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Biologists have long noted that endotherms tend to have larger bodies (Bergmann's rule) and shorter appendages (Allen's rule) in colder environments. Nevertheless, many taxonomic groups appear not to conform to these 'rules', and general explanations for these frequent exceptions are currently lacking. Here we note that by combining complementary changes in body and extremity size, lineages could theoretically respond to thermal gradients with smaller changes in either trait than those predicted by either Bergmann's or Allen's rule alone. To test this idea, we leverage geographic, ecological, phylogenetic, and morphological data on 6,974 non-migratory terrestrial bird species, and show that stronger family-wide changes in bill size over thermal gradients are correlated with more muted changes in body size. Additionally, we show that most bird families exhibit weak but appropriately directed changes in both traits, supporting the notion of complementarity in Bergmann's and Allen's rules. Finally, we show that the few families that exhibit significant gradients in either bill or body size, tend to be more speciose, widely distributed, or ecologically constrained. Our findings validate Bergmann's and Allen's logic and remind us that body and bill size are simply convenient proxies for their true quantity of interest: the surface-to-volume ratio., (© 2023. The Author(s).)

Daily torpor allows endotherms to save energy during energetically stressful (e.g. cold) conditions. Although studies on avian torpor have mostly been conducted under laboratory conditions, information on the usage of torpor in the wild is limited to few, predominantly temperate-zone species. We studied torpor under seminatural conditions from 249 individuals from 29 hummingbird species across a 1920 m elevational gradient in the western Andes of Colombia using cloacal thermistors. Small birds were more likely to use torpor than large birds, but only at low ambient temperatures, where torpor was prolonged. We also found effects of proxy variables for body condition and energy expenditure on the use of torpor, its characteristics, and impacts. Our results suggest that context-dependency and phylogenetic variation in the probability of deploying torpor can help understand clade-wide patterns of elevational distribution in Andean hummingbirds.