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<br />LITTLE COLORADO RIVER HUMPBACK CHUB <br /> <br />241 <br /> <br />The modeling approach for the age-structured Jolly- <br />Seber and ASMR methods assumes that the initial age <br />is correctly assigned based on size at fIrst capture. <br />Errors in initial age assignment could lead to a negative <br />bias in population point estimates and to the "smear- <br />ing" of estimated recruitment among cohorts in the <br />ASMR model (Coggins et al. 2006). However, the <br />population trend estimates from the TSM models are <br />not age dependent, so that incorrect age assignment <br />does not bias the population trend estimates from these <br />methods. <br />The most critical assumption in the open-population <br />models is that mortality rates of fish have been stable <br />over time. Without this assumption, cumulative <br />survivors of fIsh tagged in previous years cannot be <br />safely used in calculating capture probabilities (and <br />population estimates) for anyone year. If, for example, <br />there had been a high mortality rate of all fIsh in any <br />one year, we would have seen a subsequent drop in the <br />recapture rates of tagged fIsh from all previous years. <br />But because sampling has changed over time (so that <br />capture probabilities cannot be assumed to have been <br />stable), we would attribute that drop in recapture rates <br />to changes in capture probability rather than to the <br />change in survival and we would therefore over- <br />estimate the number of surviving fIsh. We do not see <br />trends in calculated monthly capture probabilities that <br />would indicate such an error. However, the limited <br />sampling effort in the late 1990s and the associated low <br />catch rates make it difficult to evaluate the mortality <br />and contribution of these year-classes to the overall <br />population (new recruits to the population in the late <br />1990s were unlikely to be collected given the low <br />sampling effort). <br />Is it possible that the adult population was in fact <br />stable from the early 1990s to the early 2000s and that <br />the analyses indicating large declines over this period <br />have been misleading? All of the tagging-based <br />estimates, using both open- and closed-population <br />estimates, indicate such a decline, as does the trammel <br />net catch rate index for the LCR inflow reach. Only the <br />hoop net catch rate index of larger (fL >200 mm) fIsh <br />does not show a decline over the key decade of <br />intensive monitoring (the 1990s). However, the hoop <br />net index suggests a decline from the beginning of data <br />collection (i.e., the late 1980s) to the present. <br />For the tagging-based methods, there is no assump- <br />tion that sampling methodology was consistent over <br />time (i.e., capture probabilities are not assumed to have <br />been stable). For the newer tagging estimates to be <br />biased downward by 50% or more, these estimates <br />would have to involve a doubling in recapture <br />probability for marked fIsh relative to the probability <br /> <br />of capturing an unmarked fish. In capture-recapture <br />studies, such bias is typically due to restricting <br />sampling to a reduced portion of the area occupied <br />by the population (Seber 1982). There has been no <br />such systematic reduction in area sampled within the <br />LCR or the LCR inflow reach. There has been <br />a restriction in the seasonal time coverage of sampling <br />(from monthly sampling in the early 1990s to spring <br />and fall events in the 2000s) that could have the same <br />effect as a spatial restriction of sampling. This season- <br />ality could cause downward bias in closed-population <br />estimates based on monthly aggregated data, but it is <br />difficult to see how it would affect the tagging methods <br />based on annually aggregated data (annual ASMR, <br />Jolly-Seber) where there is ample time (1 year) for <br />marked and unmarked fIsh to mix before recaptures are <br />used in estimation. <br />Another possible cause of differentially high capture <br />probabilities for marked fIsh is the use of baited hoop <br />nets in the LCR in 2001-2002. If that practice caused <br />marked fIsh to be more likely to reenter nets than <br />unmarked fIsh were to enter them in the first place, <br />then capture probabilities were overestimated for both <br />the closed- and open-population estimation methods. <br />This would have caused underestimates of the numbers <br />of unmarked fIsh at the end of 2002, and in the ASMR <br />methods this would in turn have caused the back- <br />calculated (virtual population) numbers of unmarked <br />fIsh to be too low for at least the 1998-2001 time <br />period. However, when we artificially inflated the 2002 <br />unmarked numbers by a factor of two, we found that <br />the back-calculated overall population trend from <br />ASMR methods still indicated a decline of at least <br />40% over the last decade, even though the calculated <br />2001 population size was increased by only 500-800 <br />adult fIsh. When we simply excluded the likelihood <br />terms for catches of unmarked fIsh during the baiting <br />period from the calculation of maximum likelihood <br />estimates, there was no noticeable effect on the <br />parameter estimates. When we attempted to directly <br />estimate the relative capture probability for marked <br />versus unmarked fIsh during the baiting period, we <br />obtained estimates of 0.96-D.98 for all the ASMR <br />(annual, monthly, and with or without movement) <br />formulations, suggesting that there is no differential <br />capture probability between marked and unmarked <br />fish. These statistical checks do not prove that there <br />was no strong differential baiting effect, but they do <br />indicate that it is not parsimonious to assume such an <br />effect. <br />Finally, the effects of random sampling variation on <br />the ASMR estimates can be evaluated by comparing <br />estimates of recruitment or adult population trends <br />