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Appendix 1— Growth formula from Schnute (1981) 



Y(t)-- 



l-e 



-iV6 



The model involves six parameters, Q=(t v T 2 ,y 1 ,y 2 , a, b), 

 where r, and r„ are two arbitrary ages in the life of a 

 fish, such that T„>r,. The parameter y, is the size of a 

 fish at time r v and y., is the size of a fish at time T 2 with 

 .Vo>Ji>0. Parameters a and b determine the shape of the 

 growth curve by controlling the acceleration (decelera- 

 tion! in growth from times t 1 to t 2 . The parameter a has 

 units (in time), and b is dimensionless. Although the 

 mathematical expression of the model has four cases, 

 these four cases actually represent the limiting forms of 

 a single equation as a or b (or both) approach 0. 



Appendix 2— Spawning stock biomass per recruit 



If N a is a vector of the numbers of females at each age 

 under constant conditions, such that 



N a+l =N a e 



-iFS.+M) 



where F = the instantaneous fishing mortality rate; 

 S a = the partial recruitment at age a; and 

 M = the instantaneous natural mortality rate; 



then the cumulative spawning potential of a cohort of 

 females over the lifetime of the cohort (under constant 

 FandM andS n ) is 



SSB/R = ^N a Fec a Mat n , 



i 



where Fec n = fecundity at age a, and 



Mat n = proportion mature at age a. 



The spawning potential per recruit (SSB/R) can then be 

 calculated under various estimates of F and compared 

 with the unfished SSB/R (F=0) as shown in Figure 9. 



