DELAYED‐RESPONSE PHYLOGENETIC CORRELATION: AN OPTIMIZATION‐BASED METHOD TO TEST COVARIATION OF CONTINUOUS CHARACTERS

A new phylogenetic comparative method is proposed, based on mapping two continuous characters on a tree to generate data pairs for regression or correlation analysis, which resolves problems of multiple character reconstructions, phylogenetic dependence, and asynchronous responses (evolutionary lags). Data pairs are formed in two ways (tree‐down and tree‐up) by matching corresponding changes, Δx and Δy. Delayed responses (Δy occurring later in the tree than Δx) are penalized by weighting pairs using nodal or branch‐length distance between Δx and Δy; immediate (same‐node) responses are given maximum weight. All combinations of character reconstructions (or a random sample thereof) are used to find the observed range of the weighted coefficient of correlation r (or weighted slope b). This range is used as test statistic, and the null distribution is generated by randomly reallocating changes (Δx and Δy) in the topology. Unlike randomization of terminal values, this procedure complies with Generalized Monte Carlo requirements while saving considerable computation time. Phylogenetic dependence is avoided by randomization without data transformations, yielding acceptable type‐I error rates and statistical power. We show that ignoring delayed responses can lead to falsely nonsignificant results. Issues that arise from considering delayed responses based on optimization are discussed.     

DEGREE OF SPECIALIZATION IS RELATED TO BODY SIZE IN HERBIVOROUS INSECTS: A PHYLOGENETIC CONFIRMATION

Numerous studies have suggested a general relationship between the degree of host specialization and body size in herbivorous animals. In insects, smaller species are usually shown to be more specialized than larger‐bodied ones. Various hypotheses have attempted to explain this pattern but rigorous proof of the body size–diet breadth relationship has been lacking, primarily because the scarceness of reliable phylogenetic information has precluded formal comparative analyses. Explicitly using phylogenetic information for a group of herbivores (geometrid moths) and their host plant range, we perform a comparative analysis to study the body size–diet breadth relationship. Considering several alternative measures of body size and diet breadth, our results convincingly demonstrate without previous methodological issues—a first for any taxon—a positive association between these traits, which has implications for evaluating various central aspects of the evolutionary ecology of herbivorous insects. We additionally demonstrate how the methods used in this study can be applied in assessing hypotheses to explain the body size–diet breadth relationship. By analyzing the relationship in tree‐feeders alone and finding that the positive relationship remains, the result suggests that the body size–diet breadth relationship is not solely driven by the type of host plant that species feed on.     

PHYLOGENETIC EVIDENCE FOR COMPETITIVELY DRIVEN DIVERGENCE: BODY-SIZE EVOLUTION IN CARIBBEAN TREEFROGS (HYLIDAE: OSTEOPILUS)

Understanding the role of competition in explaining phenotypic diversity is a challenging problem, given that the most divergent species may no longer compete today. However, convergent evolution of extreme body sizes across communities may offer evidence of past competition. For example, many treefrog assemblages around the world have convergently evolved species with very large and small body sizes. To better understand this global pattern, we studied body-size diversification within the small, endemic radiation of Caribbean treefrogs ( Osteopilus ). We introduce a suite of analyses designed to help reveal the signature of past competition. Diet analyses show that Osteopilus are generalist predators and that prey size is strongly associated with body size, suggesting that body-size divergence facilitates resource partitioning. Community assembly models indicate that treefrog body-size distributions in Jamaica and Hispaniola are consistent with expectations from competition. Phylogenetic analyses show that similar body-size extremes in Jamaica and Hispaniola have originated through parallel evolution on each island, and the rate of body-size evolution in Osteopilus is accelerated relative to mainland treefrogs. Together, these results suggest that competition may have driven the rapid diversification of body sizes in Caribbean treefrogs to the extremes seen in treefrog communities around the world.     

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 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.     

