phylogenetically independent contrasts (Felsenstein 1985) instead of directly from the species means. I use computer simulations to show that, on average, when the process of evolution is genetic drift, the divergence matrix calculated from independent contrasts (DIC) is more highly correlated with G than is the divergence matrix calculated ignoring phylogenetic nonindependence (D). This effect is more pronounced when speciation is initially slow but increases over time than when speciation decreases over time. Finally, when evolution is primarily by drift but phenotype space is bounded (as if by functional constraint) the average correlation is decreased between both G and D or DIC, however the correlation between G and DIC is much larger than between G and D. Although limited in scope, to my knowledge this is the first study to use individual-based quantitative genetic simulations in a phylogenetic context.