A generic model to estimate food consumption: linking von Bertalanffy's growth model with Beverton and Holt's and Ivlev's concepts of net conversion efficiency

In this paper, a mathematical derivation is presented that links von Bertalanffy's growth model with the concept of net conversion efficiency of Beverton and Holt, aiming at the development of an equation that can calculate food consumption rates of wild populations from parameters of the von Bertalanffy growth equation and an estimate of the net food conversion efficiency of Beverton and Holt. The derivation is based on Pauly's version of the generalized von Bertalanffy equation, which allows the allometric exponent of the anabolism term to differ from 2/3, as in the standard von Bertalanffy equation. As a side product, a general model is formulated that describes the gross growth conversion efficiency (K-1 of Ivlev) as a function of weight of the organism. The new equations for the estimation of food consumption are applied in two case studies, North Sea cod (Gadus morhua) and whiting (Merlangius merlangus), for which a variety of consumption estimates is available from conventional gastric evacuation-based methods. The new method produces results that show a similar degree of variability as was observed in various applications of the gastric evacuation method.