Comparing Polynomial and von Bertalanffy Growth Functions for Fitting Tag–Recapture Data

Abstract

The properties of polynomial and von Bertalanffy growth functions are compared for analysing data from tag–recapture experiments in which fish are recaptured once. For the quadratic and von Bertalanffy growth functions, explicit formulae are obtained for the expected growth increment in terms of length-at-release, time-at-liberty, and the function parameters. If the least-squares fitting technique is used the von Bertalanffy function fits tag–recapture data with no more bias (probably less) than any other growth function, including polynomial growth functions. A bias-reduction technique for fitting the von Bertalanffy growth function to tag–recapture data is not applicable to other growth functions. We conclude that, apart from the straight line, the von Bertalanffy growth function is the one with the most desirable mathematical and statistical properties for fitting to tag–recapture data. The matter of the function that best characterises the way a specific fish species grows can be adequately addressed only by analyses of multiple measurements of individual fish.