Bayesian modeling of individual growth variability using back-calculation: Application to pink cusk-eel (Genypterus blacodes) off Chile

The von Bertalanffy growth function (VBGF) with random effects has been widely used to estimate growth parameters incorporating individual variability of length-at-age. Trajectories of individual growth can be inferred using either mark-recapture or back-calculation of length-at-age from growth marks in hard body parts such as otoliths. Modern statistical methods evaluate individual variation usually from mark-recapture data, and the parameters describing this function are estimated using empirical Bayes methods assuming Gaussian error. In this paper, we combine recent studies in non-Gaussian distributions and a Bayesian approach to model growth variability using back-calculated data in harvested fish populations. We presumed that errors in the VBGF can be assumed as a Student-t distribution, given the abundance of individuals with extreme length values. The proposed method was applied and compared to the standard methods using back-calculated length-at-age data for pink cusk-eel (Genypterus blacodes) off Chile. Considering several information criteria, and comparing males and females, we have found that males grow significantly faster than females, and that length-at-age for both sexes exhibits extreme length observations. Comparisons indicated that a Student-t model with mixed effects describes best back-calculated data regarding pink cusk-eel. This framework merged the strengths of different approaches to estimate growth parameters in harvested fish populations, considering modeling of individual variability of length-at-age, Bayesian inference, and distribution of errors from the Student-t model.