Random sampling of constrained phylogenies: conducting phylogenetic analyses when the phylogeny is partially known

Statistical randomization tests in evolutionary biology often require a set of random, computer-generated trees. For example, earlier studies have shown how large numbers of computer-generated trees can be used to conduct phylogenetic comparative analyses even when the phylogeny is uncertain or unknown. These methods were limited, however, in that (in the absence of molecular sequence or other data) they allowed users to assume that no phylogenetic information was available or that all possible trees were known. Intermediate situations where only a taxonomy or other limited phylogenetic information (e.g., polytomies) are available are technically more difficult. The current study describes a procedure for generating random samples of phylogenies while incorporating limited phylogenetic information (e.g., four taxa belong together in a subclade). The procedure can be used to conduct comparative analyses when the phylogeny is only partially resolved or can be used in other randomization tests in which large numbers of possible phylogenies are needed.     

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.     

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.     

RANDOM TREES AND THE COMPARATIVE METHOD: A CAUTIONARY TALE

One of the toughest problems facing comparative biology is the paucity of robust phylogenetic hypotheses for many taxonomic groups. Martins (1996) proposed a method to analyze comparative data in the absence of a known phylogeny using randomly generated trees. Before applying this method, however, researchers should be aware that (1) parameter estimates derived from this method essentially assume a star phylogeny, and thus, estimate the same evolutionary regression or correlation coefficient as traditional cross-species analyses; and (2) statistical conclusions derived from this method may be so conservative as to mask evolutionary patterns, such as Rensch's rule, and should be interpreted with caution.     

Detecting correlation between characters in a comparative analysis with uncertain phylogeny

Abstract.— The importance of accommodating the phylogenetic history of a group when performing a comparative analysis is now widely recognized. The typical approaches either assume the tree is known without error, or they base inferences on a collection of well-supported trees or on a collection of trees generated under a stochastic model of cladogenesis. However, these approaches do not adequately account for the uncertainty of phylogenetic trees in a comparative analysis, especially when data relevant to the phylogeny of a group are available. Here, we develop a method for performing comparative analyses that is based on an extension of Felsenstein's independent contrasts method. Uncertainties in the phylogeny, branch lengths, and other parameters are accommodated by averaging over all possible trees, weighting each by the probability that the tree is correct. We do this in a Bayesian framework and use Markov chain Monte Carlo to perform the high-dimensional summations and integrations required by the analysis. We illustrate the method using comparative characters sampled from Anolis lizards.     

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.     

Recognizing the forest for the trees: testing temporal patterns of cladogenesis using a null model of stochastic diversification

Computer simulations are developed and employed to examine the expected temporal distributions of nodes under a null model of stochastic lineage bifurcation and extinction. These Markovian models of phylogenetic process were constructed so as to permit direct comparisons against empirical phylogenetic trees generated from molecular or other information available solely from extant species. For replicate simulated phylads with n extant species, cumulative distribution functions (cdf's) of branching times were calculated, and compared (using the Kolmogorov-Smirnov test statistic D) to those from three published empirical trees. Molecular phylogenies for columbine plants and avian cranes showed statistically significant departures from the null expectations, in directions indicating recent and ancient species' radiations, respectively, whereas a molecular phylogeny for the Drosophila virilis species group showed no apparent historical clustering of branching events. Effects of outgroup choice and phylogenetic frame of reference were investigated for the columbines and found to have a predictable influence on the types of conclusions to be drawn from such analyses. To enable other investigators to statistically test for nonrandomness in temporal cladogenetic pattern in empirical trees generated from data on extant species, we present tables of mean cdf's and associated probabilities under the null model for expected branching times in phylads of varying size. The approaches developed in this report complement and extend those of other recent methods for employing null models to assess the statistical significance of pattern in evolutionary trees.      

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.     

