FISHERY BULLETIN: VOL. 70, NO. 2 



Figure 11. — Block diagram of a population model for 

 Columbia River fall chinook salmon (adapted from Sha- 

 piro and Andreev, 1969). 



Mi =■ natural mortality rate. 



Fj = ocean fishing mortality rate. 

 RFi = river fishing mortality rate. 



Pj = probability of being a spawTier. 



ki = percentage of spawners taken for artificial 

 reproduction. 



El = effective fecundity/1,000 eggs. 



R = number of recruits. 



1 + , 2+, 3 + , 4+ = age of fish. 



the ocean and river recoveries of these two stocks 

 of fish. 



The procedures followed in these analyses 

 were: given a certain number of recruits 



(1,000) and a certain Mi (natural mortality) 

 value, and assuming M2 = M3 = M4, 1 calculated 

 the total yield for all ages (numbers caught X 

 average weight) from both the ocean and river 

 fisheries using the Pi values (where Pi is the 

 proportion of the ocean population entering the 

 river to spawn) for the M, as given by Henry 



(1971). I let the Pi and RFi values (where 



RFi is the river fishing mortality) remain con- 

 stant but varied the Fi's (where Fi is the ocean 

 fishing mortality) from to 1.8. This procedure 

 resulted in a 3-dimensional yield diagram (i.e., 

 Fs, Fi, and Fo) . The computations were done 

 on an IBM 1130* computer and I wrote the pro- 

 gram so the computed yields were plotted di- 

 rectly in even yield planes by a CalComp plotter. 



Regardless of the natural mortality rate as- 

 sumed for these computations, it appears that 

 total yields under actual conditions were below 

 the potential yields for both Spring Creek and 

 Kalama fall chinook. In Figure 12 are depicted 

 the calculated maximum potential yields for var- 

 ious values of natural mortality (Mi) and the 

 ocean fishing values {Fi) needed to achieve these 

 maximum yields as well as the calculated yields 

 based on estimated fishing mortality rates for 

 various values of M as given by Henry (1971). 

 It is only with the higher levels of natural mor- 

 tality (>0.60) or with the 1962 brood Spring 

 Creek fish that a troll fishery on the 3-year-olds 

 (F3) would have increased yield. At all levels 

 of natural mortality shown, maximum yield re- 

 quired maximum troll fishing effort on the 5- 

 year-old fish {F-,) . 



The calculated total yield varied considerably 

 depending on the F and M values used. The 3- 

 dimensional outputs for M = 0.24 and Ft — 

 to 1.8 for the two hatcheries for the 1961 brood 

 year are shown in Figures 13 and 14. I have 

 included a yield diagram for each stock to show 

 the differences in yield that can be generated 

 in this type of analysis as well as to emphasize 

 the differences between these two groups of 

 salmon. The calculated yield planes shown in 

 these figures are actually planes of equal yield 

 passing through the block diagrams. Each 

 yield plane shown consists of points that repre- 

 sent all possible combinations of ocean fishing 

 mortality (Fs, F4, and F:,) — such that total yield 

 will equal the value shown. In Figure 13, for 

 1961 brood Spring Creek fish (M = 0.24), the 

 maximum yield is at point A (Fa = 0, F4 = 0, 

 and Fs = 1.8) and is slightly over 6,300, the 

 same value as shown in Figure 12. Yield dia- 

 grams calculated for M = 0.96 were similar to 



* Use of trade names does not imply endorsement by 

 the National Marine Fisheries Service. 



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