BackgroundBrain signaling requires energy. The cost of maintaining and supporting energetically demanding neurons is the key constraint on brain size. The dramatic increase in brain size among mammals and birds cannot be understood without solving this conundrum: larger brains, with more neurons, consume more energy.ResultsHere we examined the intrinsic relationships between metabolism, body-brain size ratios and neuronal densities of both endothermic and ectothermic animals. We formulated a general model to elucidate the key factors that correlate with brain enlargement, and the origin of allometric body-brain size scaling. This framework identified temperature as a critical factor in brain enlargement via temperature-regulated changes in metabolism. Our framework predicts that ectothermic animals living in tropical climates should have brain sizes that are several times larger than those of ectothermic animals living in cold climates. This prediction was confirmed by data from experiments in fish brains. Our framework also suggests that a rapid increase in the number of less energy-demanding glial cells may be another important factor contributing to the ten-fold increase in the brain sizes of endotherms compared with ectotherms.ConclusionsThis study thus provides a quantitative theory that predicts the brain sizes of all the major types of animals and quantifies the contributions of temperature-dependent metabolism, body size and neuronal density.