A discrete model of ontogenetic growth

Organism growth underlies numerous ecological processes. However, existing growth models from the von Bertalanffy family do not consider variable growth states (e.g., changes in resource uptake) and/or non-instantaneous changes in the growth rate of an organism along its size gradient. To address the above two points, we derived an iterative growth model (IGM) based on the necessary respiration allocation (i.e., maintenance and growth respiration), the intrinsic growth rate of tissue, and the von Bertalanffy paradigm. Some of the model parameters not only reflect the change of growth state, but also maintain a strict relationship with other parameters of biological and/or thermodynamic significance, making the model more basic and flexible. We then tested the basic performance of the IGM and its extension, and found that they are supported by some data, with different orders of magnitude, involving animals and plants. Starting with the IGM, we found that the existing metabolic growth models (e.g., the ontogenetic growth model (OGM) and its extensions) can be characterized as a special form of IGM. Not only that, the IGM also suggests true growth dynamics should have not an explicit analytic solution in most cases and lie somewhere between the Richards and Gompertz equations. Finally, the IGM revealed that the maximum biomass of an organism (M) is determined by organism average growth rate (D/T), maintenance respiration coefficient (mr) and resting metabolism exponent (b). The resulting effect of temperature on M will depend on the sensitivity to the temperature of both D/T and mr. If the former is the more sensitive of the two, M will increase. If not, it will decrease. The IGM displays great potential for the modeling and prediction of plants, endotherms and exotherms.