Flexible Bayesian analysis of the von Bertalanffy growth function with the use of a log-skew-t distribution

Abstract

Abstract-The von Bertalanffygrowth function is the model most widely applied to describe growth in fish populations. Parameters describing this function usually are estimated from observed lengths at different ages by using maximum likelihood and by assuming Gaussian distributed errors. In harvested populations, observed length at age usually involves a high level of skewness and extreme values because of the size-selective sampling process. Some approaches, based on the maximum-likelihood method for making inferences, have been developed to resolve such issues. We propose a Bayesian framework for estimating growth parameters for nonlinear regression models-a framework that is based on the family of log-skew-t distributions and which provides an approach that is flexible enough for modeling the presence of asymmetries and heavy tails. This framework based on a method in which 1) the error accounts for both skewness and heavy-tailed distributions of a log-skew-t model, and 2) the observed length at each age has a heteroscedastic error distribution. The proposed method was applied and compared with the methods of previous models by using observed length-at-age data for the southern blue whiting (Micromesistius australis), an important fish species harvested in the southeast Pacific. Comparisons indicated that the proposed model is the best for describing data on southern blue whiting.

Drivers of growth for Atlantic cod (Gadus morhua L.) in Icelandic waters – A Bayesian approach to determine spatiotemporal variation and its causes

“…In this study we fit (Alós et al, 2009;Linde et al, 2011;de Zárate & Babcock, 2016;Contreras-Reyes, Quintero & Wiff, 2018;Harris, Newlon, Howell, Koch & Haeseker, 2018). Surprisingly, not that many studies have fit a basic growth model to direct conditional length-at-age data using a Bayesian framework (i.e., individuals measured directly for both length and age at a single time point, but see Thorson & Minte-Vera, 2016;Lopez Quintero et al, 2017), but in many cases, a wealth of data exists from standardised surveys and there is useful information to garner from them.…”

Sampling Procedure for Establishing Criteria for Sea Urchin (Loxechinus albus) Proportion under the Legal Minimum Length of landings

“…The sampling method based on individual weights did not necessarily assume a linear weight-age relationship, such as in the von Bertalanffy growth models used for fish catches based on the age-length relationship (see, e.g., [23,24]). This was because some old and young sea urchins with equal lengths could have similar weight.…”

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.…”