A new model for simulating growth in fish

Abstract

A real dynamic population model calculates change in population sizes independent of time. The Beverton & Holt (B&H) model commonly used in fish assessment includes the von Bertalanffy growth function which has age or accumulated time as an independent variable. As a result the B&H model has to assume constant fish growth. However, growth in fish is highly variable depending on food availability and environmental conditions. We propose a new growth model where the length increment of fish living under constant conditions and unlimited food supply, decreases linearly with increasing fish length until it reaches zero at a maximal fish length. The model is independent of time and includes a term which accounts for the environmental variation. In the present study, the model was validated in zebrafish held at constant conditions. There was a good fit of the model to data on observed growth in Norwegian spring spawning herring, capelin from the Barents Sea, North Sea herring and in farmed coastal cod. Growth data from Walleye Pollock from the Eastern Bering Sea and blue whiting from the Norwegian Sea also fitted reasonably well to the model, whereas data from cod from the North Sea showed a good fit to the model only above a length of 70 cm. Cod from the Barents Sea did not grow according to the model. The last results can be explained by environmental factors and variable food availability in the time under study. The model implicates that the efficiency of energy conversion from food decreases as the individual animal approaches its maximal length and is postulated to represent a natural law of fish growth.