Modelling fish growth:: multi-model inference as a better alternative to a priori using von Bertalanffy equation

The common practice among researchers who study fish growth is to a priori adopt the von Bertalanffy growth model (VBGM), which is the most used and ubiquitous equation in the fisheries literature. However, in many cases VBGM is not supported by the data and many species seem to follow different growth trajectories. The information theory approach frees the researcher from the limiting concept that a 'true' growth model exists. Multi-model inference (MMI) based on information theory is proposed as a more robust alternative to study fish growth. The proposed methodology was applied to 133 sets of length-at-age data. Four candidate models were fitted to each data set: von Bertalanffy growth model (VBGM), Gompertz model, Logistic and the Power model; the three former assume asymptotic and the latter non-asymptotic growth. In each case, the 'best' model was selected by minimizing the small-sample, bias-corrected form of the Akaike information criterion (AIC(c)). To quantify the plausibility of each model, the 'Akaike weight' w(i) of each model was calculated. Following a MMI approach, the model averaged asymptotic length (L) over bar (infinity) for each case was estimated, by model averaging estimations of L-infinity interpreting Akaike weights as a posterior probability distribution over the set of candidate models. The VBGM was not selected as the best model in 65.4% of the cases. Most often VBGM was either strongly supported by the data (with no other substantially supported model) or had very low or no support by the data. The estimation of asymptotic length was greatly model dependent; L-infinity as estimated by VBGM was in every case greater than that estimated by the Gompertz model, which in turn was always greater than that estimated by the Logistic model. The percentage underestimation of the standard error of L-infinity, when ignoring model selection uncertainty, was on average 18% with values as high as 91%. Ignoring model selection uncertainty may have serious implications, e.g. when comparing the growth parameters of different fish populations. Multi-model inference by model averaging, based on Akaike weights, is recommended as a simple and easy to implement method to model fish growth, for making robust parameter estimations and dealing with model selection uncertainty.