of fish dying after counting are mutilated and 

 rendered unrecoverable. 



fa = fraction of all deaths occurring after 



counting, 

 ra = fraction of carcasses of fish dying after 

 counting that are recoverable (i.e., not 

 mutilated and rendered unrecover- 

 able). 

 Do = number of carcasses of fish dying after 



counting that are unrecoverable. 

 Ma = proportion of those fish that are 

 counted over the dam that die near 

 the dam. 

 The quantity Do can be expressed as 



/ 20 20 \ 



Do = (1 - ra)faM(^i: CiQi + L DiQij (6) 



Because Yi is the number of untagged recoverable 

 carcasses in the river, it is clear that Yi is the dif- 

 ference between the total number of untagged 

 carcasses and the number of unrecoverable un- 

 tagged carcasses: 



(20 20 \ 



Z Ciqi + E Diqij - Do 



/ 20 20 \ 



= [1 - fa(l - ra)]M(^i: Ciqi + Z Diqij(7) 



20 



The quantity ^ Diqi represents the number of 



i=l 



mortalities occurring below the dam before count- 

 ing and can be expressed as the difference between 

 the number of untagged recoverable carcasses and 

 the number of untagged recoverable carcasses 

 dying after counting: 



20 20 - 



E D,qi = Y. - Mara Z C^qi (8) 



20 



i=l 



i = l 



(Note that at this point, we are assuming all un- 

 tagged carcasses originating below the dam are 

 recoverable.) Finally, the total number of mortal- 

 ities after counting can be expressed as follows: 



20 



M. E Ciqi = fa(Yi + Do) 



i=l 



= h^Y, + [1 - ra)faM(E Ciqi 



+ £ Diqi)] (9) 



To derive an expression for M, (9) is solved for 

 Ma, and this result is substituted into (8). Then 



(8) is solved for E Diqi, and the result is sub- 



i=l 



stituted into (7). An expression for M is then 

 derived by solving (7). The final result is: 



M = 



Yi 



(E Ciqi + Y:) (l - fa) + fara E Ciqi 



(10) 



If all mortality occurs below the dam (fa = 0), 

 then (10) becomes 



M = 



Yi 



g Ciqi + Y, 



(11) 



This situation corresponds to the manner in which 



•we performed our experiment in 1955 when we 



released all tagged carcasses below the dam. 



Recalling that t, = 4,412 untagged recoverable 



20 



carcasses and that E C^qi was estimated to be 



i=l . 



21,877.8 fish, we use (11) to calculate M = 0.1678. 

 In other words, on the assumption that all mortal- 

 ity occurs below the dam, we estimate that 16.78 

 percent of the chinook salmon run was killed near 

 Bonneville Dam in 1955 at the time of our experi- 

 ment. 



It would be desirable to set a confidence interval 

 about the estimaie of mortality level given by 

 equation (11). Unfortunately, this does not seem 

 to be possible. All quantities appearing in equa- 

 tion (11) are subject to sampling error. The 

 variances of the qi's and the variance of Yi could 

 be approximately estimated from our experi- 

 mental data for 1955, but no estimates are avail- 

 able for the variances of the d's— the daily 

 chinook salmon counts over the dam. These counts 

 are known to be inexact and may also be biased. 

 Some of the causes of counting errors are: fish are 

 counted more than once as a result of being swept 

 over the spillway; fish are not counted through the 

 ship navigation lock; and fish are misidentified, 

 especially the smaller salmon with similar appear- 

 ances such as sockeye salmon and chinook salmon 

 jacks. For example, in 1957, only 9,879 chinook 

 jack salmon were counted over Bonneville Dam, 

 but 13.415 were counted over McNary Dam and 

 8,402 into Spring Creek Hatchery, between Bonne- 

 ville and McNary Dams (Junge and Phinney, 

 1963). Thus, more than twice as many jack salmon 



CHINOOK SALMON MORTALITY IN COLUMBIA RIVER NEAR BONNEVILLE DAM 



479 



