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<br />a decline in abundance from the early 1990s to the present <br />(tig. 4). However, as is apparent in the data, these estimators <br />are very imprecise with corresponding poor ability to detect <br />significant trends. Additionally, preliminary analyses of data <br />collected in this program suggest that the 2007 estimate may <br />be up to twice as large as the 2006 estimate (R. Van Haver- <br />beke, U.S. Fish and Wildlife Service, oral commun.; 2007). <br /> <br />ASMR without Tag-Cohort Specific Data <br /> <br />Overall, the three ASMR formulations generally agree <br />that adult (age-4+) HBC abundance has gradually increased <br />since about 2001 (lig. 5). Among these three models, the <br />2006 adult abundance estimate is 6,690 (95% credible interval <br />(CI) 6,403-6.994), 6,768 (95% CI 6,397-7,131), and 6.648 <br />(95% CI 6.222-7,1(2) for models ASMR 1, 2, and 3, respec- <br />tively. These results suggest that this population has increased <br />35%-40% from an estimated low abundance of approximately <br />4,800-5.000 during 2000-01. Estimated recmitment (age-2) <br />among models is also in agreement (fig. 6). Following low <br />recmitment for brood years during the early I 990s, all the <br />models suggest that reclUitment incTea<;ed through the latter <br />part of the 1990s. The biggest discrepancy amOl;g the three <br />models is that ASMR 1 suggests a decIine in recruitment <br />following the 2000 brood year, while the other two models <br />suggest stability. The stmctural assumptions of model ASMR <br />3 (see Coggins and others, 2006b) do not permit a reliable <br />recmitment estimate for brood year 2003. An additional differ- <br />ence in the model results is in the estimation of instantaneous <br />adult mortality (M",), where adult mortality ranges from <br />0.119 (ASMR 1) to 00133 (ASMR 3). <br /> <br />Model Evaluation and Selection <br /> <br />With these results in hand, the question becomes which <br />model is best? Stated another way, which model produces <br />results most consistent with or best supported by the data? In <br />this case. the discrepancies among model results related to <br />adult abundance are not large; as a result, selecting the best <br />model is probably not critical from a management or con- <br />servation perspective. However, the models~ do reflect rather <br />different hypotheses about recmitment trends. Model ASMR I <br />supports the hypothesis that recmitment has declined follow- <br />ing the 2000 brood year, while the other two models suggest <br />relative stability. Therefore, selecting the model (hypothesis) <br />that is the most consistent with the data is desirable. <br />Model tit to the data was assessed by plotting the Pear- <br />son residuals of the observed and predicted numbers of fish <br />marked and recaptured for each year and age (figs. 7-9). The <br />patterns in Pearson residuals for both ASMR I (fig. 7) and <br />ASMR 2 (fig. 8) demonstrate systematic lack of tit for partiClI- <br />lar sets of cohorts. This is best seen in the recapture residuals <br />where it is apparent that there are more fish observed than <br />predicted for about eight pre-1990 cohorts, particularly for <br />observations after 2000. Additionally, there are fewer recap- <br />tures associated wi th the 1992 cohort than are predicted. These <br /> <br />11 <br /> <br />systematic trends are likely imposing bias in the model results <br />for ASMR I and ASMR 2. In contrast, there is much less <br />systematic lack of fit in the residual patterns for ASMR 3 (fig. <br />9). Additionally, among the three models tbe Pearson residual <br />standard deviation is smallest for ASMR 3. <br />The finding that ASMR 3 has the best fit among the three <br />models is not surprising, since it has the largest parameter set. <br />Although ASMR 3 only varies 13 parameters in the direct <br />numeric search, the conditional maximum likelihood estimates <br />are used for each age- and time-specific capture probability <br />(Coggins and others, 2006b). Therefore, assuming a liberal <br />maximum longevity of 50 years, ASMR 3 has 895 param- <br />eters. The question then becomes whether these additional <br />parameters are justified. To provide insight into this question, <br />the relative K-L distance was estimated using AIC (table 1). <br />These results strongly indicate that model ASMR 3 is superior <br />to ASMR 1 and 2; a finding congruent with the evaluation of <br />model fit using Pearson residuals. <br />Although it is comforting to find agreement between <br />these two evaluations, one should ask: why is the more <br />complicated structure of ASMR 3 needed to adequately fit <br />the data? Since the fundamental difference between ASMR <br />I and 2 and ASMR 3 is the amount of f1exibility in age- and <br />time-specific capture probabilities, the pattern in ASMR 3 <br />estimated capture probabilities is of interest (fig. 10). The <br />discrepancy in capture probabilities between sampling period <br />2 (i.e., 1991-95; heavy gray lines) and sampling period 4 (i.e., . <br />2000-06: heavy black lines) suggests a major shift in the gear <br />selectivity. Sampling since 2000 appears to be much less effec- <br />tive at capturing fish between ages 9-20 years old than was <br />sampling during the second period. Since structural assump- <br />tions in ASMR 1 and ASMR 2 require that vulnerability is <br />asymptotically related to age, it is not surprising that these <br />models are not able to account for this unexpected pattern, and <br />thus display poor model fit. <br /> <br />ASMR with Tag-Cohort Specific Data <br /> <br />In addition to repeating the analyses by Coggins and <br />others (2006a) above, the ASMR models were also fit to the <br />tag-cohort specific data using the log-likelihood in equation <br />(2). The trends in adult abundance and recruitment are quite <br />similar to those found using the simpler log-likelihood (figs. <br />II and 12). In general, adult abundance estimates are slightly <br />higher at the beginning of the time-series and slightly lower at <br />the end. Adult abundance estimates for 2006 are 6,057 (95% <br />CI 5,797-6308), 6,138 (95% CI 5,842-6,458), and 5,893 <br />(95% CI 5,554-6,242) for the ASMR 1, 2, and 3 models, <br />respectively. Adult mortality (Moo) estimates from the models <br />fit to the stratified data indicate slightly higher adult mortality <br />(0.128,0.137, and 0.148 for ASMR 1-3, respectively) than <br />when fit to the pooled data. This finding is consistent with the <br />more rapid decay observed in the time-series of adult abun- <br />dance. Another difference is a slight increase in the precision <br />of the estimates using the stratified data (fig. 13). This obser- <br />vation provides marginal confirmation of the assertion that it <br />