Modelling universality and scaling

Of the equations that have been used to describe ontogenetic growth in terms of the rate of increase in mass, m, as a function of time, t, most are merely statistical descriptions with no mechanistic basis. Our model1 is derived from fundamental biological and physical principles and relates growth to metabolic power at the cellular level. It is based on the allocation of resources to the maintenance and replacement of existing tissue and the production of new tissue, with the whole-body metabolic rate B = NcBc + Ec(dNc/dt), where Bc is the cellular metabolic rate, Ec is the energy needed to create a cell, and Nc is the total number of cells. As m = Ncmc, where mc is the average cell mass, this gives [graphic not available: see fulltext] where a = B0mc/Ec, b = Bc/Ec, β = 1 and α is the allometric exponent for B (≡B0mα), taken to be 3/4 in accordance with a large body of data and with theoretical arguments2,3. The asymptotic mass, for which dm/dt = 0, is predicted to be M = (B0mc/Bc)4.