Adaptation: Statistics and a Null Model for Estimating Phylogenetic Effects

-Tests of adaptive explanations are often critically confounded by phylogenetic heritage. In this paper we propose statistics and a null model for estimating phylogenetic effects in comparative data. We apply a model-independent measure of autocorrelation (Moran's I) for estimating whether cross-taxonomic trait variation is related to phylogeny. We develop a phylogenetic correlogram for assessing how autocorrelation varies with patristic distance and for judging the appropriateness and effectiveness of an autoregressive model. We then revise Cheverud et al.'s (1985, Evolution, 39:1335-1351) autocorrelational model to incorporate greater flexibility in the relation between trait variation and phylogenetic distance. Finally, we analyze various comparative data sets (body weight in carnivores, clutch size in birds) and phylogenies (morphological, molecular) to illustrate some of the complications that may arise from using an autoregressive model and to explore the effects of different weighting matrices in adjusting for these complications. Although our approach has limitations, it is both effective in partitioning trait variation into adaptive and phylogenetic components and flexible in adjusting to peculiarities in taxonomic distribution. [Phylogenetic effects; phylogenetic correlation; autoregressive models; comparative methods. ] The comparative method is commonly used to investigate adaptation. A researcher examines the attributes of a number of species. Statistical analyses of these data are then used to formulate and test adaptive hypotheses of life history, morphology, physiology, demography, and behavior (e.g., Clutton-Brock and Harvey, 1977; Damuth, 1981; Gittleman and Harvey, 1982; Harvey and Clutton-Brock, 1985; Gittleman, 1986a, b; Huey and Bennett, 1987). If traits are analyzed across a broad range of independently derived taxa, the resulting adaptive explanations may be quite robust (Clutton-Brock and Harvey, 1984; Huey and Bennett, 1986; Gittleman, 1989). If, however, the data reflect a highly structured phylogeny (with little statistical independence), results may be misleading (Felsenstein, 1985). To neglect phylogeny is to invite type I and type II errors (see Fig. 1). A number of techniques have been developed for removing the effects of phylogeny (see reviews in Huey, 1987; Pagel and Harvey, 1988; Gittleman, 1989; Burghardt and Gittleman, 1990). Some of these techniques are better suited for particular variables or certain evolutionary questions, and all possess limitations. Nominal or categorical data (e.g., mating system: monogamy, polygamy) may be analyzed by evaluating the agreement between the variation in a trait and an accepted phylogeny (Dobson, 1985; Greene, 1986) or by using outgroup comparisons to identify evolutionary transitions among traits (Gittleman, 1981; Ridley, 1983). For quantitative data, there are several strategies. One may avoid spurious correlation by averaging over closely related species, thereby reducing the degrees of freedom and significance of the correlation. Alternatively, one may transform the data so that phylogenetically disparate groups appear on a common scale. Even within this general framework there are several methods for evaluating the association between the ordinal or continuous values of a trait and phylogeny: (1) Nested analysis of variance partitions the total variation in a continuous character among various taxonomic levels. By selecting the taxonomic level that accounts for the greatest proportion of the total variance as the appropriate level for analysis, this method attempts to control for bias from low-level clades that are both uniform and speciesrich (Harvey and Mace, 1982; Harvey and