FISHERY BULLETIN: VOL. 84, NO. 1 



APPENDIX 



In Equation (7), the first and second terms on the main diagonal are 



V(R. tll f t ) = V(R. lU )V(f<) + R 2 . m V(ft) + fMR.m) (A-l) 



for i = 1 and 2, noting that Cov(R. !U f t ) = 0. 

 The variance of f t is given by 



V(A) = V(P t ) (1 + V(Q) + Pf V(Q (A-2) 



+ &V(P t ) + V(C) - 2V(P,)C 

 - 2V(C)Pf + 2 Cov(P t , Q. 



This last term is assumed to be zero, as noted above. The off-diagonal element in Equation 

 (7) is 



Cov(R. lU f t , R. jn f t ) = R. m R. JU V(f t ) (A-3) 



for i ¥= j = 1 and 2. 



In Equation (8), based upon Equation (5) 



Cov(Q m , Q mj ) = 



where Cov(R. m f u , R. ju f m ) (A-4) 



[R% u + V(R. jU )]Cov(f u , f m ) + f u f m V(R. m ) i = j 

 R-iuR.ju Cov(/ M , /J i # j 



assuming Cov(R. ai , R.jn) = 



and Cov(/ M , /J = Cov(P M , P m ) [V(Q + C 2 ] (A-5) 



+ V(Q.[1 + AA -P u ~P m l 



34 



