A-SCALA: an age-structured statistical catch-at-length analysis for assessing tuna stocks in the eastern tropical Pacific Ocean

English: We describe an age-structured statistical catch-at-length analysis (A-SCALA) based on the MULTIFAN-CL model of Fournier et al. (1998). The analysis is applied independently to both the yellowfin and the bigeye tuna populations of the eastern Pacific Ocean (EPO). We model the populations from 1975 to 1999, based on quarterly time steps. Only a single stock for each species is assumed for each analysis, but multiple fisheries that are spatially separate are modeled to allow for spatial differences in catchability and selectivity. The analysis allows for error in the effort-fishing mortality relationship, temporal trends in catchability, temporal variation in recruitment, relationships between the environment and recruitment and between the environment and catchability, and differences in selectivity and catchability among fisheries. The model is fit to total catch data and proportional catch-at-length data conditioned on effort. The A-SCALA method is a statistical approach, and therefore recognizes that the data collected from the fishery do not perfectly represent the population. Also, there is uncertainty in our knowledge about the dynamics of the system and uncertainty about how the observed data relate to the real population. The use of likelihood functions allow us to model the uncertainty in the data collected from the population, and the inclusion of estimable process error allows us to model the uncertainties in the dynamics of the system. The statistical approach allows for the calculation of confidence intervals and the testing of hypotheses. We use a Bayesian version of the maximum likelihood framework that includes distributional constraints on temporal variation in recruitment, the effort-fishing mortality relationship, and catchability. Curvature penalties for selectivity parameters and penalties on extreme fishing mortality rates are also included in the objective function. The mode of the joint posterior distribution is used as an estimate of the model parameters. Confidence intervals are calculated using the normal approximation method. It should be noted that the estimation method includes constraints and priors and therefore the confidence intervals are different from traditionally calculated confidence intervals. Management reference points are calculated, and forward projections are carried out to provide advice for making management decisions for the yellowfin and bigeye populations. Spanish: Describimos un análisis estadístico de captura a talla estructurado por edad, A-SCALA (del inglés age-structured statistical catch-at-length analysis), basado en el modelo MULTIFAN- CL de Fournier et al. (1998). Se aplica el análisis independientemente a las poblaciones de atunes aleta amarilla y patudo del Océano Pacífico oriental (OPO). Modelamos las poblaciones de 1975 a 1999, en pasos trimestrales. Se supone solamente una sola población para cada especie para cada análisis, pero se modelan pesquerías múltiples espacialmente separadas para tomar en cuenta diferencias espaciales en la capturabilidad y selectividad. El análisis toma en cuenta error en la relación esfuerzo-mortalidad por pesca, tendencias temporales en la capturabilidad, variación temporal en el reclutamiento, relaciones entre el medio ambiente y el reclutamiento y entre el medio ambiente y la capturabilidad, y diferencias en selectividad y capturabilidad entre pesquerías. Se ajusta el modelo a datos de captura total y a datos de captura a talla proporcional condicionados sobre esfuerzo. El método A-SCALA es un enfoque estadístico, y reconoce por lo tanto que los datos obtenidos de la pesca no representan la población perfectamente. Además, hay incertidumbre en nuestros conocimientos de la dinámica del sistema e incertidumbre sobre la relación entre los datos observados y la población real. El uso de funciones de verosimilitud nos permite modelar la incertidumbre en los datos obtenidos de la población, y la inclusión de un error de proceso estimable nos permite modelar las incertidumbres en la dinámica del sistema. El enfoque estadístico permite calcular intervalos de confianza y comprobar hipótesis. Usamos una versión bayesiana del marco de verosimilitud máxima que incluye constreñimientos distribucionales sobre la variación temporal en el reclutamiento, la relación esfuerzo-mortalidad por pesca, y la capturabilidad. Se incluyen también en la función objetivo penalidades por curvatura para los parámetros de selectividad y penalidades por tasas extremas de mortalidad por pesca. Se usa la moda de la distribución posterior conjunta como estimación de los parámetros del modelo. Se calculan los intervalos de confianza usando el método de aproximación normal. Cabe destacar que el método de estimación incluye constreñimientos y distribuciones previas y por lo tanto los intervalos de confianza son diferentes de los intervalos de confianza calculados de forma tradicional. Se calculan puntos de referencia para el ordenamiento, y se realizan proyecciones a futuro para asesorar la toma de decisiones para el ordenamiento de las poblaciones de aleta amarilla y patudo.

Using experiments and expert judgment to model catchability of Pacific rockfishes in trawl surveys, with application to bocaccio (Sebastes paucispinis) off British Columbia

The time series of abundance indices for many groundfish populations, as determined from trawl surveys, are often imprecise and short, causing stock assessment estimates of abundance to be imprecise. To improve precision, prior probability distributions (priors) have been developed for parameters in stock assessment models by using meta-analysis, expert judgment on catchability, and empirically based modeling. This article presents a synthetic approach for formulating priors for rockfish trawl survey catchability (qgross). A multivariate prior for qgross for different surveys is formulated by using 1) a correction factor for bias in estimating fish density between trawlable and untrawlable areas, 2) expert judgment on trawl net catchability, 3) observations from trawl survey experiments, and 4) data on the fraction of population biomass in each of the areas surveyed. The method is illustrated by using bocaccio (Sebastes paucipinis) in British Columbia. Results indicate that expert judgment can be updated markedly by observing the catch-rate ratio from different trawl gears in the same areas. The marginal priors for qgross are consistent with empirical estimates obtained by fitting a stock assessment model to the survey data under a noninformative prior for qgross. Despite high prior uncertainty (prior coefficients of variation ≥0.8) and high prior correlation between qgross, the prior for qgross still enhances the precision of key stock assessment quantities.

A prior for steepness in stock-recruitment relationships, based on an evolutionary persistence principle

Priors are existing information or beliefs that are needed in Bayesian analysis. Informative priors are important in obtaining the Bayesian posterior distributions for estimated parameters in stock assessment. In the case of the steepness parameter (h), the need for an informative prior is particularly important because it determines the stock-recruitment relationships in the model. However, specifications of the priors for the h parameter are often subjective. We used a simple population model to derive h priors based on life history considerations. The model was based on the evolutionary principle that persistence of any species, given its life history (i.e., natural mortality rate) and its exposure to recruitment variability, requires a minimum recruitment compensation that enables the species to rebound consistently from low critical abundances (Nc). Using the model, we derived the prior probability distributions of the h parameter for fish species that have a range of natural mortality, recruitment variabilities, and Nt values.