LANDER and HENRY: I%5-66 BROOD COHO SALMON 

 In /.•2 + I2M2 



In }!2 + 7.5M2 



then Equation 9 becomes 



0. 



6 A/ 



1 _ 



(1-m) 



In ko + i2M' 



In k.y + 7.5M 



M2 



-l.bM' 



(In ho + l.bM-y) 



1 - e ^ = ki 



(text Equation 14). 



Failure of the Basic Assumption in the 

 Limit-Mean Model 



The basic assumption of the limit-mean model 

 is that survivial (.si) from the time No smolts 

 start seaward until Ei jacks return from the 

 ocean does not exceed survival (.s-2) thereafter 

 until Eo adults return. For sockeye and pink 

 salmon not fished in offshore waters, the text 

 discusses certain evidence (Ricker, 1962; 

 Fredin, 1964; Parker, 1962, 1968) indicating 

 almost incontrovertibly that Mi > M2, i.e., the 

 monthly natural mortality rate during the 

 "early" part of ocean life exceeds the rate there- 

 after. The same probably applies to coho salmon 

 arid to all other anadromous salmonids. Coho 

 salmon smolts are about the same size as most 

 sockeye salmon smolts when they enter the sea; 

 on general grounds we would expect relatively 

 little difference, on the basis of smolt size alone, 

 in the values of Mi and M-z between these two 

 species for a common time base. (By contrast, 

 text Figure 3 shows for coho salmon that 

 monthly Mi, as averaged for the first 6.0 mo 

 after release, is much less than monthly Mi ^ 

 0.78 1/mo for tiny pink salmon during only 

 the first 40 days at sea.) Fredin (1964, Table 2) 

 reported about 13-15 mo as the time between the 

 outmigration of sockeye salmon smolts and the 

 first return. For our data, coho salmon first 

 returned as jacks after only 6 mo; furthermore, 

 those that stayed at sea were fished quite heavily 

 in offshore waters but the sockeye salmon in 

 Fredin's analysis suffered natural mortality 

 alone until they entered the coastal fishery. 

 Even if Mi > M2 in hatchery coho salmon, the 

 shorter time for Si and the effect of oceanic fish- 



ing on .S2 might conceivably result in .s'l > .s'2 

 — instead of .si ^ ,s-2 as assumed in the limit- 

 mean model. 



Bias in estimates from the limit-mean model 

 (text Table 7), or in any model giving a single 

 set of estimates where in fact only various i)os- 

 sible sets can be determined (as in text Figure 

 3), must be evaluated with hypothetical data. 

 To get a fairly realistic notion of how the 

 assumption, .s-i ^ .S2, might have affected the 

 estimates in text Table 7, we 1) used the same 

 time intervals as in the text, 2) chose hypotheti- 

 cal values of m, S2, and M-i (hence F) which were 

 quite close to the estimates, then 3) varied Si 

 so that .S'l = 0.5 .s'2, 1.0 S2, and 1.5 .S2. Values for 

 the data as observed in practice (EilNo, CI No, 

 and E2IN0) were calculated from relations given 

 in the te.xt. 



Estimates of all parameters in App^dix 

 Table 1 contain less relative bias in Example 2, 

 where si = so (= 0.10), than in Example 1 (.si 

 = 0.5 S2) or Example 3 (.s-i = 1.5 .so). In Exam- 

 ple 3, estimates of ni and .S2 are too large and 

 the estimate of .si is too small. The converse 

 happens in Example 1. The direction of bias in 

 these three estimates is the same in Examples 

 1 and 2. It is interesting to note in all examples 

 the decrease in relative bias (estimate minus 

 parameter value/parameter value) as ojie pro- 

 ceeds (in the life of a cohort) from NiINo to 

 NrINo: 



RcUiiivt' bias (^c ) in 

 ahiindunce eslinutte 



Example 



NWN, 



N /N, 



Applicable values in Appendix Table 1 were 

 rounded to three places before calculating the 

 above percentages. 



This result is perhaps not surprising because 

 1) N /Nq is actually the target j^arameter in 

 estimation by the limit-mean model when the 

 offshore catch is known and 2) the lower and 

 upper limits for N/Nq were found during 

 calculation to bracket the true values quite 

 closely in all three examples despite the fact 



693 



