Modelling fish growth: Model selection, multi-model inference and model selection uncertainty

Model selection based on information theory is a relatively new paradigm in biological sciences with several advantages over the classical approaches. The aim of the present study was to apply information theory in the area of modelling fish growth and to show how model selection uncertainty may be taken into account when estimating growth parameters. The methodology was applied for length–age data of four species of fish, taken from the literature. Five-candidate models were fitted to each dataset: von Bertalanffy growth model (VBGM), generalized VBGM, Gompertz growth model, Schnute–Richards growth model, and logistic. In each case, the ‘best’ model was selected by minimizing the small-sample, bias-corrected form of the Akaike information criterion (AIC). To quantify the plausibility of each model, given the data and the set of five models, the ‘Akaike weight’ wiwi of each model was calculated. The average model was estimated for each case based on wiwi. Following a multi-model inference (MMI) approach, the model-averaged asymptotic length L¯∞ for each species was estimated, using all five models, by model-averaging estimations of L∞ and weighting the prediction of each model by wiwi. In the examples of this study, model selection uncertainty caused a magnification of the standard error of the asymptotic length of the best model (up to 3.9 times) and thus in all four cases estimating L∞ from just the best model would have caused overestimation of precision of the asymptotic length. The VBGM, when used for inference, without being the best model, could cause biased point estimation and false evaluation of precision. Model selection uncertainty should not be ignored even if VBGM is the best model. Multi-model inference by model-averaging, based on Akaike weights, is recommended for making robust parameter estimations and for dealing with uncertainty in model selection.