FISHERY BULLETIN: VOL. 71, NO. 3 



paring only the two groups of similarly marked 

 fish (Ad-RM, Lower River; Ad-LM, Upper 

 River) the Upper River marked fish had a 

 lower estimated recruitment to the fishery for 

 both brood years. Also, recruitment was higher 

 for the 1966 brood from both these river sec- 

 tions. Few hatchery returns of the 1966 brood, 

 Leavenworth (Uppermost) marked coho salmon, 

 were obtained because of passage difficulties at 

 John Day Dam due to construction offish ladders 

 and mortalities caused by trapping at Priest 

 Rapids Dam. This factor undoubtedly contri- 

 buted to the relatively low estimated recruit- 

 ment for the 1966 brood from this area. 



Instead of assuming a certain value for M2 as 

 we have done using the Cleaver model, as 

 pointed out by Jerome Pella (see footnote 3), 

 assuming a fixed value for the proportion matur- 

 ing (m) permits unique solutions to Equations 

 1-4, combined with Equations 5-8, so that with: 



m 



m (fixed) (01 < m < 1). 



(12) 



(13) 



[_ln k2 + l.bM2j [_ J 



g-7.5M2 



where ki = 



ko = 



(14) 



g6Mi 



3 \^6Mi 



F = 



r In /?2 + 12M2I 



L 4.5 J 



(15) 



The derivations of Equations 12-15 are veri- 

 fied in the Appendix. For a particular value of 

 m (Equation 12), one solves Equation 13 

 explicitly for Mi. Then using these values of m 

 and Ml, M2 in Equation 14 is found by iteration. 

 Finally, one obtains the proper F from Equa- 

 tion 15. 



Using Equations 12-15, we again calculated 

 values for the various parameters for the 1965- 

 66 broods, based on selected values of the pro- 

 portion maturing (m). These values are listed in 

 Table '5 and graphed in Figure 3. Only values 

 of //( that gave non-negative values of Mi, M2, 

 and F were used. Values of the average monthly 

 rate during all 18.0 mo, Z^ , were calculated 

 from the relation, Z^ = (6.OM1 + I2.OM2 + 

 4.5F)/18.0. Other rates of monthly mortality 

 that can be calculated from these data are: 



Average total mortality during last 12.0 mo 

 of ocean life: 



Z2 = (I2.OM2 + 4.5F)/12.0. 



Average natural mortality from time of smolt 

 release until beginning of commercial troll 

 fishing: 



M, = (6.0M, + 7.5M2)/13.5. 



Total mortality during last 4.5 mo of ocean 

 life: 



F + Mi. 



Comparison of Two Methods 



Before examining Figure 3 in detail, we 

 would like to compare briefly these two possible 

 approaches: 1) assuming selected values for M2 

 (natural mortality during second year) and 2) 

 assuming selected values for m (proportion 

 maturing as jacks). First of all, it should be 

 recognized that the values obtained by either 

 method as used here (Cleaver applied an 

 approximation formula noted before his Equa- 

 tion 20) are identical because Equation 9, used 

 in the calculation for a given value of M2, is sim- 



, Equation 2 , . , , . • u j 



ply ?T^^^ — 7^ T used in calculations based on a 



Equation 3 



fixed value of m. Furthermore, whenever a fixed 



value for either M2 or m is selected, all the other 



unknown parameters are uniquely determined. 



Although either of these approaches give 



identical results, their conceptual basis differs. 



In selecting a fixed value for M2, one starts at 



the end of the life cycle and work backwards; by 



selecting m values, one more closely parallels 



the actual life history of the coho salmon. 



Furthermore, a wide range of selected values for 



684 



