Fitting of von Bertalanffy growth model: Stochastic differential equation approach

Abstract

In this paper, the well-known von Bertalanffy growth (VBG) model for estimating age-length relationship in fisheries is considered. It is emphasised that nonlinear estimation procedures should be adopted for fitting the von Bertalanffy nonlinear statistical (VBNS) model rather than the age-old Ford-Walford plot. Some limitations of employing VBNS modelling approach are highlighted. Employment of stochastic differential equation (SDE) approach, which does not suffer from these limitations, is advocated for fitting the VBG model. The methodology for fitting the von Bertalanffy SDE (VBSDE) model is described. Relevant computer code for fitting this model is written in SAS package and the same is included as an Appendix. Finally, as an illustration, superiority of VBSDE model over VBNS model for fitting and forecasting purposes is shown for rainbow trout (Onchorhynchus mykiss) age-length data.