Growth estimates of cardinalfish (Epigonus crassicaudus) based on scale mixtures of skew-normal distributions

Abstract

Our article presents a robust and flexible statistical modeling for the growth curve associated to the age-length relationship of Cardinalfish (Epigonus Crassicaudus). Specifically, we consider a non-linear regression model, in which the error distribution allows heteroscedasticity and belongs to the family of scale mixture of the skewnormal (SMSN) distributions, thus eliminating the need to transform the dependent variable into many data sets. The SMSN is a tractable and flexible class of asymmetric heavy-tailed distributions that are useful for robust inference when the normality assumption for error distribution is questionable. Two well-known important members of this class are the proper skew-normal and skew-t distributions. In this work emphasis is given to the skew-t model. However, the proposed methodology can be adapted for each of the SMSN models with some basic changes. The present work is motivated by previous analysis about of Cardinalfish age, in which a maximum age of 15 years has been determined. Therefore, in this study we carry out the mentioned methodology over a data set that include a long-range of ages based on an otolith sample where the determined longevity is higher than 54 years.

Reproductive biology of female cardinalfish, Epigonus crassicaudus de Buen, 1959

“…Currently, only basic knowledge for cardinalfish on growth (Gálvez et al., ; Cubillos et al., ; Ojeda et al., ; Contreras‐Reyes and Arellano‐Valle, ), natural mortality (Cubillos et al., ; Tascheri et al., ) and maturity (Gálvez et al., ; Cubillos et al., ) is available. Gálvez et al.…”

“…Currently, only basic knowledge for cardinalfish on growth (G alvez et al, 2000;Cubillos et al, 2009;Ojeda et al, 2010;Contreras-Reyes and Arellano-Valle, 2013), natural mortality (Cubillos et al, 2009;Tascheri et al, 2012) and maturity (G alvez et al, 2000;Cubillos et al, 2009) is available. G alvez et al (2000) and Cubillos et al (2009) reported on maturity ogives in this species; both reproductive studies showed significant differences between estimates of length at 50% of maturity.…”

Making the most of survey data: Incorporating age uncertainty when fitting growth parameters

“…Throughout this study we assumed multiplicative log‐normal errors in order to describe the uncertainty not captured by VBGF. This provides several advantages, such as the interpretations of and reduced standard errors (Quintero, Contreras‐Reyes, Wiff, & Arellano‐Valle, ), however other, more flexible, error distributions that have been proposed, such as the log‐skewed‐t distribution (e.g., Contreras‐Reyes & Arellano‐Valle, ). Furthermore, we plan to investigate whether fish spawned in the same time period (e.g., year) have similar growth patterns in order to try and explain some of the uncertainty not captured in our model.…”

“…The parameters of the von Mises distributions in models IV and V were taken from Datta & Blanchard (). In models III and V, was defined in equation , with , , and .…”

“…Valle, 2013). Furthermore, we plan to investigate whether fish spawned in the same time period (e.g., year) have similar growth patterns in order to try and explain some of the uncertainty not captured in our model.As shown in this article, fitting to different quarters of data can lead to different posterior distributions of the VBGF.…”