A two-stage biomass dynamic model for Bay of Biscay anchovy: a Bayesian approach

Abstract

Ibaibarriaga, L., Fernández, C., Uriarte, A., and Roel, B. A. 2008. A two-stage biomass dynamic model for Bay of Biscay anchovy: a Bayesian approach. – ICES Journal of Marine Science, 65: 191–205. A two-stage biomass-based state-space model with stochastic recruitment processes and deterministic dynamics was developed for the Bay of Biscay anchovy population. It is fitted in a Bayesian context with posterior computations carried out using Markov chain Monte Carlo techniques. The model is tested first on a simulated dataset and the effects of different modelling assumptions and of missing values evaluated. Then, it is applied to a real historical series of commercial catch and survey data from 1987 to 2006. Results are compared with those obtained by the standard assessment model for this stock, integrated catch-at-age analysis (ICA). From the posterior distribution of biomass in the latest year (2006), the distribution of unexploited biomass in 2007 can be derived assuming the distribution of recruitment in 2007 to be a mixture of the posterior distributions of past series recruitment. Hence, the effect of different catch options on future biomass levels can be quantified in probabilistic terms. Finally, directions for possible further improvements are indicated.

Validation of age determination using otoliths of the European anchovy (Engraulis encrasicolus L.) in the Bay of Biscay

“…Although if such variability turns out to be of little magnitude, finding a significant fitting to such relationship should be indicative of an overall satisfactory performance of the age determination, as well as of the biomass estimation procedures of the surveys. This is a suitable model for anchovy because the population mostly consists of two age groups; the 1-and 2þ-year-old fish (Ibaibarriaga et al 2008). 3.…”

Applying a two-stage Bayesian dynamic model to a short lived species, the anchovy in the Aegean Sea (Eastern Mediterranean). Comparison with an Integrated Catch at Age stock assessment model.

“…Integrated Catch at Age Analysis (ICA) for stock assessment (Patterson & Melvin, 1996;Patterson, 1998) as well as a two-stage biomass-based model (BBM), similar to the one used for the Bay of Biscay anchovy (Ibaibarriaga et al, 2008), were applied to the N. Aegean Sea anchovy stock. ICA was was implemented within the FLR framework (the Fisheries Library in R, Kell et al, 2007), whereas the BBM was implemented in WinBUGS (http://www.mrc-bsu.cam.ac.uk/bugs/; Lunn et al, 2000) using the R2WinBUGS package (Sturtz et al, 2005).…”

“…A Bayesian two-stage biomass-based model based on the one used for the Bay of Biscay anchovy (Ibaibarriaga et al, 2008) was developed for the N. Aegean Sea anchovy stock for the period 2003 -2008. The population dynamics are described in terms of biomass with two distinct age groups, fish aged 1 year and fish that are 2 or more years old (i.e.…”

“…This type of models have been implemented to the Bay of Biscay anchovy stock (Ibaibarriaga et al, 2008Trenkel, 2008) and shown to track sufficiently the main dynamics of the population. The two-stage biomass-based model (BBM) in Ibaibarriaga et al (2008Ibaibarriaga et al ( , 2011 was implemented within a Bayesian context (Punt & Hilborn, 1997;Gelman et al, 2004) accounting for the level of catches occurring throughout the year. The two-stage biomass random-effect model applied to the same stock by Trenkel (2008), is based on survey abundance indices and no catches were used.…”

“…The earlier years are modelled backwards by Virtual Population Analysis (VPA). In addition, a Bayesian two-stage biomass-based model, similar to the one used in ICES for the Bay of Biscay anchovy (Ibaibarriaga et al, 2008;ICES, 2009a) was applied. This application takes into account data on maturity to estimate spawning stock biomass, and the parameter accounting for growth and natural mortality is allowed to differ by age group.…”