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Procedures for the Analysis of Comparative'data Using Phylogenetically Independent Contrasts

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Procedures for the Analysis of Comparative'data Using Phylogenetically Independent Contrasts PROCEDURES FOR THE ANALYSIS OF COMPARATIVE'DATA USING PHYLOGENETICALLY INDEPENDENT CONTRASTS THEODOREGARLAND, JR.,' PAULH. HARVEY?AND ANTHONYR. IVES' 'Department of Zoology, University of Wisconsin, Madison, Wisconsin 53706, USA 2Department of Zoology, University of Oxford, South Parks Road, Oxford OX1 3PS, England Abstract.-We discuss and clarify several aspects of applying Felsenstein's (1985, Am. Nat. 125: 1-15) procedures to test for correlated evolution of continuous traits. This is one of several available comparative methods that maps data for phenotypic traits onto an existing phylogenetic tree (derived from independent information). Application of Felsenstein's method does not require an entirely dichotomous topology. It also does not require an assumption of gradual, clocklike character evolution, as might be modeled by Brownian motion. Almost any available information can be used to estimate branch lengths (e.g., genetic distances, divergence times estimated from the fossil record or from molecular clocks, numbers of character changes from a cladistic analysis). However, the adequacy for statistical purposes of any proposed branch lengths must be verified empirically for each phylogeny and for each character. We suggest a simple way of doing this, based on graphical analysis of plots of standardized independent contrasts versus their standard deviations (i.e., the square roots of the sums of their branch lengths). In some cases, the branch lengths and/or the values of traits being studied will require transformation. An example involving the scaling of mammalian home range area is presented. Once adequately standardized, sets of independent contrasts can be analyzed using either linear or nonlinear (multiple) regression. In all cases, however, regressions (or correlations) must be computed through the origin. We also discuss ways of correcting for body size effects and how this relates to making graphical representations of relationships of standardized independent contrasts. We close with a consideration of the types of traits that can be analyzed with inde- pendent contrasts procedures and conclude that any (continuous) trait that is inherited from ancestors is appropriate for analysis, regardless of the mechanism of inheritance (e.g., genetic or cultural). [Allometry; body size; branch lengths; comparative method; evolutionary rates; functional morphology; home range; statistics.] One of the fundamental topics in evo- techniques (Grafen, 1989; Martins and Gar- lutionary biology is the manner in which land, 1991), and computer programs are the evolution of different traits is correlat- available to do the necessary calculations ed throughout a phylogenetic lineage (e.g., (Grafen, 1989; Martins and Garland, 1991; Ridley, 1983; Felsenstein, 1985; Donoghue, J. Felsenstein's latest version of PHYLIP; 1989; Maddison, 1990; Harvey and Pagel, A. J. Purvis, pers. comm., whose programs 1991; Martins and Garland, 1991).Methods are available from the second author). for incorporating phylogenetic informa- The independent contrasts method is tion into statistical analyses of the corre- straightforward in principle (Burt, 1989; lated evolution of continuous traits are now Harvey and Purvis, 1991), but it does en- receiving intensive study. Although new compass several analytical complexities that or improved methods continue to appear may bewilder potential users. In particu- (e.g., Felsenstein, 1988; Bell, 1989; Grafen, lar, the possible sources and treatment of 1989; Gittleman and Kot, 1990; Harvey and phylogenetic branch lengths have not been Pagel, 1991; Lynch, 1991; Martins and Gar- adequately discussed. We therefore ex- land, 1991; Pagel, 1992), Felsenstein's (1985) amine several technical aspects of apply- independent contrasts approach is now be- ing the independent contrasts method and ing widely employed, many of its statis- illustrate these with an empirical example. tical properties have been verified analyt- Where complicated arguments or mathe- ically and through computer simulation matical proofs are required, we have rel- 1992 ANALYZING COMPARATIVE DATA BY INDEPENDENT CONTRASTS 19 egated them to appendices. We assume the 1985:13). Many comparative studies, how- reader will have read Felsenstein's (1985) ever, involve data compiled from the lit- original description and possibly relevant erature, and most practitioners feel com- portions of Grafen (1989), Harvey and Pa- pelled to analyze all available data. gel (1991), and/or Martins and Garland (1991). RATIONALEAND BRIEF OVERVIEWOF THE INDEPENDENTCONTRASTS METHOD WHATDOES THE INDEPENDENTCONTRASTS Because species are descended in