Effect of Individual Variability on the von Bertalanffy Growth Equation

Abstract

The growth in length of a group of animals is examined. Each animal is assumed to grow according to the von Bertalanffy model with fixed parameters, but these parameters are allowed to differ between individuals. Equations governing the mean and variance of length at given age and growth increment at given length are provided, and their implications discussed. Results indicate that the traditional growth equation is likely to result in an underestimate of the mean value of K when either length at age or growth increment data are analyzed. This problem does not appear serious when using length at age data. However, the problems of interpretation are more serious in the case of growth increment data where serious overestimates of the reconstructed mean length at age can result. A thorough analysis of growth cannot be made for a population exhibiting individual variability in L∞ and K from growth increment data alone. In particular a nonlinear relationship between growth increment and initial length does not necessarily imply that the von Bertalanffy model is inappropriate to the species in question. A topic urgently in need of examination is the form of the joint distribution of K and L∞ in animal populations.Key words: von Bertalanffy, growth models