A Model for the Mass-Growth of Wild-Caught Fish

Abstract

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.

Best-fitting growth curves of the von Bertalanffy-Pütter type

“…Further, the parameters p and q relate to biological parameters, namely to asymptotic mass m max , to mass m inc at the inception point, and to the maximal growth rate. This, in turn, provides for another biological explanation of the exponents: ( a / b ) 1/( b – a ) = m inc / m max (for details: Renner-Martin et al, 2018, 2019).…”

“…Similarly, for the generalized von Bertalanffy model, b = 1 and 0 ≤ a < 1 is a free parameter. The authors (Renner-Martin et al, 2019) developed an alternative biological explanation for the exponents, based on a model by Parks (1982): The first exponent a relates instantaneous energy intake to body mass and the difference b – a relates energy consumption to growth (a larger difference meaning a faster growth for the same consumption).…”