Modernising fish and shark growth curves with Bayesian length-at-age models

Abstract

Growth modelling is a fundamental component of fisheries assessments but is often hindered by poor quality data from biased sampling. Several methods have attempted to account for sample bias in growth analyses. However, in many cases this bias is not overcome, especially when large individuals are under-sampled. In growth models, two key parameters have a direct biological interpretation: L0, which should correspond to length-at-birth and L∞, which should approximate the average length of full-grown individuals. Here, we present an approach of fitting Bayesian growth models using Markov Chain Monte Carlo (MCMC), with informative priors on these parameters to improve the biological plausibility of growth estimates. A generalised framework is provided in an R package ‘BayesGrowth’, which removes the hurdle of programming an MCMC model for new users. Four case studies representing different sampling scenarios as well as three simulations with different selectivity functions were used to compare this Bayesian framework to standard frequentist growth models. The Bayesian models either outperformed or matched the results of frequentist growth models in all examples, demonstrating the broad benefits offered by this approach. This study highlights the impact that Bayesian models could provide in age and growth studies if applied more routinely rather than being limited to only complex or sophisticated applications.

Life-history characteristics of the eastern shovelnose ray,

“…As such, biased estimates of growth result in biased estimates of M (D'Alberto et al 2019), leading to inaccurate assessments of stock status (Pardo et al 2013). Estimating growth parameters in a Bayesian framework overcomes this bias (Smart and Grammer 2021). Campbell et al (2017) quantified the ecological risk posed to A. rostrata by the ECOTF, by using the sustainability assessment for fishing effects (SAFE) quantitative ERA developed by (Zhou et al 2009).…”

“…Bayesian models were fit using the 'BayesGrowth' package (Smart 2020; accessed 18 February 2021), by using R statistical software (ver. 3.6.1, R Foundation for Statistical Computing, Vienna, Austria, see https://www.R-project.org/, accessed 18 February 2021), in accord with methods described by Smart and Grammer (2021) and Emmons et al (2021). The 'Bayes-Growth' package uses the 'Stan' computer program (Carpenter et al 2017), via the 'Rstan' package (Stan Development Team 2020) to perform MCMC using no U-turn sampling (NUTS).…”

Modelling Fish Growth with Imperfect Data: The Case of Trachurus picturatus

“…Finally, in the third step, the four growth models derived from length-at-age data from direct readings, with and without t 0 constraint and using the Bayesian approach and from the back-calculated length-at-age data were evaluated for relative suitability. Because differences in sample sizes precluded the use of model selection statistics such as the AIC [18], models were visually inspected for their fit to the data, and the model that provided the most biologically reliable parameter estimates according to the species biology was judged as most plausible, as in other fisheries studies [8].…”

“…This adds to previous evidence demonstrating the utility of Bayesian inference in modelling fish growth with imperfect data and sample sizes. Bayesian approaches have been shown to produce equivalent or improved growth estimates relative to frequentist approaches in multiple species, except for large samples including all age classes [8]. Although the Bayesian inference needs considerably more statistical and programming expertise, it is simple to implement in open-source statistical environments, such as R [30].…”

“…Several methods have been used to deal with under-sampling, including back-calculating, length-at-age [4] and constraining model fits by fixing asymptotic length (L ∞ ), or age at length zero (t 0 ) parameters when large and small individuals are missed, respectively [3]. More recently, Bayesian approaches incorporating prior knowledge into the analysis and producing a combined output from the priors and the data available have also gained emphasis in length-at-age analyses (e.g., [5][6][7][8]). However, applications of Bayesian inference in growth modelling are still limited, and more empirical evidence on the relative benefits of the different methods dealing with poor quality data from biased sampling is needed.…”