Estimation of von Bertalanffy Growth Curve Parameters Using both Length Increment and Age–Length Data

Abstract

Many fish species cannot be aged directly over their full range of lengths. Therefore, to estimate a growth curve, one often uses length increment data from a mark–recapture experiment, supplemented by whatever age–length data are available. I describe a new method for maximum likelihood estimation of the three von Bertalanffy growth curve parameters, using the length increment and age–length data jointly. Also, I describe a likelihood ratio test for determining whether the same growth curve fits both data sets adequately. The von Bertalanffy growth curve can be taken as a predictive regression with either length or age as the dependent variable. Here, age is taken as the dependent variable, as would be appropriate for estimation of age from length, but only minor modifications are necessary for the more common alternative predictive regression of length on age. As an illustration, the techniques are applied to data for southern bluefin tuna, Thunnus maccoyii.