# Reassessment Individual Growth Analysis of the Gulf Corvina, Cynoscion othonopterus (Teleostei: Sciaenidae), Using Observed Residual Error

## TL;DR

This study evaluates the growth patterns of the Gulf corvina fish using a new statistical approach to improve model accuracy for sustainable fisheries management.

## Contribution

The study introduces observed variance as a novel criterion for improving the accuracy of fish growth modeling.

## Key findings

- The observed variance approach provided the best fit for the logistic growth model of the Gulf corvina.
- Using observed variance improved model performance compared to traditional variance approaches.
- The Bayesian information criterion confirmed observed variance as the optimal method for parametrizing growth.

## Abstract

The Gulf corvina (Cynoscion othonopterus) is a fish belonging to the Sciaenidae family endemic to the Gulf of California, commonly known as croaker. This species is migratory, annually moving to the Upper Gulf of California and the Colorado River Delta biosphere reserve between February and May to reproduce. It is highly valued in fisheries due to its catch volume and its availability during Lent, a period when Mexicans traditionally consume more fish in place of red meat, following Catholic customs. Therefore, responsible management is essential to ensure sustainable exploitation. Effective management requires an understanding of the species growth patterns, which has led to the development of various mathematical models and analytical approaches. In this study, we use a criterion that is gaining prominence for estimating parameters within mathematical growth equations: observed variance. This criterion is compared to those traditionally used in previous studies aimed at assessing the growth of fish in fisheries and aquaculture.

Growth is the most influential aspect in demographic species analysis. Collecting data on ages and sizes (such as length and weight) is a fundamental step in growth modeling, particularly in fishery science. Residual analysis plays a crucial role in parameterizing the mathematical models chosen to describe the growth patterns of the species under investigation. Using optimal residual criteria is essential to improving model performance and accuracy. In the present study, the length-at-age data of the Gulf corvina (Cynoscion othonopterus) were evaluated with the Schnute model to obtain the best error type and to establish the most accurate growth pattern. Later, the observed, constant, depensatory, and compensatory variance approaches were tested using the logistic model. The Bayesian information criterion (BIC) was used as the goodness-of-fit test to obtain the best variance approach parametrizing the growth model. The BIC values selected the observed variance as the best approach to parametrize the logistic growth model. The conclusion is that the observed variance approach produces robust results—that is, the observed variance produced the most plausible fits. It is suggested that the observed error structure should be used to estimate individual growth.