The Use (and Misuse) of Phylogenetic Trees in Comparative Behavioral Analyses

Phylogenetic comparative methods play a critical role in our understanding of the adaptive origin of primate behaviors. To incorporate evolutionary history directly into comparative behavioral research, behavioral ecologists rely on strong, well-resolved phylogenetic trees. Phylogenies provide the framework on which behaviors can be compared and homologies can be distinguished from similarities due to convergent or parallel evolution. Phylogenetic reconstructions are also of critical importance when inferring the ancestral state of behavioral patterns and when suggesting the evolutionary changes that behavior has undergone. Improvements in genome sequencing technologies have increased the amount of data available to researchers. Recently, several primate phylogenetic studies have used multiple loci to produce robust phylogenetic trees that include hundreds of primate species. These trees are now commonly used in comparative analyses and there is a perception that we have a complete picture of the primate tree. But how confident can we be in those phylogenies? And how reliable are comparative analyses based on such trees? Herein, we argue that even recent molecular phylogenies should be treated cautiously because they rely on many assumptions and have many shortcomings. Most phylogenetic studies do not model gene tree diversity and can produce misleading results, such as strong support for an incorrect species tree, especially in the case of rapid and recent radiations. We discuss implications that incorrect phylogenies can have for reconstructing the evolution of primate behaviors and we urge primatologists to be aware of the current limitations of phylogenetic reconstructions when applying phylogenetic comparative methods.     

Phylogenetic analysis under reticulate evolution

The usual assumption that species have evolved from a common ancestor by a simple branching process--where each branch is genetically isolated--has been challenged by the observation of frequent hybridization between species in natural populations. In fact, most plant species are thought to have hybrid origins. This reticulate pattern of species evolution has posed problems in the definition of speciation and in phylogenetic reconstruction, especially when molecular data are used. As a result, hybridization has been largely treated as an evolutionary accident or statistical error in phylogenetic analysis. In this paper, I explicitly incorporate hybridization as an evolutionary occurrence and then conduct phylogenetic reconstruction. I first examine the reticulate evolution under a pure drift model, and then extend the theory to fit a mutation model. A least-squares method is developed for reconstructing a reticulate phylogeny using gene frequency data. The efficacy of the method under the pure drift model is verified via Monte Carlo simulations.     

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.     

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.     

The best of both worlds: Phylogenetic eigenvector regression and mapping

Eigenfunction analyses have been widely used to model patterns of autocorrelation in time, space and phylogeny. In a phylogenetic context, Diniz-Filho et al. (1998) proposed what they called Phylogenetic Eigenvector Regression (PVR), in which pairwise phylogenetic distances among species are submitted to a Principal Coordinate Analysis, and eigenvectors are then used as explanatory variables in regression, correlation or ANOVAs. More recently, a new approach called Phylogenetic Eigenvector Mapping (PEM) was proposed, with the main advantage of explicitly incorporating a model-based warping in phylogenetic distance in which an Ornstein-Uhlenbeck (O-U) process is fitted to data before eigenvector extraction. Here we compared PVR and PEM in respect to estimated phylogenetic signal, correlated evolution under alternative evolutionary models and phylogenetic imputation, using simulated data. Despite similarity between the two approaches, PEM has a slightly higher prediction ability and is more general than the original PVR. Even so, in a conceptual sense, PEM may provide a technique in the best of both worlds, combining the flexibility of data-driven and empirical eigenfunction analyses and the sounding insights provided by evolutionary models well known in comparative analyses.     

Reanalysis of oviposition and development rates in the Phytoseiidae using a phylogenetic autoregressive method

