Storage and the regulation of body mass in animals: A general growth equation based on an energy balance model

The traditional growth models, such as the von Bertalanffy and logistic models, and their generalized forms have been frequently used for several decades in animal physiology, theoretical ecology, and applied ecology as experimental equations for describing finite animal growth. The coefficients of these models have, however, no meaning in relation to the structure of the model. In the present study, a simple energy balance model incorporating the reallocation of stored energy was developed, and its derivative growth equation is presented as follows:dBdt=Bα−β1+(γ/B)where B is the body mass, excluding storage and gonads, α is a coefficient representing the residual amount of surplus energy, which means assimilated energy minus allocated energy to body mass, and β is a coefficient representing the allocation rate to storage. This equation can express both infinite and finite growth curves. When β/α≤1, the system shows indeterminate growth without an upper limit of body weight, and when β/α>1, it shows determinate growth. The growth equation developed has characteristics that are intermediate between those of the traditional models with respect to the specific growth rate in relation to body mass. Moreover, it can be used to demonstrate that control of the residual amount of surplus energy through storage is essential for the regulation of body mass, i.e. the growth process.