Revising the distributive networks models of West, Brown and Enquist (1997) and Banavar, Maritan and Rinaldo (1999): metabolic inequity of living tissues provides clues for the observed allometric scaling rules

Basic assumptions of two distributive network models designed to explain the 3/4 power scaling between metabolic rate and body mass are re-analysed. It is shown that these models could have consistently accounted for the observed scaling patterns if and only if body mass M had scaled as L4, where L is body length, in the model of Banavar et al. (1999, Nature 399, 130-132), or if spatial volume VF occupied by the distributive network had scaled as M3/4 in the model of West et al. (1997, Science 276, 122-126). Lack of agreement between these predictions and observational evidence invalidates both models rendering them mathematically controversial. It is further shown that consideration of distributive networks can nevertheless yield realistic values of scaling exponents under the major assumption that living organisms are designed so as to keep the mass-specific metabolic rate of important functional tissues in the vicinity of a size-independent optimum value. Mass-specific metabolic rate of subsidiary mechanical tissues can be small and vary with body mass. Different patterns of spatial distribution of metabolically active biomass within the organism result in different patterns of allometric scaling. From the available evidence the presumable optimum value of mass-specific metabolic rate of living matter is estimated to be in the vicinity of 1-10 W kg-1.