Allometry reveals trade-offs between Bergmann's and Allen's rules, and different avian adaptive strategies for thermoregulation.

Animals tend to decrease in body size (Bergmann's rule) and elongate appendages (Allen's rule) in warm climates. However, it is unknown whether these patterns depend on each other or constitute independent responses to the thermal environment. Here, based on a global phylogenetic comparative analysis across 99.7% of the world's bird species, we show that the way in which the relative length of unfeathered appendages co-varies with temperature depends on body size and vice versa. First, the larger the body, the greater the increase in beak length with temperature. Second, the temperature-based increase in tarsus length is apparent only in larger birds, whereas in smaller birds, tarsus length decreases with temperature. Third, body size and the length of beak and tarsus interact with each other to predict the species' environmental temperature. These findings suggest that the animals' body size and shape are products of an evolutionary compromise that reflects distinct alternative thermoregulatory adaptations.