LANDER: PROBLEM OF BIAS IN MODELS 



Few jacks are recorded from offshore fisheries 

 but some are taken in freshwater fisheries. 

 Time t = ti ends our first mortality interval 

 and starts the second. 



The immature age-2 fish remaining at sea 

 (males plus females) are reduced in numbers by 

 natural mortality alone for about 6-8 more mo 

 until their recruitment to offshore fishing at 

 time / = fi-. For about 5 mo thereafter, offshore 

 then inshore fishing operate along with natural 

 mortality. About a year after the jacks return, 

 age-3 adults appear in the final escapement at 

 time t = T to render the smolt class extinct 

 for our purposes. Thus ti and t ,■ divide the 

 effective life span, T - fo. into three subintervals. 



Basic notation follows: 



Er = 



Ni = 



Nr = 



C = 

 Eo = 



H = 



e = 



number of smolts at time f = to 

 number of jacks in first return or 



spawning escapement at time f = d 

 number of age-2 immatures at sea at 



time t = fi 

 number of recruits to offshore fishing 



at time t — t y 

 number offish caught offshore 

 number of adults in second (last) return 



or spawning escapement at time / = T 

 fraction of the cohort which matures 



as jacks near time t = ti 

 — survival fractions during ^1 — ^0 



and f — ti, respectively 

 2 = monthly coefficients of natural plus 



fishing mortality during ^1— to and 



T ~ tu respectively 

 monthly coefficient of natural mortality 



during T — ti 

 monthly coefficient of fishing mortality 



in offshore waters during T — t,- 

 monthly coefficient of total mortality 



during T — to 

 exploitation rate in offshore fisheries 

 base of natural logarithms. 



The following relations summarize the actual 

 situation: 



E^ = N^s^m = mN^e ^i^'i " 'o>. 



^1 = Vi(l-m) 



2i(fi - t^) 



(1) 



(2) 



Ny = N^e 



M^it^- fj) 



(3) 



C = uN^ = [FliF + M^)] 



(4) 



£n 



^^^-(F + M2)(T-f^) 





Z^{T - t.) 



NqS^s^ (1 - m) = NqS-^s^ -E^S2 



{l-m)NQe~^T 



Z^{T - U) 



(5) 



We have also the general definitions of the 

 mortality coefficients: 



Z^ = (-lnSiS2)/(?-^o) 



= [Z,{t,-t^)-^Z^iT-t^)]l{T-t^). (6) 



Z. = 



Z. = 



(-lns2)/(T-fi) 



[M2{T-t^) + Fit-t,}]liT-t^). 



(-In s-,) I (t^-t^). 



(7) 

 (8) 



If the smolts are not marked (or otherwise 

 identified) to estimate C and the inshore catch 

 by origin, then the escapement data (£■.) come 

 from hatchery counts or natural spawning 

 areas. If only the inshore catch is identified by 

 origin, a value of E- is the sum of inshore 

 catch plus "escapement" from inshore fishing 

 to the spawning area in a given year (usually 

 called the "return" or "run" by salmon biolo- 

 gists): it occurs somewhat earlier in time and 

 of course exceeds the value of E. without 

 inshore catch data available. Thus with inshore 

 catch data available. Zi = Mi (the offshore 

 catch of jacks being absent or negligible), Zo 

 includes only offshore mortality, and Zo = .I/2 

 if no offshore fishery exists (F == C = 0). The 

 indirect approach was developed mainly from 

 data without offshore fi.shing mortality but 

 with inshore catches known. If an offshore 

 fishery exists (as on the coho salmon emphasized 



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