Comments on proper (and improper) solutions of bioenergetic equations for modeling fish growth

This paper demonstrates that conventional bioenergetic models, that are commonly used to simulate fish growth or consumption, violate basic requirements of energy conservation when improperly applied for cases where the energy density of the fish is either a function of fish wet weight or an independent function of time. It appears that many previously published modeling results suffer from this deficiency unless the authors have made perspicuous provisions to avoid implicit imbalances that occur in the equations under these conditions. The incorrect solutions tend to overestimate fish growth and net energy consumption. The magnitude of these errors is a function of how rapidly the fish energy density changes as the fish increases in size. The errors can be as much as 30% for small fish in the range of 1 to 5 g per individual where the energy density changes rapidly. Although this mathematical error does not occur if fish energy density is modeled as a constant, this assumption is probably inadequate for most applications and results in a substantial “biological error.” It is recommended that published results for these various cases be critically reviewed and corrected where warranted. The errors can be readily eliminated when the bioenergetic model equations are handled properly as demonstrated in this paper.