Model uncertainty and Bayesian estimation of growth parameters of Yellowtail Snapper (Ocyurus chrysurus) from Veracruz, Mexico

Abstract

Background. Most growth analyses of Yellowtail Snapper neglect consideration of model and parameter uncertainty. Goals. In this paper, we explore model uncertainty using three models (von Bertalanffy, logistic, and Gompertz) as well as the Akaike criterion for model selection. We also estimate growth parameters and its uncertainty using the maximum likelihood estimation approach (under different assumptions of error variance) and Bayesian methods. Methods. Models were fitted to length-at-age data from organisms caught in Antón Lizardo, Veracruz. Regarding the Bayesian methods, a prior distribution for the asymptotic length was built based on data gathered from literature. We used Monte Carlo Markov Chains (MCMC) methods to fit the logistic model. Results. The Akaike criterion results suggest that the logistic model provided the best fit for the observed data (lowest AIC = 31.4). Parameter estimates included asymptotic length (L? = 64.9 ± 5.43), growth rate (K = 0.49 ± 0.07), and age at the curve inflection point (I = 3.28 ± 0.42). Regarding the Bayesian analysis, MCMC simulations suggest that the most probable value for the asymptotic length was 64.3 cm with an interval of 95% probability (58.7,70.1). The most probable value for the growth rate was 0.48 with an interval of 95% probability (0.42, 0.55). Last, the most probable value for the age at the curve inflection point was 1.7 years with a range of 95% probability (1.31, 2.16). Conclusions. The maximum likelihood estimation (MLE) and the Bayesian framework should be considered basic statistical techniques in the evaluation of individual growth of the species of interest, as they provide a robust analysis of available information of the species and the opportunity to incorporate such analysis to sustainable management practices.