a hi- METHODREQUIRE? erarchical fashion from common ancestors, Three types of information are required they generally cannot be considered as to use Felsenstein's (1985) method: (1) data independent data points in statistical for two or more phenotypic traits for a se- analyses (review in Harvey and Pagel, ries of extant and/or extinct species, (2) the 1991:Ch. 2). This phylogenetic nonin- cladistic relationships of these species, and dependence reduces degrees of freedom (3) phylogenetic branch lengths in units available for hypothesis testing, lowers sta- of expected variance of change. Although tistical power, and affects parameter esti- a fully dichotomous topology simplifies the mation (Grafen, 1989; Harvey and Pagel, analysis, it is not required. Grafen (1989, 1991; Martins and Garland, 1991). Felsen- 1992), Harvey and Page1 (1991), Page1 stein (1985) therefore proposed computing (1992), and Page1 and Harvey (1992) ex- (weighted) differences ("contrasts") be- plained how unresolved polytomies can be tween the character values of pairs of sister analyzed, although with some loss of in- species and/or nodes, as indicated by a formation and of statistical power (see also phylogenetic topology, and working down Felsenstein, 1985:lO). In essence, if our the tree from its tips. This procedure re- knowledge of topology is incomplete, then sults in n - 1 contrasts from n original tip we are forced to lump some species to- species. Insofar as the ancestral nodes are gether (or delete some from the analysis) correctly determined, each of these con- when computing independent contrasts. A trasts is independent of the others in terms number of workers have used the inde- of the evolutionary changes that have oc- pendent contrasts method in the absence curred to produce differences between the of complete topological information. two members of a single contrast (although Sometimes, they have used taxonomic in- phenomena such as character displace- formation alone or in part to construct a ment might violate this assumption). Be- topology, assuming that named taxa (e.g., cause the n - 1 contrasts are statistically each genus within a family) represent independent, they generally can be em- monophyletic groups (cf. Cheverud et al., ployed in standard statistical analyses. 1985; see Grafen [1989], Harvey and Page1 Contrasts involving longer periods of [1991], and Page1 [I9921 for further details time are likely to be greater in absolute and examples). Obviously, such a practice value and would, in effect, be given greater may be misleading if the taxonomy is not weight in statistical analyses such as cor- cladistic, but it does allow analysis of the relation or regression. This increased data now, rather than waiting for actual weight would be wrong because it would phylogenetic information to become avail- negate the use of standard probability ta- able. For the remainder of this paper, we bles for hypothesis testing. (However, such assume that a fully dichotomous phylog- a weighting may be desirable for estima- eny is available and that its topology is tion of certain types of evolutionary cor- known without error. In the process of de- relations [see Martins and Garland, 19911.) signing a comparative study (i.e., deciding The usual probability tables can be em- which species should be measured, given ployed if independent contrasts are first limited resources), it might be possible to standardized. Standardization customarily avoid sets of species whose cladistic rela- denotes subtraction of the mean and di- tionships were in doubt (cf. Felsenstein, vision by the standard deviation. The ex- 20 SYSTEMATIC BIOLOGY VOL. 41 Body mass Home range (kg) (km2t Ursus horribilis 251.3 82.8 Ursus americanus 93.4 56.8 Mephitis mephitis 2.5 0.09 MeleS mele.9 11.6 0.87 Canis lupus 35.3 394.0 Canis latrans 13.3 45 Lycaon pictus 20 160 Canis aureus 8.8 9.1 Urocyon cinereoargenteus 3.7 vulpe~fulva 4.8 Hyaena hyaena 26.8 Crocutta crocutta 52 Acinonyx jubatus 58.8 Panthera pardus 52.4 Panther. tigris 161 Pdnthera leo 155.8 Diceros bicornis 1,200 Cerdtotherium simum 2,000 Equus hemionus 200 Equus caballus 350 Equus burchelli 235 Girdffa camelopardalis 1,075 Syncerus caffer 620 Bison bison 865 Taurotragus oryx 511 Garella granti 62.5 Garella thomsonii 20.5 Antilope cervicapra 37.5 Madoqua kirki 5.0 Oreamnos americanus 113.5 Ovis canadensis nelsoni 85 Hippotragus equinus 226.5 Aepyceros melampus 53.25 Connochaetes taurinus 216 Damaliscus lunatus 130 Alcelaphus buseldphus 136 Antilocapra americana 50 Cerws canadensis 300 Dama dama 55 Alces alces 384 Rangifer tarandus 100 Odocoileus virginianus 57 Odocoileus hemionus 74 FIGURE 1. Phylogeny and data for body mass (kg) and home range area (km2)for 43 species of mammals (from Garland and Janis, 1992; Janis, in press). Branch lengths are in units of time, as estimated from first fossil appearances and from molecular
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