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112 Status of Razorback Sucker (~) as an estimator of physical survival rate (,S). Analysis with the CJS models has two objectives: (1) fmd a best estimate of apparent survival rate <it may vary by time) and (2) test for time variation in ~ and/orp (hence there are primarily four models considered). AIC-based model selection was used to accomplish both objectives. Another- parameter of interest is size of the sampled population, N. Population size may vary by year, and we wanted to know, in particular, if N was going down or up. In principle, Jolly-Seber models can be used to esti- mate population size and numbers of fish recruited an- nually (B) into the sampled population. But our data were too sparse to allow useful yearly estimates of N or B by the usual Jolly-Seber methods (such as with the pro- gram JOLLY; Pollock et al. 1990). A modified Jolly-Seber method (Buckland 1980) was used as a consistency check in comparison to a more intensive closed model used to generate yearly population abundance estimates, 1V. Population Size Estimates The assumptions one can reasonably make about a sam- pled population being "open" (mortality and recruit- ment are occurring) versus "closed" (no mortality, no re- cruitment) dictate what statistical analysis methods are reasonable. The useable capture-recapture data here spanned 13 years (1980-1992); we must allow that this is an open population. Yet the data are too sparse to al- low useful annual _abundance estimates by usual Jolly- Seber methods (about Jolly-Seber: models see Pollock et al. 1990; Lebreton et al. 1992). We therefore estimated an index to annual population size from the Lincoln-Pe- tersen method (Otis et al. 1978; White et al. 1982), using sequential pairs of years, as the basis for testing for a time trend in abundance of razorback suckers in the sampled population. Using only captures and recaptures in years i and i + 1, we computed (with program CAPTURE, White et al. 1982) an estimate of population abundance in year i + 1: nini + 1 Ni + 1 - mi,i + 1 where mi,a+1 is the number of fish caught iri both years i and i + 1, and nx'is the number of fish caught in year x. Other versions of this estimator could be used, but those versions are no better in terms of the biases that result from assumption fallures. The program CAPTURE also provides an estimate of the sampling error of N: se(N) = var(N). This estimator of abundance is consistent for (that is, its approximate expected value is) ( (Nipi) (Ni + lpi + 1) Ni + 1 E Ni+i) _ _ Nipi ~ipi + 1 ~ i Modde et al. Given an estimator of ~~, a bias-corrected population size estimator in year j is N~~~. Note that Ni+1 can be related to Ni: Ni+1 -" Ni¢i+Bi, where Bi is recruitment of new (unmarked) fish into the sampled population at year i. Moreover, when there may be unrecognized tag loss, BE = Bi a = BiiT, where the latter two terms are -(true) recruitment of never- marked individuals in year i, and the "recruitment" of previously marked fish that lost their tags. In an attempt to get some bounds, based on the Jolly-Seber time-spe- cific model of what average annual abundance (N) and recruitment (B) might be, we used Buckland's (1980) method and -his :program RECAPCO. That method uses constrained Jolly-Seber estimators, which can be very important for sparse capture-recapture data. To test for trend with the individual annual estimates, Ni, we needed to know their covariances; that informa- tion is not supplied by CAPTURE or RECAPCO. We did evaluate covariances for pairwise Lincoln-Petersen abun- dance estimators. Only pairs NZ and NZ+1 need be consid- ered as estimators Nt and N~ because j , i + 2 are inde- pendent (zero covariance) because they share no data in -common. We used Monte Carlo simulation (SAS 1985) based on the general values of abundance and capture probabilities applicable to these data (1000 trials at sev- eral parameter sets) to confirm that the covariance of Nt and 1Vi + 1 is zero within the limits of the simulation. If this study were a controlled experiment, an a priori analysis of the power of the test for a time trend in N would be expected. In retrospect, the best we can do is compute some test power values once we know the av erage sampling variation of the annual 1Vt values. We did a few power calculations for that test using the program TRENDS (Gerrodette 1987; Taylor & Gerrodette 1993). The program TRENDS assumes one has an abundance estimate each year for k consecutive years. We had nine estimates spread over 11 years, so we compromised and did power calculations for k = 10 years for cone-sided test of Ho (no linear trend in log [N]) versus Ha (a linear decreasing log [N]), with alpha set at 0.05. Thus, the test is of log (1Vi) versus time (i ), and herein it used a con- stant coefficient of variation of Ni. Under these condi- tions the test is based on a standard regression approach which is an option in the program TRENDS. Given that alpha = 0.05, the test of power depends only on k (number of years of data), assumed rate of annual change (r), and per-year coefficient of variation in N. Relationship of Discharge to Recruitment The relationship of recruitment to flow was determined by regressing the number of smaller fish (less than 475 mm) captured with discharge that occurred with the approximate year of birth. Based on data collected by Conservation Biology Volume 10, No. 1, February 1996