The beak size of birds is optimized for thermal regulation because they vary in size relative to latitude and environmental temperature, a concept called Allen's rule.
"Allen's rule proposes that the appendages of endotherms are smaller, relative to body size, in colder climates, in order to reduce heat loss. Empirical support for Allen's rule is mainly derived from occasional reports of geographical clines in extremity size of individual species. Interspecific evidence is restricted to two studies of leg proportions in seabirds and shorebirds. We used phylogenetic comparative analyses of 214 bird species to examine whether bird bills, significant sites of heat exchange, conform to Allen's rule. The species comprised eight diverse taxonomic groups—toucans, African barbets, Australian parrots, estrildid finches, Canadian galliforms, penguins, gulls, and terns. Across all species, there were strongly significant relationships between bill length and both latitude and environmental temperature, with species in colder climates having significantly shorter bills. Patterns supporting Allen's rule in relation to latitudinal or altitudinal distribution held within all groups except the finches. Evidence for a direct association with temperature was found within four groups (parrots, galliforms, penguins, and gulls). Support for Allen's rule in leg elements was weaker, suggesting that bird bills may be more susceptible to thermoregulatory constraints generally. Our results provide the strongest comparative support yet published for Allen's rule and demonstrate that thermoregulation has been an important factor in shaping the evolution of bird bills." (Symonds and Tattersall 2010:188)
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