FISHERY BULLETIN: VOL. 73, NO. 4 



APPENDIX 



The parameter, s, in the starvation mortality 

 Equations (16) and (17) is found as follows: 



During starvation, since kC<Q and S = 0, 

 Equation (1) simplifies to 



Q = ^= kC-Q = kC - aw"^ (A-1) 



dt 



At any constant level of ration, C, this in- 

 tegrates to give 



_5j r,.j J + ^^-^^ 





4a 1 I ./ - PrO-20 



^0.20' 



+ 2 tan-^ — 

 J J 



5iyo.20 



Iv (A-2) 



a 



^ - m 



, n.25 

 where: 



/j is a constant of integration. Taking the boun- 

 dary condition that W = W^^, i.e., the initial weight 

 of each original A^o individual, at time t = 0, the 

 constant I^ can be evaluated any any level of ra- 

 tion. 



The boundary condition at 100% mortality is 

 taken to correspond with a critical frac- 

 tion-0.6-of the body weight of a normal, well-fed 

 individual (the critical fraction is estimated from 

 a variety of sources, including: Dawes 1930; 

 Lawrence 1940; Phillips 1954; Adelman et al. 1955; 

 Brett 1962; Brett et al. 1969). Using this critical 

 lethal body weight for W, Equation (A-2) can be 

 solved to give the critical time, t,. , to 100% mor- 

 tality. Using this f^in Equation (16) when N/Nq = 

 gives the value of s. 



716 



