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

Ibaibarriaga, L., Fernandez, 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.

[1]  Stephen T. Buckland,et al.  Fitting Population Dynamics Models to Count and Cull Data Using Sequential Importance Sampling , 2000 .

[2]  Russell B. Millar,et al.  Bayesian state-space modeling of age-structured data: fitting a model is just the beginning , 2000 .

[3]  C. Walters,et al.  Quantitative Fisheries Stock Assessment , 1992, Springer US.

[4]  Russell B. Millar,et al.  Bayesian stock assessment using a state-space implementation of the delay difference model , 1999 .

[5]  Samu Mäntyniemi,et al.  Bayesian mark-recapture estimation with an application to a salmonid smolt population , 2002 .

[6]  C. Walters,et al.  Quantitative fisheries stock assessment: Choice, dynamics and uncertainty , 2004, Reviews in Fish Biology and Fisheries.

[7]  Murdoch K. McAllister,et al.  A Bayesian state-space mark-recapture model to estimate exploitation rates in mixed-stock fisheries , 2006 .

[8]  Patrick Prouzet,et al.  Bay of Biscay and Ibero Atlantic anchovy populations and their fisheries , 1996 .

[9]  Ángel Borja,et al.  Relationships between anchovy (Engraulis encrasicolus L.) recruitment and the environment in the Bay of Biscay , 1996 .

[10]  Ángel Borja,et al.  Relationships between anchovy (Engraulis encrasicolus recruitment and environment in the Bay of Biscay (1967-1996) , 1998 .

[11]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[12]  Bradley P. Carlin,et al.  Markov Chain Monte Carlo conver-gence diagnostics: a comparative review , 1996 .

[13]  P. Petitgas,et al.  The selection process from larval to juvenile stages of anchovy (Engraulis encrasicolus) in the Bay of Biscay investigated by Lagrangian simulations and comparative otolith growth , 2003 .

[14]  Peter Green,et al.  Markov chain Monte Carlo in Practice , 1996 .

[15]  Andrew Thomas,et al.  WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility , 2000, Stat. Comput..

[16]  Stephen T. Buckland,et al.  A UNIFIED FRAMEWORK FOR MODELLING WILDLIFE POPULATION DYNAMICS † , 2005 .

[17]  R. Hilborn,et al.  Fisheries stock assessment and decision analysis: the Bayesian approach , 1997, Reviews in Fish Biology and Fisheries.

[18]  Robert Gentleman.  Personal Crunching: A Review of BUGS: Bayesian Inference Using Gibbs Sampling , 1997 .

[19]  James N. Ianelli,et al.  Bayesian stock assessment using catch-age data and the sampling - importance resampling algorithm , 1997 .

[20]  A. Uriarte,et al.  The spawning environment of the Bay of Biscay anchovy (Engraulis encrasicolus L.) , 1996 .

[21]  D. Butterworth,et al.  Assessment of the South African chokka squid Loligo vulgaris reynaudii: Is disturbance of aggregations by the recent jig fishery having a negative impact on recruitment? , 2000 .

[22]  Russell B. Millar,et al.  Non‐linear state space modelling of fisheries biomass dynamics by using Metropolis‐Hastings within‐Gibbs sampling , 2000 .

[23]  Russell B. Millar,et al.  BUGS in Bayesian stock assessments , 1999 .

[24]  Timothy J. Robinson,et al.  Sequential Monte Carlo Methods in Practice , 2003 .

[25]  Jeremy S. Collie,et al.  Estimating Population Size from Relative Abundance Data Measured with Error , 1983 .

[26]  S. T. Bucklanda,et al.  State-space models for the dynamics of wild animal populations , 2003 .

[27]  Benoit Mesnil,et al.  The Catch-Survey Analysis (CSA) method of fish stock assessment: an evaluation using simulated data , 2003 .

[28]  A. Brix.  Bayesian Data Analysis, 2nd edn , 2005 .

[29]  S. T. Buckland,et al.  Hidden process models for animal population dynamics. , 2006, Ecological applications : a publication of the Ecological Society of America.

[30]  K. Cowles,et al.  CODA: convergence diagnosis and output analysis software for Gibbs sampling output , 1995 .

[31]  P. Cury,et al.  Sustainable exploitation of small pelagic fish stocks challenged by environmental and ecosystem changes : a review , 2005 .