The relationship whereby metabolic rate (R) varies with body mass (M) of an organism raised to the power 3/4; i.e. R ∝ M3/4. This example of ‘quarter power’ biological scaling was first established by Swiss-born animal physiologist Max Kleiber (1893–1976) in 1932 and has since been shown to apply to organisms ranging in size from bacteria to whales, and for plants as well as animals. It is now established that physiological attributes, such as heart rate and respiratory rate, generally change with mass raised to some multiple of 1/4. Kleiber's work contradicted earlier reasoning that R should vary with M2/3, on the basis that heat loss varies with surface area, which is proportional to M2/3 – that is, ‘cube root’ scaling. In the 1990s, two US biologists, James Brown and Brian Enquist, collaborated with US particle physicist Geoffrey West to construct a theoretical model to explain quarter power scaling. It is based on the geometric properties of fluid-conducting networks, such as the blood circulatory system of animals and vascular tissue of plants, and the constraints these impose on biological designs. To supply, say, double the number of cells, the supply network must more than double in volume. But the maximally efficient network in terms of energy cost is one that occupies a fairly constant proportion of the body's volume. Consequently, metabolic rate must fall as body mass increases, to compensate for a necessarily more sparsely distributed supply network. The mathematics of the model predicts that the log-log relationship between R and M will be a straight line with a slope of 3/4, as indeed is observed experimentally. See also allometric growth.
Subjects: Biological Sciences.