FISHERY BULLETIN: VOL. 71, NO. 3 



Table 6. — Calculated monthly values of F, Mi. and M^ 

 for 1965-66 broods of marked coho salmon from Columbia 

 River hatcheries — river sections combined (in = 0.0006). 



the relatively low value of m (< 0.008) needed to 

 be comparable with all the data is considerably 

 lower than we feel it should be because the cal- 

 culated values of Mt greatly exceed those for 

 Ml for the lower river areas as they also do for 

 all coho salmon combined in Figure 3. This is 

 contrary to all previously published data as dis- 

 cussed in the next section. On the basis of these 

 analyses, we believe that the proportion matur- 

 ing as jacks for these two brood years con- 

 sistently decreased for coho salmon released 

 farther and farther upriver. 



Returning to Table 5 and Figure 3, these data 

 show the same pattern for both broods as m in- 

 creases. Thus Ml and F both increase (Mi much 

 more rapidly), M2 decreases sharply, and (the 

 linear function) Z^ decreases so slightly as to be 

 nearly independent of m. Figure 3 also shows 

 that the lower limit of m (when Mi = 0) is about 

 0.003 for both broods: ^1 = EilNo = 0.00333 

 (1965 brood) and 0.00316 (1966 brood). The 

 upper limit of m (when M2 = 0) is about 0.068 

 for the 1965 brood but only about 0.057 for the 

 1966 brood. These latter values again agree with 

 data in Table 1. Of course, when M2 = 0, m = 

 EiKEi + C + E2). This is the highest possible 

 value of m. 



Figure 3 emphasizes that a unique set of 

 nominally unbiased estimates would be avail- 

 able if m were estimated independently. It is 

 now evident from Cleaver's (1969) model and 

 Equations 12-15 here that the same applies to 



hatchery chinook salmon, or indeed to any sal- 

 mon stock or species with two or more returns 

 when the offshore catch from a group of smolts 

 is known by origin. Thus, for / returns one 

 would use assigned values of m^ {i= 1, 2'- 1- 1) 

 and solve the extended counterparts of Equa- 

 tions 12-15 to estimate the various parameters 

 (however, this gets to be very complicated to 

 display graphically). Unfortunately, indepen- 

 dent estimation of mi{m for coho salmon) is not 

 feasible on a practical scale under present 

 management of most ocean fisheries for coho 

 and chinook salmon on the Pacific coast 

 because minimum size limits are imposed. 



Before turning to summary estimates with 

 unknown bias, we emphasize that unique esti- 

 mates could be obtained also if the present data 

 included estimates of the sex ratio of the No 

 smolts and E2 adults (Example 5 of Paulik and 

 Robson, 1969). Change-in-ratio estimates for 

 hatchery coho salmon are to be recommended 

 highly: not only is the field work relatively 

 inexpensive and straightforward, but these 

 nominally unbiased estimates would provide 

 definitive tests of other methods. 



ANALYSES BASED ON 



CONSIDERATION OF 



INDEPENDENT ESTIMATES OF 



LIMITS FOR M2 



It is useful at this stage to note some pub- 

 lished values (or derivatives thereof) which may 

 help to 1) delimit from the possibilities shown 

 for Ml and M2 in Figure 3 the actual time dis- 

 tribution of natural mortality in 1965-66 brood 

 coho salmon, and 2) justify assumptions leading 

 to unique estimates (other than in Tables 4 and 

 6) with unknown bias. The following include 

 corrections for marking mortality; data in 

 Table 1 (see footnote 2) and all our estimates 

 are for marked fish. 



Source Species 



Parker 

 (1962) 



Ricker 

 (1962) 



All Onco- 

 rhynchiis 

 except 

 O. nuisii 



O. nerka 



Value and explanation 



M2 ^ 0.026/mo, a rough average 

 for all species during offshore life 

 only. 



Mi(lower) > M2(upper) = 0.038/ 

 mo during last 2 yr at sea. 



686 



