Optimal and near-optimal exponent-pairs for the Bertalanffy-Pütter growth model

Area of Science:

• Ecology
• Fisheries Science
• Mathematical Biology

Background:

• The Bertalanffy-Pütter growth model offers a flexible framework for describing organismal mass-growth.
• The common von Bertalanffy growth function (VBGF) is a special case, widely used in fisheries.
• Generalizing the model involves optimizing additional exponents, increasing complexity.

Purpose of the Study:

• To test if optimizing both exponents (a, b) in the Bertalanffy-Pütter model significantly improves fit to mass-growth data.
• To evaluate the trade-off between model complexity and predictive performance.
• To assess the utility of the generalized model in natural resources management.

Main Methods:

• Fitted the Bertalanffy-Pütter model to a large dataset (20,166 Walleye, Sander vitreus) of mass-at-age data.
• Assessed model fit across a grid of 14,281 exponent pairs (a, b).
• Utilized the Akaike information criterion (AIC) for model selection.

Main Results:

• The optimal exponent pair was found on the boundary a=b=0.686, corresponding to the generalized Gompertz equation.
• AIC indicated that the standard von Bertalanffy exponent-pair model provided a more parsimonious fit than the generalized model.
• Despite not improving AIC, the optimized exponents offered potential bias reduction.

Conclusions:

• Optimizing both exponents in the Bertalanffy-Pütter model did not yield a significantly better fit compared to the standard VBGF for the tested dataset.
• The increased complexity of the generalized Bertalanffy-Pütter model may not be justified by improved parsimony alone.
• The model's bias reduction capabilities warrant consideration in natural resources management, particularly in fisheries stock assessments, where predictive power is paramount.