PHYLOGENETIC ANALYSES OF THE CORRELATED EVOLUTION OF CONTINUOUS CHARACTERS: A SIMULATION STUDY

We use computer simulation to compare the statistical properties of several methods that have been proposed for estimating the evolutionary correlation between two continuous traits, and define alternative evolutionary correlations that may be of interest. We focus on Felsenstein's (1985) method and some variations of it and on several “minimum evolution” methods (of which the procedure of Huey and Bennett [1987] is a special case), as compared with a nonphylogenetic correlation. The last, a simple correlation of trait values across the tips of a phylogeny, virtually always yields inflated Type I error rates, relatively low power, and relatively poor estimates of evolutionary correlations. We therefore cannot recommend its use. In contrast, Felsenstein's (1985) method yields acceptable significance tests, high power, and good estimates of what we term the input correlation and the standardized realized evolutionary correlation, given complete phylogenetic information and knowledge of the rate and mode of character change (e.g., gradual and proportional to time [“Brownian motion”] or punctuational, with change only at speciation events). Inaccurate branch length information may affect any method adversely, but only rarely does it cause Felsenstein's (1985) method to perform worse than do the others tested. Other proposed methods generally yield inflated Type I error rates and have lower power. However, certain minimum evolution methods (although not the specific procedure used by Huey and Bennett [1987]) often provide more accurate estimates of what we term the unstandardized realized evolutionary correlation, and their use is recommended when estimation of this correlation is desired. We also demonstrate how correct Type I error rates can be obtained for any method by reference to an empirical null distribution derived from computer simulations, and provide practical suggestions on choosing an analytical method, based both on the evolutionary correlation of interest and on the availability of branch lengths and knowledge of the model of evolutionary change appropriate for the characters being analyzed. Computer programs that implement the various methods and that will simulate (correlated) character evolution along a known phylogeny are available from the authors on request. These programs can be used to test the effectiveness of any new methods that might be proposed, and to check the generality of our conclusions with regard to other phylogenies.     

Spatial autocorrelation,phylogenetic constraints,and the causes of sexual dimorphism in primates

Cheverud et al. (1985) apply the important and relatively new methodology of spatial autocorrelation to the quantification of phylogenetic constraints on adaptation and illustrate the use of these methods in an allometric study of sexual dimorphism in body size among extant nonhuman primates. Though of potentially broad applicability, the technique was completely overlooked in a recent review of methods to control for the effects of common descent in comparative studies (Bell, 1989). Their approach therefore deserves a wider recognition. However, their specific conclusion, that phytogeny is the primary determinant of patterns of sexual dimorphism among primates, has been uncritically accepted. We present four main methodological problems with their approach that should temper the interpretation of their analysis: biased phylogenetic relatedness scores, biased sample selection, size dependence in sex dimorphism measurement, and deficiencies in selection of a structural path model. We conclude that, even in terms of the analysis by Cheverud and co-workers (1985), phylogenetic inertia is not the primary reason for body size dimorphism.     

COMPARATIVE METHODS FOR THE ANALYSIS OF CONTINUOUS VARIABLES: GEOMETRIC INTERPRETATIONS

Abstract This study is concerned with statistical methods used for the analysis of comparative data (in which observations are not expected to be independent because they are sampled across phylogenetically related species). The phylogenetically independent contrasts (PIC), phylogenetic generalized least‐squares (PGLS), and phylogenetic autocorrelation (PA) methods are compared. Although the independent contrasts are not orthogonal, they are independent if the data conform to the Brownian motion model of evolution on which they are based. It is shown that uncentered correlations and regressions through the origin using the PIC method are identical to those obtained using PGLS with an intercept included in the model. The PIC method is a special case of PGLS. Corrected standard errors are given for estimates of the ancestral states based on the PGLS approach. The treatment of trees with hard polytomies is discussed and is shown to be an algorithmic rather than a statistical problem. Some of the relationships among the methods are shown graphically using the multivariate space in which variables are represented as vectors with respect to OTUs used as coordinate axes. The maximum‐likelihood estimate of the autoregressive parameter, ρ, has not been computed correctly in previous studies (an appendix with MATLAB code provides a corrected algorithm). The importance of the eigenvalues and eigenvectors of the connection matrix, W, for the distribution of ρ is discussed. The PA method is shown to have several problems that limit its usefulness in comparative studies. Although the PA method is a generalized least‐squares procedure, it cannot be made equivalent to the PGLS method using a phylogenetic model.     

Scaling of Sexual Dimorphism in Body Mass: A Phylogenetic Analysis of Rensch's Rule in Primates

We examined the relationship between body mass dimorphism, measured as the natural logarithm of the male/female ratio, and body mass, defined as ln (female mass), with interspecific allometry, phylogenetically independent contrasts, and phylogenetic autocorrelation in 105 primate species. We repeated the analyses for Strepsirhini (N = 23), Haplorhini (N = 82), Platyrrhinii (N = 32), and Catarrhini (N = 47). With independent contrasts, there is statistically significant (p < .05) positive allometry in Primates in general, Haplorhini, and Catarrhini, but not in Strepsirhini or Platyrrhini. The steepest slope (0.134) is for Catarrhini. Results differed when we conducted analyses with traditional interspecific allometry. For example, not only was the Catarrhini slope not statistically significant but also the magnitude of the slope was shallower than that of all other groups, except Strepsirhini. The results indicate that phylogenetic effects influence the scaling of sexual size dimorphism, and that the statistical method used has a large impact on the interpretation of this biological relationship. We discuss issues involved in applying these statistical methods in detail.     

