Implementation of sigmoidal models with different functional forms to estimate length at 50% maturity: A case study of the Pacific red snapper Lutjanus peru

Abstract

To estimate mean size at sexual maturity (L50), a particular model is usually selected arbitrarily, and this decision does not consider the functional form (FF) of both the model (FFM) and the observed data (FFD). In this study, the performance of different sigmoidal models was evaluated by using data sources with different FF. To illustrate this, five sigmoidal models—Gompertz (GoM), logistic (LoM), Hill (HiM), Weibull (WeM), and gamma (GaM)—were used to estimate L50 for each sex and for the combined sexes of Lutjanus peru captured in the Eastern Central Pacific. To avoid redundancy, the models were selected based on different statistical properties: parameters in common L50; the same number of parameters (2); non-nested; different FF including symmetric or asymmetric; and asymptotic maturity equal to 1. Each model was fit to minimize the negative log likelihood by using a binomial probabilistic density function. Bias-corrected non-parametric confidence intervals CI were estimated for the parameters and predictions. The model average (AvM) and their CI were calculated by using the multi-model inference approach. According to the FFD, the best-fitting model was different for females (WeM), males (HiM), and the combined sexes (GaM). The comparison among the models revealed three features: i) the CI values overlapped among the data sets; ii) the estimate of L50 showed a gradient from right-skewed to left-skewed FF, which increases its value by ca. 7 cm; and iii) according to the selected model, it was possible to identify a marked variability in the computed L50. According to the multi-model approach, AvM was estimated for: i) females, L50 = 42.3 cm standard length LS computed from the WeM and LoM; ii) males, L50 = 37.4 cm LS computed from the GoM and WeM; and iii) the combined sexes, L50 = 39.5 cm LS estimated from the GaM as the unique model. The results show the importance of considering the FFD when L50 is estimated. By following this procedure, the AvM could be more informative regarding L50 estimates. This study proposes the implementation of sigmoidal models with different FF so that they can be fit to different FFD; this procedure exhibits the potential uncertainty linked to the candidate models.