earlier tagging experiments in which salmon were 

 tagged as they emerged from the ladders above 

 the dam showed that some salmon are swept down 

 over the dam and are caught by fishermen below 

 or counted as they reascend the ladders (Schoning 

 and Johnson, 1956). Some of the salmon that are 

 swept over the dam probably do not survive, 

 although we have no direct evidence of what por- 

 tion is killed. The mortality model that we have 

 developed provides for the possibility that some 

 of the salmon counted over the dam are subse- 

 quently killed by being swept back over the dam. 

 We have evidence from our 1954 experiments 

 (previously described) that carcasses of fish 

 killed by being swept over the spillway may be 

 so severely mutilated by the extreme turbulence 

 that they are rendered unrecoverable. Thus, the 

 second additional factor taken into account in 

 our mortality model is the possible presence of 

 unrecoverable carcasses from mortality occurring 

 after counting. 



To derive the mortality model, some additional 

 symbolism is required. In these symbols, the sub- 

 script i refers to days on which mortality occurs 

 that could possibly produce floating carcasses for 

 recovery during the recovery period. (Recall that 

 recoverable carcasses may float and be available 

 for recovery 7, 8, . . . , or 16 days after death.) 

 Thus, i = 1 corresponds to June 21 because this 

 is the first day which could have produced float- 

 ing carcasses for recovery during the recovery 

 period. (The first day of the recovery period, 

 July 7, is the 16th day after June 21.) Similarly, 

 i = 20 corresponds to July 10, the last day which 

 could have produced floating carcasses for re- 

 covery during the recovery period. (The last day 

 of the recovery period, July 17, is the 7th day 

 after July 10.) Reference to figure 7 will help to 

 clarify this subscripting scheme. 



M = proportion of the chinook salmon run 

 dying near Bonneville Dam. (M is the 

 quantity to be estimated. If the propor- 

 tion of the run dying at Bonneville 

 Dam remained constant from June 21 

 through July 10, then M is this quan- 

 tity. However, if the proportion dying 

 varied during this period, M can be 

 thought of as a weighted average of 

 the daily proportions dying, with the 

 weighting being related to the extent to 

 which carcasses from a given day's 



mortality become available for re- 

 covery during the July 7 to 17 recovery 

 period.) 

 Ci = count over fish ladders on day i. 

 Di = mortalities on day i below the dam. 

 Qi = proportion of total mortality on day i 

 producing carcasses which, if recover- 

 able, could be recovered during the 

 July 7 to 17 recovery period. 

 Note that Ci -f- Di is the total run on day i and 

 that M(Ci + Di)qi is the total number of mortal- 

 ities on day i producing carcasses, which, if re- 

 coverable, could be recovered during the recovery 

 period. Therefore, 



20 



Z M(Ci + DOqi = M E 



20 



■) 



Diq; (5) 



is an expression for the total number of mortalities 

 producing carcasses (both recoverable and unre- 

 coverable) which, if recoverable, could be re- 

 covered during the recovery period. For 1955, the 



20 



term ^ Ciqi can be estimated from our experi- 



i = l 



mental data and the observed fish ladder counts 

 at Bonneville Dam. Table 6 shows this calculation. 



Table 6.— Estimation of ^ C,g, for 1955 experiment at 



i = l 



Bonneville Dam 



We now define the quantities required to take 

 account of (1) deaths that occur after counting 

 and (2) the possibility that some of the carcasses 



478 



U.S. FISH AND WILDLIFE SERVICE 



