Extension of von Bertalanffy growth model incorporating growth patterns of soft and hard tissues in bivalve molluscs

Abstract

A new practical growth model through the partial reconstruction for the von Bertalanffy function (VBF) has been proposed. In numerous studies on various species, VBF has been recognized as an appropriate function to describe growth. Here the difference in growth dynamics between soft and hard tissues is considered using VBF. A differential equation in which the growth rates of these two tissue types are described, gives a four parameter model. This advanced model showed characteristics such as: (i) S-shape curve similar to the Gompertz model; (ii) unfixed point of inflection; and (iii) definition as an implicit function. The characteristic indicated in (iii) makes it impossible to apply the method of least squares to data analysis. Therefore, a solution was introduced combining Lagrange’s method of indeterminate coefficients and the Newton method. Data analysis for verifying the performance of the advanced model was conducted on published data on growth of the bivalve Spisula sachalinensis. As a result of the comparison among the existing growth models, the advanced model produced the minimum value of Akaike information criterion (AIC).