Brain mass and BMR for 347 mammalian species were assembled from several sources listed in appendix A of the electronic supplementary material. The data on BMR (W) and the corresponding body mass (g) are taken from the compilations of

White & Seymour (2003) and Lovegrove (

2000,

2003). Thirty-four species were excluded from the analysis following

White & Seymour (2003): Soricidae enter a state of hyperactivity as soon as they are truly post-absorptive, Artiodactyla digest very slowly and the measurements of BMR might have not been truly post-absorptive, and Lagomorpha have a heightened BMR owing to foregut fermentation. However, inclusion of those species did not alter the levels of significance of our results.

To test whether phylogenetic effects are present in our data, we used Pagel's software

Continuous (

Pagel 1994) on a composite molecular supertree (see appendix B of the electronic supplementary material). The maximum likelihood estimations of Lambda, which measures the degree to which the phylogeny predicts the pattern of covariance among species (

Pagel 1999), were close to 1 for all parameters, indicating that phylogenetic correction is indeed required. Thus, we conducted both an analysis of family means and an analysis using phylogenetically independent contrasts, as proposed by

Felsenstein (1985). Contrasts were generated using the PDAP

:

PDTree package (

Garland *et al*. 1992) of the

Mesquite computer program (

Maddison & Maddison 2005).

In order to minimize the correlation between the absolute values of the standardized contrasts and their standard deviations (square roots of sums of branch lengths,

Garland *et al*. 1992), we estimated branch lengths using the method of Nee (cited in

Purvis 1995), where each node is set at a depth equal to the log of the number of descendant tips. The appropriateness of these branch length estimations was then tested using

Continuous (

Pagel 1994). The maximum likelihood estimation of Kappa, which differentially stretches or compresses individual phylogenetic branch lengths (

Pagel 1997), was close to 1 for all parameters, justifying the use of Nee's branch length estimations. All the variables were log

_{e} transformed before analysis.

Comparing brain mass to BMR requires the removal of the effects of body mass on both variables. For BMR, we used body mass data from the original studies of BMR to calculate residuals using least-squares regression (JMP v. 6, SAS Institute Inc., Cary, NC, USA). For brain mass, we used the corresponding body mass from the brain mass sources, if available, and species mean body mass otherwise, to calculate residuals. The same procedure was applied to family means and to independent contrasts. For independent contrasts, the regression lines were constrained to pass through the origin (

Garland *et al*. 1992). Alternatively, the use of orthogonal regression with equal variances (major axis regression) to calculate residuals does not affect the level of significance of our results.

To account for possible grade shifts, data for species with altricial and precocial developmental modes were analysed separately. Species were defined as precocial if the young open their eyes at birth or shortly thereafter. Most families of Chiroptera produce a single, large offspring after a long gestation time, but the young opens its eyes only after some days. Thus, all Chiroptera were omitted from the analyses where the data are split by development mode, but included in the analysis of the combined dataset.