FISHERY BULLETIN: VOL. 84, NO. 2 



(N 5 ) as the sample size (n 5 ) divided by the capture 

 probability (P 5 ). 



Standard errors and 95% confidence limits for the 

 third method were obtained by simulation. The sam- 

 pling process was simulated by generating a popula- 

 tion of carcasses based on population size estimates 

 from the third method. We then sampled the popula- 

 tion by comparing a uniformly distributed random 

 number with the appropriate probability of capture 

 [see Sykes (1982) for a more detailed description of 

 the simulation process, and a Fortran program]. 



From each simulation we calculated Jolly-Seber 

 estimates of survival, immigration, population sizes, 

 and their standard errors. An estimate of E was 

 then calculated as above. This simulation process 

 was repeated 1,000 times. In addition to calculating 

 the average and standard error of each of these 

 estimates, 95% confidence limits were calculated by 

 Buckland's (1980) method 1. To obtain 95% con- 

 fidence limits by this method, one adds the dif- 

 ference between the average of the 25th and 26th 

 lowest estimates (out of 1,000) and the average value 

 to the field estimate to obtain the upper bound and 

 subtracts the difference between the average of the 

 25th and 26th highest estimates and the average 

 value to obtain the lower bound. 



All three methods assume that all individuals are 

 equally catchable. The methods based on the Jolly- 

 Seber model also assume that all individuals have 

 equal probabilities of survival. Since violation of 

 these assumptions could result in biased estimates, 

 we determined whether catchability and survival 

 varied and the effects of these on the estimates. 



Several statistical tests can be used to check for 

 differential catchability and mortality, but only 

 among animals that are already marked. Two x 2 

 tests, which compare expected frequencies of cap- 

 ture histories with actual frequencies (Seber 1982; 

 Jolly 1982) were calculated from the unmodified field 

 data. The test of Leslie and Carothers (Carothers 

 1971) was not performed because of the small 

 number of sampling periods. Since both tests yielded 

 expected values less than unity, pooled x 2 values 

 were also calculated, using a conservative df value 

 of df = (number of pools - 1). For Seber's test, all 

 values less than unity were pooled; for Jolly's, each 

 value less than unity was pooled with the next 

 highest value. 



Following Leslie et al. (1953, cited by Seber 1982) 

 we tested for homogeneity of catchability and sur- 

 vival by comparing estimates of population param- 

 eters obtained by different methods. These methods 

 differ in sensitivity to survival and capture heter- 

 ogeneity, hence the presence of heterogeneity 



should cause differences in estimates of the same 

 parameter by the different methods. We tested the 

 unmodified field data by calculating the following 

 parameter estimates as per Leslie et al. (1953): 



v { : the estimated number of new marks re- 

 leased at time i 



4> . { : the estimated survival for the subpopulation 

 of marked carcasses, and 



N. z : the number of marked carcasses. 



and compared them with, respectively, 



v { : the actual number of new marks released 



at time i 

 fy: the Jolly-Seber estimate of survival, and 

 M^ the Jolly-Seber estimate of the number of 



marked carcasses. 



If differential catchability or survival, when present, 

 results in significant bias, these estimates will be 

 different. 



Since only marked (and thus decayed) carcasses 

 are considered in the statistical tests discussed thus 

 far, these tests do not address the potential for age- 

 dependent catchability. To evaluate possible effects 

 of age-dependent catchabilities we "corrected" the 

 sample size n { by reducing it to account for the fact 

 that fewer fresh (shiny, silver colored) carcasses 

 would have been captured if they had not been more 

 visible than decayed (dull brown colored) carcasses. 

 We then recalculated the escapement estimates 

 using the corrected sample size. We used two ratios 

 of average fresh to decayed catchability: 2.0 and 1.4. 

 Since visibility only differed among carcasses on the 

 stream bed, and only 30% of the captures were on 

 the stream bed, these values represented actual 

 ratios for carcasses on the stream bed of approx- 

 imately 6.7 and 4.7, respectively. 



To evaluate the potential advantage of increasing 

 the efficiency of the third method by lowering the 

 sampling effort we examined the effect of lowered 

 sampling intensity on behavior of the three 

 estimators. Lower effort would most likely result 

 in less searching on the bottom of the stream for 

 carcasses. We therefore simulated lowered sampling 

 by generating new capture histories for each in- 

 dividual according to the following set of rules: 1) 

 If an individual was buried at a capture event, that 

 and all subsequent captures were ignored, 2) cap- 

 tures of decayed carcasses on the stream bed and 

 surface were ignored according to comparison of a 

 uniform random number with the appropriate 

 decrease in capture probability, and 3) the next cap- 



264 



