A flexible maximum likelihood approach for fitting growth curves to tag–recapture data

Abstract

We describe a novel maximum likelihood method for fitting general growth curves to tag–recapture data. The growth model allows for the asymptotic length and the time to tagging to vary from individual to individual, with other parameters being fixed. Unlike the Fabens approach, we do not take differences to fit the parameters, but instead model the joint density of the release and recapture lengths. We simulate data to examine the bias and precision of the estimated parameters obtained using our fitting method. We include simulations for which the time to tagging model is incorrect, but find that the growth curve is usually still fitted with small bias. Furthermore, we introduce a new growth curve that allows for different growth rates for juveniles and adults. The new growth curve needs sufficient data coverage before and after the transition from juvenile to adult for all parameters to be estimated precisely. We illustrate the method on real data by fitting this new growth curve to southern bluefin tuna tag–recapture data.