I ANDER: PROBLEM OF BIAS IN MODELS 



recorded for most coho salmon reared artifi- 

 cially in that watershed. I assume the intervals 

 are known to within 1.0 mo even if C > is 

 unknown. Incidentally, all input values are 

 the same as used for Figure 1 to illustrate 

 the extinction of a smolt class with and without 

 offshore fishing. 



Table 1 summarizes the hypothetical input 



values, data, models, assumptions, and estimat- 

 ing schemes as applied to calculate the esti- 

 mates and values of bias in Table 2. The latter 

 incorporates a few measures to simplify pre- 

 sentation and facilitate comparisons within 

 and between models. Parameter values are 

 repeated from Table 1 and all values are 

 rounded to four places after carrying six in 



Table 1. — Parameter values, data, models, assumptions, and estimating equations as numbered in text and applied in 



Table 2 to a hypothetical smolt class of coho salmon. 



Parameter value used as input and defined 

 from Equations 1-9 



Data 



Models, assumptions, and equations 



My = 0.40/mo 



Mj = 0.06/mo 



F =0, 0.30/mo 



Zj = 0.185000/mo 

 (for F = 30/mo) 



M'^ = 230000/mo 



Mj= 0,185263/mo 



Z^ = 264211/mo 

 (for F = 0.30/mo) 



m =0 10 



r-] - tg = 7 mo 



'1 



7 mo 



r - f^ = 5 mo 



f^ - fQ = 14 mo 



r - f^ = 12 mo 



r - fg = 19 mo 



s^ = 060810 



S2 = 486752 

 (for F = 0) 



$2 = 0.108609 

 (for F = 30) 



SyS2 =0.029599 

 (forF = 0) 



SyS2 =0 006605 

 (forF = 0.30) 



u = (for F = 0) 



u = 695584 

 (for F = 30) 



A/^/A/g = 0.054729 



A/^ /A/g = 0.035960 



E-^INq = 0,006081 

 C/A/g = (for F = 0) 



C/A/, 







0025013 



(forF = 30) 



Fj/Z^o " 022640 

 (for F = 0) 



Fj/A/g = 0.005944 

 (for F = 30) 



Time intervals as 

 at left 



1. With no offshore fishing \F - C = 0), apply limit mean 

 model by assuming Syy ^ 59^. " ^ (Equation 20) and i2U~ 

 50 (Equation 21 ). Solve Equations 22-27 



2. With offshore fishing but C > unknown, assume m = 

 and So = 10 on F, Wg, hence Z^ = Zj- for Ricker model 

 (Equation 10): use Z* = Zt, solve Equation 7 for ?2. '^^6" 

 Equation 5 for $^$2 ~ ^9 ^ '^1''^Q.'*2' ^"^ Equations 

 24-27. For Fredin model, assume Z^ "- Z^ and solve Equa 

 tions 15 and 22-27. For limit-mean model, proceed as m 

 Item 1 above, noting F2/A/g is now smaller 



3 With offshore fishing and C > known, apply limit-mean 

 model by assuming s-^^j = Sj/, = s (Equation 20), ^2 = ^ 

 during T - t^ (Equation 28) and F during T - t^ Solve 

 Equations 20 and 28-37, then Eciuations 7, 5, 26. 1. and 6 



4. Although M2. F and u are solved only as in Item 3 above, 

 solutions for various mortality coefficients are availalile 

 from Equations 6-9 by applying survival estimates and 

 F ^ as appropriate in Items 1-2 (see section on Actual 

 Situation in text). 



Table 2. — Values of parameters, selected estimates, and relative bias in estimates (read each set down in that order), 

 from models as summarized in Table 1. Values are rounded to four places after carrying six in calculations; a dash ( — ) 

 indicates no estimate. 



521 



