SYKES and BOTSFORD: CHINOOK SALMON SPAWNING ESCAPEMENT 



While both Jolly's (1982) and Seber's (1982) tests 

 indicate differential catchability and/or mortality are 

 present, the issue of real importance is the amount 

 of any resulting bias. Manly (1970) concluded that 

 if age-specific mortality is present in a sampled 

 population, Manly and Parr (1968) estimates should 

 fare better than those of Jolly and Seber (Seber 

 1982). Both methods, however, are biased for the 

 case in which mortality increases with age; in fact, 

 Manly's (1970) estimates of bias for additions (B) are 

 greater for Manly and Parr estimates than for Jolly- 

 Seber estimates for those simulations with param- 

 eters closest to our population. Survival, population 

 size, and catchability estimates were negatively bi- 

 ased by only 1 or 2%. Seber (1982) pointed out that 

 Jolly-Seber estimates should be relatively unbiased 

 even with differential mortality if mark status and 

 mortality were not correlated. Both estimators, 

 then, should have relatively unbiased estimates of 

 survival and catchability for "marked" animals. A 

 positive bias in estimates of immigration, B, (and 

 consequently in E) would arise primarily from apply- 

 ing mortality of marked animals to the entire 

 population, when marked animals are in general 

 older, and thus have lower survival than unmarked 

 animals. 



The age-dependent catchability detected in this 

 study would be expected to result in a positive bias 

 in the estimate of total escapement, E. Because each 

 capture sample includes fresh, recently immigrated 

 individuals, and recapture samples include older, 

 decayed individuals, we expect N to be overesti- 

 mated (i.e., nIN > m/M in Jolly-Seber and pN < n 

 in Manly and Parr), which results in estimates of 

 B and E being positively biased also. Since bias from 

 age-dependent catchability in N decreases as M ap- 



frash 



decayed 



Age 



Figure 4.— Expected changes in capture prob- 

 abilities with age at different sizes. 



proaches N, and removing carcasses after capture 

 in the third method decreases the ratio of marked 

 to total carcasses, we would expect the third esti- 

 mator to be more biased by age-dependent catch- 

 ability problems than the first two methods. 



However, the simulations of lower sampling in- 

 tensity, which would exacerbate the effects of age- 

 dependent catchability, show that the estimate 

 obtained by the third method is more robust with 

 regard to lowered sampling intensity. This unex- 

 pected result is probably due to compensating 

 effects which decrease bias in E. The two most im- 

 portant components of E are the second ((N 2 - Ri 

 Oi)/$i' 5 ) and third (D 2 ). In the standard estimates 

 these values both increase with increases in the 

 number of captures ignored. In the third method, 

 however, the second component increases, but the 

 third decreases. This is because as catchability 

 declines, fewer marks are captured and "removed", 

 hence more carcasses are available for later capture. 

 This is not the case in the first two methods because 

 marked carcasses are not removed at capture. Since 

 in the third method the composition of M and N is 

 relatively unchanged at the second sample period, 

 but at the third sample period, M increases relative 

 to N (because of the increase in the number of 

 decayed marks present), the estimate of population 

 size at the third sample period will be less biased 

 than the estimate for the second sample period. This 

 results in a negative bias in the estimated immigra- 

 tion from time period two to three. This compensa- 

 tion makes the third method more robust with 

 respect to age-dependent catchability problems than 

 the other two methods. Bias in the estimates is not 

 severe until large numbers of capture events are ig- 

 nored (Table 7). While all three methods produce 

 accurate estimates, even when lowered sampling 

 exacerbates differential catchability problems, the 

 magnitude of the bias relative to standard errors can 

 be substantial. For this reason, samples must be 

 carefully taken if estimates from different streams 

 or different years (which will have different biases 

 because of different conditions) are to be compared 

 statistically. 



Heterogeneity of capture probabilities affects 

 Jolly-Seber and Manly and Parr estimates in the 

 same manner. Since in the Jolly-Seber method the 

 individuals marked and released at sample i, R it 

 are on the average younger than the individuals 

 marked and released prior to sample i, M { is a low 

 estimate (i.e., rlR > zl(M - m), or M > (Rzlr) + m). 

 This decreases the positive bias in N which is caused 

 by age-dependent catchability. Since bias in M in- 

 creases as more individuals are marked, we expect 



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