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CAB Reviews

A reviews journal covering agriculture, global health, nutrition, natural resources and veterinary science

CAB Review

Selection of growth functions for describing length-at-age relationships in fish species displaying different life history traits: unexpected alternatives to the von Bertalanffy equation and advantages of a pluralistic statistical approach.


Simple growth models have proven helpful to study and predict growth trajectories of fish with different life histories and from various environments, and have found numerous applications in ecology, fisheries and aquaculture worldwide. The most applied simple models (e.g. von Bertalanffy) convey little information about life history traits, are facing criticism, and their goodness of fit is assessed using a limited number of statistical outputs. This review challenges the von Bertalanffy and certain statistical outputs using real-life data, and proposes more explanatory alternatives. The length-at-age relationship from three different wild populations of four fish species (lake herring, lake whitefish, northern pike and walleye) is described using the monomolecular, Schumacher, Gompertz, logistic, von Bertalanffy and Richards equations. Comparison between models was based on least squares and likelihood theories involving several statistical outputs currently encountered in model comparison and selection studies. The analysis demonstrates that the monomolecular, Schumacher and Richards equations often stood as alternatives to the von Bertalanffy and highlighted residual sum of squares, standard error (SE) of parameter estimates and, to a lesser extent, Akaike weight as statistical outputs facilitating discrimination between candidate models. Based on visual appraisal, different equations fitted similar trajectories across the 12 growth profiles. However, the assumptions and statistical performance served to select the most appropriate models and discern life history traits of the species under study. Results indicate that comparison and selection of models should consider not only the statistical performance of equations but also the purpose of the study along with the biological/physical interpretation of parameters.