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12 Abundance Trends and the Status of the Little Colorado River Population of Humpback Chub 1989-2006 might be possible to extract additional information considering the stratified, rather than pooled, data. Model Evaluation and Selection Examination 'of Pearson residuals for the tag-cohort specific models suggests similar patterns in model misspecifi- cation for ASMR 1 and ASMR 2 (figs. 14 and 15). However, there appears to be even less residual pattern for ASMR 3 (fig. 16), suggesting slightly better agreement with the data than the pooled data model fit. This, again, suggests that segregation of the data is permitting greater extraction of information. Model evaluation using AIC methods su'ongly indicates that ASMR 3 is preferable (table 2), which is generally in agreement with the residual evaluation. Finally, a very similar pattern in estill1ated capture probability from ASMR 3 emerges, suggest- ing a similar mechanism to explain the poor perfonnance of models ASMRl and 2 (fig. 17). Assessment Update Summary The adult portion of the LCR HBC population appears to have increased in recent years as a result of increased recruit- ment, particularly associated with brood years 1999 .md later. In addition, model evaluation procedures indicate that the results from model ASMR 3 are most consistent with the available data. Using data stratified by tagging cohort added additional infonnation to the assessment, as indicated by the slightly higher precision of adult abundance estimates. How- ever, adult abundance estimates, as reported, are extremely precise. This level of precision is questionable, since the assess- ment doesn't incorporate uncertainty in the assignment of age. Estimating the Humpback Chub Growth Function Using Mark-Recapture Data Both the temperature-independent (TIOM) and temper- ature-dependent (TDOM) growth models described in the methods section were fit to 14,971 observed growth intervals extracted from the HBC mark-recapture database. All tish were larger than 150 mm TL and the time interval between capture and recapture exceeded 30 days. Though greater than 6OC;7() of the fish were at large for 1 year or less, a small fraction of the observations were for much longer time intervals (fig. 18). The longest time interval in the dataset was 5,538 days (about 15 years). The measurement error contained in the dataset was estimated by computing the observed difference in measured lengths of tish captured and recaptured within 10 days. This resulted in a measurement error variance of 31.8 mm" across all sizes offish, implying that most TL measurements were within II mm of the true TL. This amount of measurement error is fairly high but not unexpected, considering the dif- ficulty in measuring live tish. However. this error rate contrib- utes substantially to the variability of observed growth rate. The TIOM was fit with prior variance weighting terms on the dand n parameters A ={0.00001, 0.0001, 0.001, 0.01, 0.1.0.5,1,10,100,1.000, and 1O,000} to explore the effect of constraining these parameters to values near standard von Ber- talanffy values. The log-likelihood is nearly identical for all values of ii = 0.01 and greater, but reducing below A = 0.01 caused large changes in the log-likelihood (tig. 19). Therefore, ii = 0.01 was specified as the optimal weighting value for both the TIOM and TDGM. To estimate the parmneters of the TDOM it was necessary to first iit the time-dependent LCR water temperature model. Fortunately, the sine curve function with parameters t peak = -0.011, TID,e = 17 .9, and Tilla. = 23.2 fit the observed average monthly temperatures very well (fig. 20). The estimated parameters, log-likelihood, and AlC statistics for the TIGM mldTDGM are presented in table 3. The pmllmeter values for the TIOM suggest an extremely low value for the catabolic constant (m) and a catabolic scaling parameter value (n) greater than unity. This is a rather unlikely situation from a biological perspective and indicates that this model may not be well supported by the data. In contrast, the estimated scaling parameters for the TDGM are not much different than what would be expected under the standard van Bertalanffy model, where the anabolic scaling parameter (d) should be close to 2/3 and the catabolic scaling parameter (n) should be close to unity. Results from AIC indicate strong support for the IDOM over the TIOM. However, the pal1lm- eter correlation matrices for each of these models show very high cOlTelation, indicating that all of the parameters are not separately estimable (table 4). In situations such as this, where the model is not full rank, it has been suggested that the K-L distance is undefined (Viallefont and others, 1998; Bozdogan, 2(00). An altemative way to arbitrate among these two models is simply to examine the model fit to the data. The observed growth rate as a function TL at the start of the interval is extremely variable, particularly at smaller sizes (fig. 21). It' is also apparent that all three lines (the tit of the TIOM and the tit of the TDOM corresponding to LCR water tempera- tures during summer and winter) differ from the strict linear relationship implied by a standard van Bertalanffy model. The temperature-independent model is somewhat of a compro- mise between the temperature-dependent summer fit and the temperature-dependent winter fit. Jt is also clear that observed summer grmvth is generally greater than observed winter growth, suggesting that growth rate is oscillating with tem- perature (fig. 22). Each of the models was used to predict length as a func- tion of age. In addition to the two models fit above, length-at- age was also predicted using the growth function reported in the USFWS recovery goals document (U.S. Fish and Wildlife Service, 2002) and using the TDOM for a constant tempera- ' ture of 100C (fig. 23). This last curve is equivalent to a fish experiencing a constant 1 WC temperature and is a predic- tion of length-at-age for a fish spending its entire life in the mainstem Colorado River. Examination of these curves show