Author(s)

Katharina Renner-Martin, Norbert Brunner, Manfred Kühleitner, Werner-Georg Nowak, Klaus Scheicher

Institute of Mathematics, University of Natural Resources and Life Sciences, Vienna, Austria.

The paper searched for raw data about wild-caught fish, where a sigmoidal growth function described the mass growth significantly better than non-sigmoidal functions. Specifically, von Bertalanffy’s sigmoidal growth function (metabolic exponent-pair a = 2/3, b = 1) was compared with unbounded linear growth and with bounded exponential growth using the Akaike information criterion. Thereby the maximum likelihood fits were compared, assuming a lognormal distribution of mass (i.e. a higher variance for heavier animals). Starting from 70+ size-at-age data, the paper focused on 15 data coming from large datasets. Of them, six data with 400 - 20,000 data-points were suitable for sigmoidal growth modeling. For these, a custom-made optimization tool identified the best fitting growth function from the general von Bertalanffy-Pütter class of models. This class generalizes the well-known models of Verhulst (logistic growth), Gompertz and von Bertalanffy. Whereas the best-fitting models varied widely, their exponent-pairs displayed a remarkable pattern, as their difference was close to 1/3 (example: von Bertalanffy exponent-pair). This defined a new class of models, for which the paper provided a biological motivation that relates growth to food consumption.

Growth Models Described by the von Bertalanffy-Pütter Differential Equation, Model Selection Using the Akaike Information Criterion, Maximum Likelihood Fit Based on a Lognormal Distribution of Mass, Optimization Using Simulated Annealing

Renner-Martin, K. , Brunner, N. , Kühleitner, M. , Nowak, W. and Scheicher, K. (2019) A Model for the Mass-Growth of Wild-Caught Fish. Open Journal of Modelling and Simulation, 7, 19-40. doi: 10.4236/ojmsi.2019.71002.