CLUTCH SIZE AND EGG SIZE IN FREE-LIVING AND PARASITIC COPEPODS: A COMPARATIVE ANALYSIS

The evolution of reproductive strategies and the trade-off between number and size of eggs were investigated in a comparative analysis of free-living and parasitic copepods. Data from 1038 copepod species were used to obtain family averages for 105 families; the phylogenetic relationships among these families include 94 branching events or 94 independent contrasts on which the analysis was based. Transition from a free-living existence to parasitism on invertebrates resulted in small increases in body size. Transition from parasitism on invertebrates to parasitism on fish was associated with greater increases in body size. After controlling for body size, a switch to fish hosts resulted in an increase in the number of eggs produced and a reduction in egg size. Among all contrasts, there was a negative relationship between changes in relative clutch size and changes in relative egg size, suggesting the existence of a trade-off between egg size and numbers. However, opposite changes in these measures of clutch size and egg size were not quite more frequent than expected by chance, therefore indicating that investments into egg numbers are not necessarily made at the expense of egg size, and vice versa. Latitude affected copepod body size, clutch size, and egg size, whereas the effects of freshwater colonization or size of the fish host were not significant. Comparative analyses at either the genus or species levels within given taxa of copepods parasitic on fish provided limited support for a trade-off between clutch size and egg size, but were hampered by the small number of independent phylogenetic contrasts available. From the family-level comparative analysis, it appears that the evolutionary transition from a free life to parasitism on invertebrates, and the transition from parasitism on invertebrates to parasitism on fish, have led to changes in life-history traits in response to the different selective pressures associated with the different modes of life.     

TESTING FOR UNEQUAL AMOUNTS OF EVOLUTION IN A CONTINUOUS CHARACTER ON DIFFERENT BRANCHES OF A PHYLOGENETIC TREE USING LINEAR AND SQUARED-CHANGE PARSIMONY: AN EXAMPLE USING LESSER ANTILLEAN ANOLIS LIZARDS

Although a large body of work investigating tests of correlated evolution of two continuous characters exists, hypotheses such as character displacement are really tests of whether substantial evolutionary change has occurred on a particular branch or branches of the phylogenetic tree. In this study, we present a methodology for testing such a hypothesis using ancestral character state reconstruction and simulation. Furthermore, we suggest how to investigate the robustness of the hypothesis test by varying the reconstruction methods or simulation parameters. As a case study, we tested a hypothesis of character displacement in body size of Caribbean Anolis lizards. We compared squared-change, weighted squared-change, and linear parsimony reconstruction methods, gradual Brownian motion and speciational models of evolution, and several resolution methods for linear parsimony. We used ancestor reconstruction methods to infer the amount of body size evolution, and tested whether evolutionary change in body size was greater on branches of the phylogenetic tree in which a transition from occupying a single-species island to a two-species island occurred. Simulations were used to generate null distributions of reconstructed body size change. The hypothesis of character displacement was tested using Wilcoxon Rank-Sums. When tested against simulated null distributions, all of the reconstruction methods resulted in more significant P-values than when standard statistical tables were used. These results confirm that P-values for tests using ancestor reconstruction methods should be assessed via simulation rather than from standard statistical tables. Linear parsimony can produce an infinite number of most parsimonious reconstructions in continuous characters. We present an example of assessing the robustness of our statistical test by exploring the sample space of possible resolutions. We compare ACCTRAN and DELTRAN resolutions of ambiguous character reconstructions in linear parsimony to the most and least conservative resolutions for our particular hypothesis.     

The ecology of lizard reproductive output

Aim We provide a new quantitative analysis of lizard reproductive ecology. Comparative studies of lizard reproduction to date have usually considered life‐history components separately. Instead, we examine the rate of production (productivity hereafter) calculated as the total mass of offspring produced in a year. We test whether productivity is influenced by proxies of adult mortality rates such as insularity and fossorial habits, by measures of temperature such as environmental and body temperatures, mode of reproduction and activity times, and by environmental productivity and diet. We further examine whether low productivity is linked to high extinction risk. Location World‐wide. Methods We assembled a database containing 551 lizard species, their phylogenetic relationships and multiple life history and ecological variables from the literature. We use phylogenetically informed statistical models to estimate the factors related to lizard productivity. Results Some, but not all, predictions of metabolic and life‐history theories are supported. When analysed separately, clutch size, relative clutch mass and brood frequency are poorly correlated with body mass, but their product – productivity – is well correlated with mass. The allometry of productivity scales similarly to metabolic rate, suggesting that a constant fraction of assimilated energy is allocated to production irrespective of body size. Island species were less productive than continental species. Mass‐specific productivity was positively correlated with environmental temperature, but not with body temperature. Viviparous lizards were less productive than egg‐laying species. Diet and primary productivity were not associated with productivity in any model. Other effects, including lower productivity of fossorial, nocturnal and active foraging species were confounded with phylogeny. Productivity was not lower in species at risk of extinction. Main conclusions Our analyses show the value of focusing on the rate of annual biomass production (productivity), and generally supported associations between productivity and environmental temperature, factors that affect mortality and the number of broods a lizard can produce in a year, but not with measures of body temperature, environmental productivity or diet.