470 



Abstract — A generalized Bayes- 

 ian population dynamics model was 

 developed for analysis of historical 

 mark-recapture studies. The Bayesian 

 approach builds upon existing maxi- 

 mum likelihood methods and is useful 

 when substantial uncertainties exist 

 in the data or little information is 

 available about auxiliary parameters 

 such as tag loss and reporting rates. 

 Movement rates are obtained through 

 Markov-chain Monte-Carlo (MCMC) 

 simulation, which are suitable for use 

 as input in subsequent stock assess- 

 ment analysis. The mark-recapture 

 model was applied to English sole 

 iParophrys vetulus) off the west coast 

 of the United States and Canada and 

 migration rates were estimated to be 

 2% per month to the north and A'7c 

 per month to the south. These poste- 

 rior parameter distributions and the 

 Bayesian framework for comparing 

 hypotheses can guide fishery scien- 

 tists in structuring the spatial and 

 temporal complexity of future analy- 

 ses of this kind. This approach could 

 be easily generalized for application 

 to other species and more data-rich 

 fishery analyses. 



Defining plausible migration rates 

 based on historical tagging data: 

 a Bayesian mark-recapture model 

 applied to English sole iParophrys vetulus) 



Ian J. Stewart 



Email address: lan.Stewart@noaa.gov 



National Oceanic & Atmospheric Administration 

 National Marine Fishenes Service 

 Northwest Fisheries Science Center 

 2725 Montlake Boulevard East (F/NWC4) 

 Seattle, Washington 98112-2097 



Manuscript submitted 6 Novembber 

 2006 to the Scientific Editor. 



Manuscript approved for publication 

 22 May 2007 by the Scientific Editor. 



Fish. Bull. 105:470-484 (2007). 



Mark-recapture data are used to 

 estimate growth parameters, mor- 

 tality rates, and population size (Hil- 

 born and Walters, 1992; Quinn and 

 Deriso, 1999). However, researchers 

 are often interested in home range, 

 site-fidelity, or migration rates which 

 are important quantities for manage- 

 ment and the design or evaluation of 

 marine protected areas. The stan- 

 dard approach with mark-recapture 

 data is to use an integrated model 

 linking the underlying dynamics of 

 the tagged population with an obser- 

 vation model describing the predicted 

 recoveries and a likelihood function 

 relating observations with model pre- 

 dictions (Hilborn, 1990). This inte- 

 grated method has been applied to 

 many fisheries, ranging from those 

 for sablefish (Anoplopoma fimbria; 

 Heifetz and Fujioka, 1991) to those for 

 yellowfin tuna (Thunnus albacares; 

 Hampton and Fournier, 2001). 



Requirements of the integrated 

 method include extensive tag re- 

 covery, data on fishing effort, aux- 

 iliary information on tag loss, as 

 well as reporting rates in order to 

 adequately estimate movement rates 

 and other parameters (Punt et al., 

 2000). Analysis often benefits from 

 fixing some model parameters at 

 reasonable values based on exter- 

 nal analysis or expert opinion. How- 

 ever, the values selected for these 

 parameters can represent a substan- 

 tial source of uncertainty in the es- 

 timates of movement rates because 

 these parameters are poorly known 

 for many historical tagging projects. 



Bayesian methods start with prior 

 distributions for the parameters of 

 interest (information available be- 

 fore the analysis), and integrate over 

 the joint posterior distribution of 

 all model parameters, capturing pa- 

 rameter uncertainty as well as the 

 correlation structure among these 

 parameters. The Bayesian approach 

 provides a logical alternative to like- 

 lihood methods when the researcher 

 is faced with substantial uncertainty 

 in the data and input parameters 

 and has a desire for a probabilistic 

 interpretation of the results (Punt 

 and Hilborn, 1997). 



One way in which uncertainty and 

 auxiliary information about migra- 

 tion rates could be included in stock 

 assessments is through the use of 

 informative priors based on Bayes- 

 ian analysis of mark-recapture data. 

 Priors specifically applicable to west 

 coast groundfish stock assessments 

 have been derived for survey catch- 

 ability (Millar and Methot, 2002), 

 the steepness of the stock-recruit 

 function (Dorn, 2002), the relation- 

 ship between catch per unit of effort 

 (CPUE) and abundance (Harley et 

 al., 2001), and for other studies cur- 

 rently underway. Researchers in oth- 

 er regions have aggregated historical 

 tagging information for commercial- 

 ly important species, such as north 

 Atlantic cod iGadiis morhiia; Robi- 

 chaud and Rose, 2004). However, in 

 the northeast Pacific there are many 

 groundfish tagging studies that have 

 never been analyzed simultaneously 

 or used in stock assessments. 



