,0 



for 0<s<Sq -1 



^ = { 

 1 f 



for SQ'.s<b^ 



(2.12) 



Furthermore, we will assume the quantity f, which characterizes 

 this reproductive capacity, to be a function of the summary probability 



h= 



^1 



I 



s=s 







Is 



of the reproductive age groups. Then, equation (2.11), considering 

 (2.8) and 2.12), can be rewritten as: 



^t+1 = V(St). 



where 



^t+1 



{p 



t+1 

 11 



t t 



p (1-P 

 ^11 11 



t t 



has the sense of "supplementation," while S^ has the sense of a 



of this  



reserve. Recurrent equations 

 literature without a probabilistic 

 using a deterministic matrix model 

 Stocks and Recruitment (1970); for 

 available, while for f (S)=( aS+B)-l 



type are widely used in the 

 basis. A basis is developed for them 

 developed by Lesley in the book Fish 

 f (S) = aexp(-BS), a Ricker model i"s 

 the model of Beverton and Holt can be 



used, or a and p are constants (Beverton, Holt, 1957). 



The remainder of our brief presentation concerns the case of an a- 

 component community (a>l) with components not divided into age groups 

 (bc(=l). Representing ycti = Uct and Pal=Pcx. using equation (2.7) for the 

 steady case, we obtained: 



g 



Pa ~ p Pct+l ' 



a 



a X 



a=l a 



a,-l 



(2.13) 



For the remainder of our presentation, the particular case of 

 equation (2.9) when K=2 is important: 



X +y -2x V 

 y^ = m(x^, y J = 1 „ ., (a = 1, a). 



TTx 



or a 



(2.14) 



where x^ and y^ are the probabilities of death of an a-individual due to 

 causes inside and outside the community, respectively. 



346 



