Along tropical mountains, species often occupy narrow altitude ranges. Numerous biotic and abiotic factors have been proposed as determinants of altitude occupancy. We measured several aspects of thermal physiology of 215 bird species across a 2·6-km altitude gradient in the Peruvian Andes. We predicted that highland species would show adaptation to the colder high-altitude climate and that energy costs of thermoregulation might limit upslope dispersal of lowland natives. We found reductions in thermal conductance, body temperature and lower critical temperature in highland birds compared with lowland species. These combine to make highland natives more resistant to heat loss. We did not find convincing evidence that acute thermal limits or energy costs of thermoregulation constrained altitude distributions. Heat-budget models predicted low-to-moderate long-term costs at native altitudes. Costs increased for lowland natives modelled in the highland climate, but for all but a few species, costs remained within putative expenditure limits. Although we did not test heat tolerances, we measured all species at temperatures similar to the hottest air temperatures at the lowland site. There was no evidence that high lowland temperatures preclude downslope movements of highland birds. While thermal tolerances probably do not directly determine altitude occupancy by most species, the additional energy cost of thermoregulation experienced by lowland species moving upslope may trade off against investment in important life-history components such as breeding, and thereby affect altitude range limits. A Lay Summary is available for this article.

We compiled published values of mammalian maximum oxygen consumption during exercise ( ) and supplemented these data with new measurements of for the largest rodent (capybara), 20 species of smaller-bodied rodents, two species of weasels and one small marsupial. Many of the new data were obtained with running-wheel respirometers instead of the treadmill systems used in most previous measurements of mammalian . We used both conventional and phylogenetically informed allometric regression models to analyze of 77 'species' (including subspecies or separate populations within species) in relation to body size, phylogeny, diet and measurement method. Both body mass and allometrically mass-corrected showed highly significant phylogenetic signals (i.e. related species tended to resemble each other). The Akaike information criterion corrected for sample size was used to compare 27 candidate models predicting (all of which included body mass). In addition to mass, the two best-fitting models (cumulative Akaike weight=0.93) included dummy variables coding for three species previously shown to have high (pronghorn, horse and a bat), and incorporated a transformation of the phylogenetic branch lengths under an Ornstein-Uhlenbeck model of residual variation (thus indicating phylogenetic signal in the residuals). We found no statistical difference between wheel- and treadmill-elicited values, and diet had no predictive ability for . Averaged across all models, the allometric scaling exponent was 0.839, with 95% confidence limits of 0.795 and 0.883, which does not provide support for a scaling exponent of 0.67, 0.75 or unity.