The idea that the size of homoiothermic animals in a single, closely related, evolutionary line increases along a gradient from warm to cold temperatures (i.e. that races of species from cold climates tend to be composed of individuals physically larger than those of races from warm climates). This is because the surface area : body weight ratio decreases as body weight increases. Thus a large body loses proportionately less heat than a small one. This is advantageous in a cold climate but disadvantageous in a warm one. The rule was proposed in 1847 by the German biologist C. Bergmann. Its universal validity has recently been called into question as studies of the musk ox in the Arctic have failed to demonstrate its operation. See also Allen's rule; Gloger's rule.