can be recovered, whereas an unrecoverable car- 

 cass has no chance of floating to the surface. 

 (All floating salmonid carcasses are considered 

 here as floaters.) 



We follow Paulik and Robson (1969) in intro- 

 ducing the following notation: 



Yi = number of untagged recoverable car- 

 casses at time 1. (We wish to estimate 

 Yi. In our estimate based on 1955 data, 

 this quantity is interpreted as the 

 number of recoverable carcasses below 

 Bonneville Dam resulting from earlier 

 mortalities that could possibly be re- 

 covered during our sampling period.) 

 Ni = number of tagged and untagged re- 

 coverable carcasses combined at time 1. 

 Pi = fraction of marked recoverable car- 

 casses at time 1. 

 P2 = fraction of marked recoverable car- 

 casses at time 2. 

 Ri = change in population of marked re- 

 coverable carcasses between time 1 

 and time 2 (i.e., the number of tagged 

 carcasses introduced into the river be- 

 cause it is reasonably assumed that 

 all marked carcasses are recoverable). 

 R = change in total population of marked 

 and unmarked recoverable carcasses 

 between time 1 and time 2. 

 n2 = number of carcasses observed in a 



sample at time 2. 

 X2 = number of marked carcasses observed 



in a sample at time 2. 

 P2 = X2/n2 = estimate of p2. 

 The fraction of marked recoverable carcasses at 

 time 2 can be written as the ratio of the number 

 of these carcasses at time 1 corrected for changes 

 that have taken place between times 1 and 2 to 

 the total number of tagged and untagged re- 

 coverable carcasses at time 2. That is, 



P2 = 



PiNi + Rx 

 Ni-fR 



Solving (1) for Ni gives 



Rx - P2R 



N, = 



P2 - Pi 



(1) 



(2) 



Because in our experiment there was no change 

 in the population of unmarked recoverable car- 

 casses, R = Rx, and because the population con- 

 sisted entirely of unmarked recoverable carcasses 



at time 1, Ni = Yi and pi = 0. Substituting these 

 quantities and replacing unknown quantities with 

 their estimates, we arrive at an equation for esti- 

 mating the number of recoverable chinook salmon 

 carcasses that were killed near Bonneville Dam: 



^^ = 4i - 



(3) 



If all recoverable carcasses, marked and un- 

 marked, are equally likely to be included in the 

 recovery sample and if the recovery sampling is 

 with replacement (as it was), then it is appro- 

 priate to make use of binomial sampling theory 

 to set a confidence interval about Yi. To do this, 

 upper and lower limits are set on p2 (the propor- 

 tion of marked carcasses in the recovery sample 

 (Pearson and Hartley, 1966)), and these limits are 

 then converted to upper and lower limits for ^1 

 by substituting in equation (3). 



As was noted above, this same result can be 

 developed from a Petersen-type estimate by 

 noting that the total number of recoverable car- 

 casses at time of release is Yi + Rx; the number 

 tagged is Rx," the size of the recovery sample is 

 n2; and the number of recoveries is X2. Hence, 



Yi + Rx 



RxHj 



X2 



(4) 



When solved for Yi, this yields expression (3) 

 above. 



The validity of this method for estimating the 

 number of recoverable carcasses in the river be- 

 low Bonneville Dam depends on several basic 

 assumptions. First, we assume that carcasses of 

 untagged chinook salmon float and are similar 

 in all other significant respects to the tagged 

 carcasses we introduced into the river. With re- 

 gard to floating qualities, we demonstrated the 

 validity of this assumption experimentally by 

 using fresh and frozen chinook salmon carcasses. 

 (These experiments are described in the appendix.) 

 Differences in floating characteristics were insig- 

 nificant at water temperatures similar to those 

 at the time of our 1955 experiment. 



Broadly interpreted, the above assumption im- 

 plies that all of the untagged carcasses were of 

 fish that had died near the dam; our extensive 

 observations substantiate this implication. In the 

 fall of 1954, when riverflow was low and carcasses 

 were unlikely to be swept far downstream after 

 death before becoming sufficiently buoyant to 



CHINOOK SALMON MORTALITY IN COLUMBIA RIVER NEAR BONNEVILLE DAM 



471 



