Fitting the individual growth from otolith marks using a Bayesian non-linear mixed effect model in marine fish

Abstract

We used back-calculated lengths-at-age data from sagittal otoliths of Serranus scriba (a widely distribute exploited fish) to describe the individual growth of this Serranid and its intra-population variability by means of a Bayesian approach. The conventional three-parameter based von Bertalanffy model (i.e., which assumes that the growth rate parameter is constant along fish life) systematically biases individual growth. Here we propose an extension of the von Bertalanffy model that accommodates for one change of growth rate at some moment of the life span (motivated by the maturation). This alternative five-parameter model (L∞, k0, k1, t0 and t1, i.e., size at infinite age, initial and final growth rate, age at size zero and age at the change of growth rate). Results showed how the change in growth rate caused by the different allocation of the energy to the somatic growth or reproduction prior- and post-sexual maturity can be identified from he growth pattern contained in the otoliths. Regarding the relationships between the Bayesian means of the individual growth parameters, results showed different tendencies and contributed to understand the individual growth of this species. Intra-population variability is noticeable and depicts a remarkable plasticity of growth that usually remains unreported. This novel individual growth model and its intra-population variability suggested some interesting relationships with environmental cues that should guide future research