Kleiber's law

Kleiber's law, named after Max Kleiber for his biology work in the early 1930s, is the observation that, for the vast majority of animals, an animal's metabolic rate scales to the power of the animal's mass. Symbolically: if q0 is the animal's metabolic rate, and M is the animal's mass, then Kleiber's law states that q0~M3/4. Thus, over the same time span, a cat having a mass 100 times that of a mouse will consume only about 32 times the energy the mouse uses. The exact value of the exponent in Kleiber's law is unclear, in part because the law currently lacks a single theoretical explanation that is entirely satisfactory. Kleiber's law, as many other biological allometric laws, is a consequence of the physics and/or geometry of animal circulatory systems. Max Kleiber first discovered the law when analyzing a large number of independent studies on respiration within individual species. Kleiber expected to find an exponent of (for reasons explained below), and was confounded by the exponent of he discovered. One explanation for Kleiber's law lies in the difference between structural and growth mass. Structural mass involves maintenance costs, reserve mass does not. Hence, small adults of one species respire more per unit of weight than large adults of another species because a larger fraction of their body mass consists of structure rather than reserve. Within each species, young (i.e., small) organisms respire more per unit of weight than old (large) ones of the same species because of the overhead costs of growth. Explanations for -scaling tend to assume that metabolic rates scale to avoid heat exhaustion. Because bodies lose heat passively via their surface, but produce heat metabolically throughout their mass, the metabolic rate must scale in such a way as to counteract the square–cube law. The precise exponent to do so is . Such an argument does not address the fact that different organisms exhibit different shapes (and hence have different surface-area-to-volume ratios, even when scaled to the same size).