Phylogenetic Analyses of the Correlated Evolution of Continuous Characters: A Simulation Study

Abstract

Abstract. -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 ofit 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 ofour conclusions with regard to other phylogenies.

Comparative methods for studying primate adaptation and allometry

“…32,33,37 This conclusion runs counter to the commonly expressed opinion that nonindependence is simply a "degrees of freedom" problem, one in which phylogenetic comparative methods are thought to reduce the number of data points for analysis and therefore result in lower statistical power. Although some phylogenetic comparative methods do appropriately result in fewer degrees of freedom, the most commonly used comparative method, independent contrasts, has the same degrees of freedom as a species analysis when the phylogeny is fully resolved.…”

“…[32][33][34][35][36][37] The effects are staggering. A recent simulation study, for example, showed that Type I error rates (the probability of rejecting a true null hypothesis) can be as high as 44% when phylogeny is ignored, compared to an expected error rate of 5%.…”

Comparative transcriptomics across 14 Drosophila species reveals signatures of longevity

“…To identify the genes that correlate with species longevity, the phylogenetic generalized least‐squares approach was employed to adjust for the evolutionary relationship (Felsenstein, 1985; Freckleton, Harvey & Pagel, 2002; Grafen, 1989; Martins & Garland, 1991). Regression was performed between expression values and male median lifespan (“ML”), different models of trait evolution were tested, and the best‐fit model was then selected based on maximal likelihood (Table S3).…”

Activities of DNA base excision repair enzymes in liver and brain correlate with body mass, but not lifespan

“…The analysis was repeated with all branch lengths set to one, as described for speciation models of character change (Martins andGarland 1991 andPrice 1997). This latter approach avoids errors associated with the estimation of branch lengths.…”