Allometric scaling and central source systems - art. no. 038101

Allometric scaling relations abound in nature. Examples include the power l aw relating the metabolic rate of animals and plants to their masses and th e power law describing the dependence of the size of the drainage basin of a river on the total amount of water contained In that river. The exponent is of the form D/D + 1, where D is the dimension of the system. We show cha t this scaling exponent is simply a consequence of the source distribution of the systems considered and requires no further assumptions. To demonstra te the wide range of validity of the result we present a simple experiment that shows the predicted behavior in one dimension.