FISHERY BULLETIN: VOL. 85, NO. 1 



sented. However the most important finding is that 

 it is shown that trends in recruitment rate and 

 changes in selection pattern are confounded. 



DERIVATION OF RECRUITMENT 

 RATE ESTIMATOR 



Allen's (1966, 1968) definition of recruitment rate 

 is the proportion of new recruits to total recruited 

 stock, that is, the number of animals newly avail- 

 able for capture compared with the total available 

 in that year. It is explicitly defined through Equa- 

 tion (1) below. Retaining the same nomenclature as 

 Allen (1966) let us define the following terms: 



N, 



i,t 



Ci,t 



u, 



i,t 



i,t 



: numbers in the population of age i in year 



t, 

 : catch in numbers of age i in year t, 

 : proportion of age group i in year t that are 



exploitable, i.e., recruited, 

 : proportion of the total catch from age i in 



year t, 



Qit : proportion in the catch of year t from all 



fully recruited age groups > i, 

 CTi : total catch in year t, 

 M : instantaneous natural mortality rate, 

 Ff : instantaneous fishing mortality rate on 



fully recruited ages in year t, ages i > 



k, 

 Zf : instantaneous total mortality rate, F" + 



M, on fully recruited ages, 

 F-^p Z-^ : instantaneous fishing and total mortality 



rates on pre-fully recruited ages, ages i 



< k, 

 Ff, Zf : instantaneous mortality rates if there are 



no differences between juvenile and adult 



rates, 

 k : age of first full recruitment, U^t. = 1-0 i ^ 



k, 

 Tf : net recruitment rate in year t. 



Let us define ^ = Fjil.O - exp(-Z^))/Zj and 

 similarly for <})". By definition, the recruitment rate 

 is 



rz = 



new recruits 

 total exploitable 



A--1 



^ Ni,2 U,, - (exp(-Zi)) I iV,.i U,j 



(1) 



^N,^2 U2 



where x is the age of first partial recruitment. This can be rewritten as 



k-l 



k-l 



l=X l-X 



k-l <x. 



i=x i=k 



Multiplying top and bottom by ^{ICT^ gives 



k-l 



k-l 



^ P..2 + Pk ¥2!^ - (exp(-Z^,)) I C,i Hjk\CT, 



To = 



k-l 



1 P,2 + {Uli^l) 1 P, 



2'T2/^^x,2 



Note that 



Qk.1,2 ^J.i^-^^^^^ CT,\lexv{-Z\) 



Qk,i 



(1 a,)CT, 



CT, <}.« 



i=k 



Therefore 



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