Compositional analysis of catch curve data, with an application to Sebastes maliger

Abstract

Schnute, J. T. and Haigh, R. 2007. Compositional analysis of catch curve data, with an application to Sebastes maliger. – ICES Journal of Marine Science, 64: 218–233. This paper applies modern compositional analysis to catch curve data from a quillback rockfish (Sebastes maliger) population in British Columbia, Canada. Bubble plots and ternary diagrams portray variable age distributions and highlight distinctions between commercial and survey sample data. The models formalize important historical issues in catch curve analysis related to selectivity and recruitment variability, where a particular model corresponds to a prescribed vector of design parameters. The roles that compositional distributions (multinomial, Dirichlet, logistic-normal) can play in fishery data analysis are described, and Bayesian methods are used to examine how the distribution of a key mortality parameter depends on model choice. The framework provides a direct link between model designs and policy outcomes that depend on estimated mortalities or mortality ratios.

Review and evaluation of likelihood functions for composition data in stock-assessment models: Estimating the effective sample size

“…temporal variability in selectivity or growth). Schnute and Haigh (2007) use the logistic-normal (or multivariate logistic; Schnute and Richards, 1995) distribution, which they show can be converted into a multivariate normal with appropriate transformations.…”

“…Fournier et al (1990) added a constant to the variance, and Schnute and Haigh (2007) amalgamated ages to avoid this problem. Simulation analysis should be conducted to determine the influence of these modifications on the results and provide guidelines on the size of the constant or how to amalgamate ages.…”

“…It was not clear from my analysis whether observed or predicted proportions should be used in the likelihood so I recommend using observed proportions based on previous research (Starr et al, 1999). Finally, to avoid computational errors, a constant may need to be added to the variance when the observed proportion is zero following Fournier et al (1990) or ages amalgamating together (Schnute and Haigh, 2007).…”

A general model for reconstructing salmon runs

“…This step can of course be omitted if the samples are randomly obtained from the population, or alternatively a different likelihood could be used. The logit-normal and Dirichlet likelihoods (Schnute and Haigh 2007) both estimate the uncertainty directly from the data but are unsuitable in this instance because they are undefined when the observed proportions are zero for any age group (which leads to divide-by-zero and log-zero errors). The robust normal likelihood (Fournier et al 1990;Hilborn et al 2003a) offers some advantages in terms of robustness but is not as widely used as the multinomial and also requires the estimation of effective sample sizes.…”

An individual-based approach to year-class strength estimation

“…In reality, most of the assumptions underlying the catch-curve approach are violated (Dunn et al, 2002;Catalano et al, 2009), thus requiring modifications of the simple approach outlined above (Xiao, 2005;Schnute and Haigh, 2007;Wayte and Klaer, 2010;Thorson and Prager, 2011). One core issue that is common to all approaches utilizing catch-at-age data is that sampled individuals are pooled into discrete (integer) age-classes.…”