174 



Fishery Bulletin 97(1), 1999 



P{i,0,B.t( 



P{i,0,0,t{ 

 C{i,A,B,t( 

 C(i,A,0,t{ 

 C(i,0,B,t( 



C{i,O.Oji 

 U(i,A,B,t{ 

 U(i,A,0,t{ 

 U{i,0,B,t( 



U(i, 0,0, t( 

 D{i,A,B,t{ 

 D{i,A,0,t( 

 D{i,0,B,t( 



D(i, 0,0, t( 



)) = -[F{i,t(i)) + M{i,t(i)) + Mi,B,t{i))]P{i,0,B,tti)) + ?i{i,A,t{i))P{i,A,B,tli)) 



)) = -[F{i,t{i)) + M{i,t{i))]P{i,0,0,t(i)) + Mt,A,tli))P(i,A,0,t{i)) + Mi,B,Hi))P{i,0,B,t(i)) 



)) = F{i,t{i))R(i,A,B,tU))P(i,A,B,t{i)) 



)) = F{i,t(i))R(i,A,0,t{i))P{i,A,0,t{i)) 



)) = F(i,t{i))R{i,0,B,t{i))P{i,0,B,t{i)) 



)) = F{i,t(i)) = R{i,0,0,fii))P{i,0,0,t(i)) 



)) = F{i,t(i))[l-R(i,A,B,t{i))]P(i,A,B,t{i)) [to{i)<t{i)] 



}) = F(i,t(i))[l- R{i,A,0,t(i))]P{i,A.O,t(i)) 



)) = F(i,t(i))[l- R{i,0,B,tii))]P(i,0,B,t(i)) 



)) = F{i,t{i))[l- R{i,0,0,t{i))]P{i,0,0,t{i)) 



)) = M{i,t(i))P(i,A,B,t(i)) 



)) = M{i,t(i))P(i.A,0,t{i)) 



)) = M{i,t{i))P{i,0,B,t(i)) 



)) = M(i,t{i))P{i,0,0,t[i)} 



(1) 

 continued 



with initial conditions 



P{i,A,B 



P{i,A,0 



P{i,0,B 



P{i, 0,0 



C{i,A,B 

 C(i,A,0 

 C{i,0,B 

 C{i,0,0 



U(i,A,B. 

 U{i,A,0 

 U{i,0,B 

 U{i,0,0 



D{i,A,B 

 D{i,A,0 

 D{i,0,B 

 D{i,0,0 



tot 



tot 

 tot 



= 7tii)pii,A)p(i,B) 



= nii)p{i,A)[l- p(i,B)] 



= /tii)[l-pii,A)]p{i,B) 



= 7t(i)[l- p{i.A)][l- p(i,B) 



= 



= 



= 



= 



= 



= 



= 



= 



= 



= 



= 



= 



Solution of this system of ordinary differential equations as an initial value problem gives 



