FISHERY BULLETIN: VOL. 71, NO. 2. 1973 



calculations. Bias is expressed as the ratio, 

 (estimate-parameter value)/parameter value. 

 Values for F, Mo, and // are given for the 

 limit-mean model with C > known but values 

 for mortality and bias are not given for the 

 other examples. Values of £'//A'o include the 

 inshore catch as if smolts are marked. It 

 should be noted for the last two items that 

 1) bias in estimated mortality coefficients not 

 shown in Table 1 can be calculated readily 

 from the survival estimates, Equations 6-9, 

 and parameter values in Table 1; and 2) when- 

 ever the EjINo are from spawning areas only, 

 C > and the inshore catch are unknown but 

 the calculations proceed exactly as in Tables 

 1 and 2 with lower values of EjINo which 

 include the effects of inshore fishing (see section 

 on Actual Situation). 



Table 2 shows striking contrasts in bias 

 between estimates of different parameters from 

 a given model. The limit-mean model with no 

 offshore fishing, for instance, underestimates 

 the target parameter, .s-i.so, by only 4% but over- 

 estimates NJNo by 61% and N^INo by 20% . Also 

 in that example, .*2 ^ 49% is close to the 

 assumed upper limit, s-^^/ = 50% (Table 1); .so is 

 35% too low and Mo ^ 0.0965/mo (calculation 

 from Equation 7 with F = not shown) exceeds 

 Mo = 0.0600/mo. Thus M2 = M,^ and (iV,./No) = 

 (NylNo)u i^i the example. 



With C > and unknown, the Ricker model 

 as used here gives smaller bias in estimates of 

 .s-i.s'2, .s'l and in; the Fredin model as used here, 

 of Nil No and N^INi)-, and the limit-mean model, 

 of III. For these and all examples, bias in 

 estimates of .s-i.s'2, s., and in is in the same direction ; 

 of the .s^- and of -si and in, in opposite directions: 

 this result is completely general and is dictated 

 by the fixed relations between these parameters 

 and data (No and Ej) in Equations 1 and 5. 

 Again evident is the wide range of bias values 

 for different parameter estimates within a 

 model: -4% to 77% for the Ricker model, -6% 

 to 153% for the Fredin model, and -72% to 

 151% for the limit-mean model. 



With C > known, iV^./N,, (instead of .si.s-a) is 

 the target parameter (Table 1) and the estimate 

 is 6% too large. In addition to providing the 

 only point estimates shown for F, Mo and », 

 the limit-mean model performs better in these 



examples for the six other parameters than 

 when offshore fishing is absent or when C > 

 is unknown. Bias in all six estimates is in the 

 same direction as without offshore fishing and 

 opposite in direction to bias from the limit- 

 mean model with C > unknown. Finally, the 

 addition of offshore catch data given the small- 

 est range of bias values for estimates of all six 

 parameters: -22% to 27% . 



SUMMARY AND CONCLUSIONS 



1. The indirect approach for approximating 

 interval-specific mortality parameters is appli- 

 cable to multireturn species of salmon when 

 data are available on at least a) the origin- 

 specific number of smolts, b) the origin-specific 

 numbers of adults returning from the sea 

 each year until the smolt class is extinct, and 

 c) the time intervals between seaward migra- 

 tion of smolts and each return. An offshore 

 fishery may or may not exist and the origin- 

 specific catches inshore or offshore may be 

 known (as from marking/recovery experiments) 

 or unknown. 



2. Nominally unbiased estimators of mortal- 

 ity (or survival), maturity, and abundance do 

 not exist in this situation because different 

 combinations of mortality and maturity sched- 

 ules can generate the same set of observable 

 data. In connection with biomass computations, 

 Parker (1962), Ricker (1962), Fredin (1964), 

 and Cleaver (1969) developed models for ap- 

 proximating interval-specific mortality. The 

 latter three models are reviewed in connection 

 with the problem of bias and a new model is 

 introduced. Observable data are assumed to be 

 accurate in order to focus attention on bias 

 from the models themselves. To sharpen the 

 focus, the problem is reduced to the case of 

 two returns and the i)ertinent portion of the 

 life history of coho salmon south of British 

 Columbia is emphasized. 



3. Equations 1-9 and Figure 1 summarize 

 the actual situation and include the situation 

 with no offshore fishing ( F = C = 0) to helj) relate 

 the case of two returns to models developed 

 mainly with data from more returns and, 

 except for Cleaver's model, with natural but 



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