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Fishery Bulletin 105(4) 



maximum instantaneous rate of tag loss of 1.52, which 

 was used as the upper bound for this parameter. The tag 

 loss rate was given a lower bound of 0.01 in the absence 

 of other information. The median rate of fishing mortal- 

 ity across data sets (f,,,^^) was bounded to lie between 

 0.01 and 0.8. Reporting rate, tag loss rate, and median 

 fishing mortality rate were all assigned a scaled-beta 

 distributed prior with both shape parameters equal 

 to 1.02. This prior has the desirable properties of a 

 nearly uniform density over most of the parameter space, 

 except immediately adjacent to the bounds, which have 

 zero density. Data set-specific fishing rates (Fj) were 

 assumed to be related in a common hierarchy; the values 

 of these parameters were constrained with a lognormal 

 prior (F^jgrf, 0.25). The overdispersion parameters (one 

 for each category of data) were given a gamma-distrib- 

 uted prior (shape = 1.001, rate = 0.01) and bounded to 

 lie between 0.001 and 1000. This choice reflected the 

 desire for a generally uninformative prior, but one that 

 favored a substantially larger variance than that in a 

 simple Poisson likelihood. Exploration of the sensitivity 

 of the model inference to the choice of priors was con- 

 ducted by changing the values, rerunning the analysis, 

 and comparing the results. The effect of six key prior 

 distributions were explored through sensitivity analysis 

 by modifying the shape of these distributions: doubling 

 the coefficient of variation of the prior on deviations 

 from f ,,,j.£/, using a uniform prior on the log scale for the 

 overdispersion parameter ik), reducing the upper bound 

 on movement parameters to 0.25, extending the prior 

 bounds on reporting rate (0.01 to 1.0), and sequentially 

 setting the priors on tag loss and f „,p^ to be uniform. 



This model was programmed in AD Model Builder© 

 (Otter Research Ltd., Sidney, B.C., Canada), which 

 uses a Metropolis-Hastings algorithm to sample from 

 the joint posterior distribution of all model quantities. 

 Markov-chain Monte-Carlo (MCMC) sampling was per- 

 formed for five to fifteen million iterations for each 

 hypothesis. Each chain was thinned by taking every 

 1000"^ (or fewer) draws to achieve low autocorrelations 

 (<0.3) within chains and by taking nearly equal actual 

 and effective (modified to account for autocorrelation) 

 sample sizes. Convergence was assumed to have oc- 

 curred for each chain when the criteria above were 

 met, visual inspection of trace plots and cumulative 

 quantiles (0.05, 0.5, 0.95) indicated stationarity in all 

 model parameters, and most parameters had a Geweke 

 statistic (Geweke, 1992) less than 1.96 (this statistic 

 can be interpreted as a z-score and will produce some 

 significant values due to random chance). 



Bayes factors are frequently used in Bayesian analy- 

 ses to compare the weight of evidence among various 

 model hypotheses, accounting for differences in the 

 number of estimated parameters (Gelman et al., 1995; 

 Burnham and Anderson, 2002). In the present analysis, 

 harmonic mean posterior likelihood for each model was 

 used to calculate approximate Bayes factors (Kass and 

 Raftery, 1995). Model support (amonth those compared) 

 is based on twice the log of the ratio of mean likeli- 

 hoods (hereafter referred to as the Transformed Bayes 



Factor, TBF), judged on the following scale: 0-2, not 

 worth more than a bare mention; 2-6, positive; 6-10, 

 strong; and >10, very strong support for one model over 

 another (Kass and Raftery, 1995). For this application, 

 the TBF metric appeared quite stable and robust to 

 sampling effects arising from the posterior distributions 

 in preliminary testing. 



Results 



Most of the recoveries of tagged fish across all data sets 

 occurred in the area that initial tagging took place, 

 indicating relatively low rates of movement over all 

 areas and time periods. Of the 3464 tagged English sole 

 recovered off the open coast, only 130 (3.8%) of these 

 had moved from the area of tagging and only 55 (1.6%) 

 had moved more than one area. Low levels of exchange 

 were particularly pronounced for those fish released in 

 Puget Sound and the Strait of Georgia. Of 24,408 tagged 

 English sole released in Puget Sound and the Strait of 

 Georgia, only 12 (0.002%) of the 5756 recoveries were 

 captured off the open coast. Conversely, only 3 (0.001%) 

 of 4232 tagged fish recovered from 32,431 released fish 

 (including some that could not be included in the quan- 

 titative analysis) on the open coast were recaptured 

 within Puget Sound or the Strait of Georgia. A single 

 release of 282 English sole in the Strait of Juan de Fuca 

 (Forrester, 1969) resulted in 59 recoveries, 34 of which 

 were from the open coast, mostly off Washington, but 

 recoveries ranged as far south as Oregon. In aggregate, 

 these results indicate that Puget Sound and the Strait of 

 Georgia are substantially isolated from the open coast, 

 but that mixing of adults does occur in the Strait of Juan 

 de Fuca (and possibly at the north end of the Strait of 

 Georgia). Therefore, in all model hypotheses considered 

 in this analysis, Puget Sound and the Strait of Georgia 

 were not included as part of the coastal population. 



All five single time-step models resulted in English 

 sole movement estimates that were three to four times 

 more southerly than northerly, although the posterior 

 distributions for the movement parameters were not 

 identical (Fig. 2). TBFs of 49-152 indicated strong sup- 

 port for the model, allowing movement only in November 

 over all other single time-step models (Table 5) . In this 

 model, the posterior median proportion of English sole 

 expected to move to the north each year was 0.08, and 

 the 90% posterior interval ranged from 0.05 to 0.12, 

 and 0.31 (0.25-0.39) to the south. The model including 

 movement in January was second best (TBF=49) and 

 qualitatively similar with 0.06 (0.04-0.09) moving to 

 the north, and 0.26 (0.19-0.34) moving to the south 

 each year. 



The two-season models also showed some consistency 

 in parameter estimates regardless of the months in 

 which movement was allowed to occur (Fig. 3). TBFs 

 of 16-26 indicated strong support for the model allow- 

 ing movement in November and May (Table 5). Results 

 from this two-season model showed that the propor- 

 tion of English sole moving in the spring and to the 



