The question is often raised whether it is statistically necessary to control for phylogenetic associations in comparative studies. To investigate this question, we explore the use of a measure of phylogenetic correlation, lambda, introduced by Pagel (1999), that normally varies between 0 (phylogenetic independence) and 1 (species' traits covary in direct proportion to their shared evolutionary history). Simulations show lambda to be a statistically powerful index for measuring whether data exhibit phylogenetic dependence or not and whether it has low rates of Type I error. Moreover, lambda is robust to incomplete phylogenetic information, which demonstrates that even partial information on phylogeny will improve the accuracy of phylogenetic analyses. To assess whether traits generally show phylogenetic associations, we present a quantitative review of 26 published phylogenetic comparative data sets. The data sets include 103 traits and were chosen from the ecological literature in which debate about the need for phylogenetic correction has been most acute. Eighty-eight percent of data sets contained at least one character that displayed significant phylogenetic dependence, and 60% of characters overall (pooled across studies) showed significant evidence of phylogenetic association. In 16% of tests, phylogenetic correlation could be neither supported nor rejected. However, most of these equivocal results were found in small phylogenies and probably reflect a lack of power. We suggest that the parameter lambda be routinely estimated when analyzing comparative data, since it can also be used simultaneously to adjust the phylogenetic correction in a manner that is optimal for the data set, and we present an example of how this may be done.

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 independent 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.] SYSTEMATIC BIOLOGY

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Phylogenies reconstructed from gene sequences can be used to investigate the tempo and mode of species diversi¢cation. Here we develop and use new statistical methods to infer past patterns of speciation and extinction from molecular phylogenies. Speci¢cally, we test the null hypothesis that per-lineage speciation and extinction rates have remained constant through time. Rejection of this hypothesis may provide evidence for evolutionary events such as adaptive radiations or key adaptations. In contrast to previous approaches, our methods are robust to incomplete taxon sampling and are conservative with respect to extinction. Using simulation we investigate, ¢rst, the adverse e¡ects of failing to take incomplete sampling into account and, second, the power and reliability of our tests. When applied to published phylogenies our tests suggest that, in some cases, speciation rates have decreased through time.

Recent comparative studies point to the importance of mortality schedules as determinants in the evolution of life‐history characteristics. In this paper, we compare patterns of mortality from natural populations of mammals with a variety of life histories. We find that, after removing the effects of body weight, mortality is the best predictor of variation in life‐history traits. Mammals with high levels of natural mortality tend to mature early and give birth to small offspring in large litters after a short gestation, before and after body size effects are factored out. We examine the way in which life‐history traits relate to juvenile mortality versus adult mortality and find that juvenile mortality is more highly correlated with life‐history traits than is adult mortality. We discuss the necessity of distinguishing between extrinsic sources of mortality (e.g. predation) and mortality caused by intrinsic sources (e.g. costs of reproduction), and the role that ecology might play in the evolution of patterns of mortality and fecundity. We conclude that these results must be explained not simply in the light of the demographic necessity of balancing mortality and fecundity, but as a result of age‐specific costs and benefits of reproduction and parental investment. Detailed comparative studies of mortality patterns in natural populations of mammals offer a promising avenue towards understanding the evolution of life‐history strategies.