Porch et al. A catch free assessment model with application to Epinephelus ita/aia 



101 



and, since a = a/J^/Sy, 



R- 



^^^A«l-S«o 



Rn 



aS/Sn 



'l + (a-l)S/S„ 



Ricker 



Beverton and Holt 



(A. 5) 



Dividing through by i?y and defining s as S/Sq gives 

 Equation 4. 



Appendix 2: formula for equilibrium 

 spawning biomass 



The spawning potential ratio (p) is defined as the number 

 of spawners produced by each recruit at equilibrium with 

 a given fishing mortality rate F divided by the number 



of spawners per recruit under virgin conditions (F-O). 

 This may be written 



Vo Sq / /?o ^f ^ ^0 



(A.6) 



where the tilde signifies equilibrium values. 

 At equilibrium we also obtain from Equation 4 



sa^-' 



as 



(l + s(a-l)) 



Ricker 



Beverton and Holt 



(A.7) 



Dividing both sides of Equation A.7 by r, substituting p 

 for Equation A.6, and solving for s gives Equation 10. 



