118 FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



1. The fraction of the total run (R) derived from that portion normally spawning 

 above Rock Island. This will be -gr- 



2. The fraction of the total catch (C) referable to the Rock Island escapement 



(Rock Island count). This also will be jgr" 



1 W 



3. The catch derived from the Rock Island contingent. This will be -gC. This 



catch in numbers of fish can then be converted into pounds weight on the basis of the 

 assumed average weight per fish. 



4. The total run referable to Rock Island. This will be I jfC+E 2 .j Likewise, 



the ratio of the catch referable to Rock Island to the total run referable to Rock 



Island. This will be ^C-M ^C+E 2 which reduces directly to C-HC+E,) or to 



total catch divided by total run, as might be expected. This may also be written, 



rather neatly, as ^ • That is, the ratio of the catch referable to Rock Island to 



1+3 

 ' C 



the run referable to Rock Island is the same as the ratio of the total catch to the total 

 run. This again follows from the assumptions A and B. 



In carrying out the analysis along the lines indicated above, the catch in number 

 of fish and in pounds that may properly be ascribed to fish of the runs to the river 

 above Rock Island has been taken as a measure of what may be termed the absolute 

 importance of the Rock Island factor in the commercial fishery. The percentage of 

 the entire run that, for any period, may be ascribed to these Rock Island fish, may 

 similarly be taken as a measure of the relative importance of the Rock Island factor. 

 These two series serve somewhat different purposes. These values may be determined 

 for any selected portion of the season, and this is important because the Rock Island 

 complement in the total run varies widely from time to time and the ratio of catch 

 to escapement also varies during the fishing season. But for any one period it is 

 possible to determine the ratio of catch to escapement — a ratio that may be applied 

 to the entire run for the period or to fish bound for other tributaries above Bonneville 

 Dam as well as to those destined to tributaries above Rock Island Dam. Given the 

 ratio for any period, the catch ascribable to the upper Columbia may be deter- 

 mined by multiplying the Rock Island count, E 2 , for the corresponding period, by this 



ratio,Sr> giving ( -^ )E 2 . Or, on the other hand, we may use the fraction of the entire 



'El \El/ yp 



run that may be attributed to the river above Rock Island, -g?> and multiply the total 

 catch C by this fraction to get the number of fish derived from those spawning 

 above Rock Island giving \VjP- Mathematically these two procedures are obvi- 

 ously identical and, where either may be applied, they will give identical results; 

 but the latter procedure, making use of fractions of Rock Island fish in the run, may 

 be applied when necessary to determine the part that the Rock Island fish play in 

 producing the catch in any portion of the river, while the former can only be applied 

 to the catch as a whole. 



