Variation in the temperature preference and growth rate of individual fish reconciles differences between two growth models

Abstract

1. A growth model, originally developed for brown trout (Salmo trutta), has now been fitted to data for Atlantic salmon (S. salar) and stone-loach (Barbatula barbatula) from English populations, and Arctic charr (Salvelinus alpinus) from Sweden. The model relates growth rate to temperature for a fish of standard size and the functional relationship has a triangular shape with a sharp peak at the optimal temperature for growth and zero growth at the base of the triangle. It was unsuitable for growth data for Norwegian salmon, and a curvilinear Ratkowsky model provided a better fit, though the experimental protocol was different in the Norwegian and English experiments.

2. The Norwegian salmon were kept in groups in each tank, had to compete for food, and had to be divided into slow, moderate and fast growers before the Ratkowsky model could be fitted. Each English salmon was kept in its own tank and fed individually. For replicate experiments, fish of similar size were selected. Variation among fish kept under similar conditions was therefore small, and the triangular model was essentially for individual fish, not groups of fish.

3. The present simulation study tests the hypothesis that individual differences in the growth response could account for the curvilinear growth-temperature relationship for the Norwegian salmon. The triangular model was used to generate the growth response to temperature for a group of salmon, each fish having a slightly different temperature preference and growth rate. The result was a curvilinear response, well approximated by the Ratkowsky model (adjusted R2 = 0.96). When the variability in individual temperature preference was increased, the Ratkowsky model was an even better fit (adjusted R2 = 0.98). Therefore, the apparent discrepancy between the two models was reconciled by allowing for individual differences in temperature preference and growth rate within groups of fish.