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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
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