Life history patterns are usually identified by comparisons of extant species. Because of inferences regarding phylogenetic constraints, comparative data are often not statistically independent. In order to remove phylogenetic patterns embedded in life history data completely, we adopted a phylogenetic autoregressive method to reanalyse a data set of the ovipositional and developmental rates of 45 Phytoseiidae species. We first calculated the phylogenetic correlation in relation to different taxonomic levels using Moran's I statistics. Significant and positive phylogenetic correlations were found at the subgenus and subfamily levels. This indicates that some variation in both of these life-history traits could be accounted for by phylogeny. Phylogenetic associations, therefore, were removed by a phylogenetic autoregressive method. Using corrected data from this method, the specific components of the ovipositional rate are positively correlated with the specific components of th e developmental rate. The method that we have used obtains the same conclusion as others but differs from the phylogenetic effect in the way that it influences the relationship between comparative data. Because of no data reduction in the phylogenetic autoregressive method, the specific components are more useful than the mean values derived from the higher taxonomic nodes for testing ecological and evolutionary hypotheses about life history patterns. © Rapid Science Ltd. 1998     

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.     

Phylogenetic representativeness: a new method for evaluating taxon sampling in evolutionary studies

Background  

Taxon sampling is a major concern in phylogenetic studies. Incomplete, biased, or improper taxon sampling can lead to misleading results in reconstructing evolutionary relationships. Several theoretical methods are available to optimize taxon choice in phylogenetic analyses. However, most involve some knowledge about the genetic relationships of the group of interest (i.e., the ingroup), or even a well-established phylogeny itself; these data are not always available in general phylogenetic applications.     

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 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.     

Fels-Rand: an Xlisp-Stat program for the comparative analysis of data under phylogenetic uncertainty

MOTIVATION: Currently available programs for the comparative analysis of phylogenetic data do not perform optimally when the phylogeny is not completely specified (i.e. the phylogeny contains polytomies). Recent literature suggests that a better way to analyse the data would be to create random trees from the known phylogeny that are fully-resolved but consistent with the known tree. A computer program is presented, Fels-Rand, that performs such analyses. A randomisation procedure is used to generate trees that are fully resolved but whose structure is consistent with the original tree. Statistics are then calculated on a large number of these randomly-generated trees. Fels-Rand uses the object-oriented features of Xlisp-Stat to manipulate internal tree representations. Xlisp-Stat's dynamic graphing features are used to provide heuristic tools to aid in analysis, particularly outlier analysis. The usefulness of Xlisp-Stat as a system for phylogenetic computation is discussed. AVAILABILITY: Available from the author or at http://www.uq.edu.au/~ansblomb/Fels-Rand.sit.hqx. Xlisp-Stat is available from http://stat.umn.edu/~luke/xls/xlsinfo/xlsinfo.html. CONTACT: s.blomberg@abdn.ac.uk     

Molecular phylogeny of the marmots (Rodentia: Sciuridae): tests of evolutionary and biogeographic hypotheses

There are 14 species of marmots distributed across the Holarctic, and despite extensive systematic study, their phylogenetic relationships remain largely unresolved. In particular, comprehensive studies have been lacking. A well-supported phylogeny is needed to place the numerous ecological and behavioral studies on marmots in an evolutionary context. To address this situation, we obtained complete cytochrome (cyt) b sequences for 13 of the species and a partial sequence for the 14th. We applied a statistical approach to both phylogeny estimation and hypothesis testing, using parsimony and maximum likelihood-based methods. We conducted statistical tests on a suite of previously proposed hypotheses of phylogenetic relationships and biogeographic histories. The cyt b data strongly support the monophyly of Marmota and a western montane clade in the Nearctic. Although some other scenarios cannot be rejected, the results are consistent with an initial diversification in North America, followed by an invasion and subsequent rapid diversification in the Palearctic. These analyses reject the two major competing hypotheses of M. broweri's phylogenetic relationships--namely, that it is the sister species to M. camtschatica of eastern Siberia, and that it is related closely to M. caligata of the Nearctic. The Alaskan distribution of M. broweri is best explained as a reinvasion from the Palearctic, but a Nearctic origin can not be rejected. Several other conventionally recognized species groups can also be rejected. Social evolution has been homoplastic, with large colonial systems evolving in two groups convergently. The cyt b data do not provide unambiguous resolution of several basal nodes in the Palearctic radiation, leaving some aspects of pelage and karyotypic evolution equivocal.