An introduction to phylogenetically based statistical methods, with a new method for confidence intervals on ancestral values

American Zoologist, Apr 1999 by Garland, Theodore Jr, Midford, Peter E, Ives, Anthony R

An Introduction to Phylogenetically Based Statistical Methods, with a New Method for Confidence Intervals on Ancestral Values1

SYNOPSIS. Interspecific comparisons have played a prominent role in evolutionary biology at least since the time of Charles Darwin. Since 1985, the "comparative method" has been revitalized by new analytical techniques that use phylogenetic information and by increased availability of phylogenies (often from molecular data sets). Because species descend from common ancestors in a hierarchical fashion, related species tend to resemble each other (elephants look like elephants); therefore, cross-species data sets generally do not comprise independent and identically distributed data points. Phylogenetically based statistical methods attempt to account for this fact. Phylogenetic methods allow traditional topics in comparative and ecological physiology to be addressed with greater rigor, including the form of allometric relationships and whether physiological phenotypes vary predictably in relation to behavior, ecology or environmental characteristics, which provides evidence about adaptation. They can also address new topics, such as whether rates of physiological evolution have differed among lineages (clades), and where and when a phenotype first evolved. We present brief overviews of three phylogenetically based statistical methods: phylogenetically independent contrasts, Monte Carlo computer simulations to obtain null distributions of test statistics, and phylogenetic autocorrelation. In a new result, we show analytically how to use independent contrasts to estimate ancestral values and confidence intervals about them. These confidence intervals often exceed the range of variation observed among extant species, which points out the relatively great uncertainty inherent in such inferences. The use of phylogenies should become as common as the use of body size and scaling relationships in the analysis of physiological diversity.

INTRODUCTION

Many approaches can and should be used in evolutionary physiology (Feder et al., 1987; Bennett, 1997; Gibbs, 1999; Koteja et al., 1999), and combinations of approaches are often necessary (Garland and Carter, 1994; Leroi et al., 1994; Hayes and Garland, 1995). Interspecific comparisons are the primary way to study long-term evolutionary changes in the phenotype or genotype, and they have undergone a renaissance in the last decade (Brooks and McLennan, 1991; Harvey and Pagel, 1991; Eggleton and Vane-Wright, 1994; Martins, 1996a). They are used both to generate and to test hypotheses (Doughty, 1996; Larson and Losos, 1996), not only in evolutionary biology per se but also in such related fields as behavioral ecology (Krebs and Davies, 1997), functional morphology (Wainwright and Reilly, 1994), and ecological physiology (Garland and Adolph, 1994).

Comparative data sets are now routinely analyzed by phylogenetic methods (e.g., Garland et al., 1993; Miles and Dunham, 1993; Losos and Miles, 1994; Maddison, 1994; Maddison, 1995; Larson and Losos, 1996; Butler and Losos, 1997; Garland et al., 1997; Schluter et al., 1997; Barraclough et al., 1998; Martins and Lamont, 1998; Pagel, 1998). Most traits studied by physiologists show continuous variation (e.g., organ size, metabolic rate, blood hemoglobin level), and several phylogenetically based statistical methods are available for continuous-valued characters (Martins and Hansen, 1996, 1997). We provide an introduction to three of these: phylogenetically independent contrasts (Felsenstein, 1985; Garland et al., 1992; Purvis and Garland, 1993), computer simulation to obtain phylogenetically correct null distributions of test statistics (Martins and Garland, 1991; Garland et al., 1993), and phylogenetic autocorrelation (Cheverud et al., 1985; Gittleman and Kot, 1990). We also show how independent contrasts can be used to estimate phenotypes of hypothetical ancestors (and confidence intervals about those estimates). Elsewhere, we will show how to place a confidence or prediction interval (in the original data space) on regression equations derived from independent contrasts (Garland and Ives, in preparation). All of these computations are performed by the Phenotypic Diversity Analysis Program (PDAP), which is available on request from T.G.

PHYLOGENETICALLY INDEPENDENT CONTRASTS

Felsenstein (1985) proposed the first fully phylogenetic statistical method for analysis of comparative data. By fully phylogenetic, we mean that it can be applied to any topology and set of branch lengths. Although the original presentation of independent contrasts was couched in terms of a Brownian motion model of character evolution (Felsenstein, 1985), it can also be justified on first-principles statistical grounds (Grafen, 1989; Pagel, 1993). Felsenstein (1985) emphasized applications of independent contrasts to simple correlation and linear regression, but they can also be applied to almost any problem that requires such related statistical techniques as principal components analysis, multiple regression, path analysis, analysis of variance, and analysis of covariance (e.g., Garland, 1992, 1994; Garland et al., 1993; Martins, 1993; Diaz et al., 1996; Martin and Clobert, 1996; Bauwens and Diaz-Uriarte, 1997; Clobert et al., 1998; Wolf et al., 1998). As well, they can be used to compare single species with a set of others (Garland and Adolph, 1994, pp. 809-812; Martinez et al., 1995; McPeek, 1995; Eppley, 1996). Moreover, as with many other phylogenetic methods (Brooks and McLennan, 1991; Harvey and Pagel, 1991; Block et al., 1993; Eggleton and Vane-Wright, 1994; Ryan and Rand, 1995; Gittleman et al., 1996; Martins, 1996a; Butler and Losos, 1997; Garland et al., 1997; Martins and Lamont, 1998; Pagel, 1998), independent contrasts can be used to address questions that are not accessible without phylogenetic information. For example, they can be used to compare rates of evolution across clades (Garland, 1992; Barbosa, 1993; Clobert et al., 1998).