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Appendix 1: reparameterized spawner-recruit 

 relationships 



The number of young fish recruiting to a population (R) 

 is often relateci to the aggregate fecundity of the spawn- 

 ing stock (S) by using one of two functional forms: 



fl = 



abS 



Ricker 



Beverton and Holt 



(A.l) 



b + S 



The parameter a is the slope of the curve at the origin 

 and the parameter b controls the degree of density 

 dependence. Notice that the domain of both functions 

 extends from zero to infinity, whereas in practice there 

 must be some limitation on S and R even in the absence 

 of fishing owing to environmental constraints (call them 

 jSq and i?0' respectively). This being so, we obtain 



12.- 



,*s„ 



l-i-So/6. 



Ricker 



Beverton and Holt 



(A.2) 



The ratio S„/Ry represents the maximum expected life- 

 time fecundity of each recruit and a represents the sur- 

 vival of recruits in the absence of density dependence. 

 Accordingly, the product o = qSq/Rq may be interpreted 

 as the maximum possible number of recruits produced 

 by each spawner over its lifetime (Myers et al., 1999). 



The dimensionless character of a makes it useful for 

 interspecies comparisons, or for borrowing values from 

 species with similar life history strategies. Solving for 

 b in terms of a one obtains 



log,, a I Sf, 



Ricker 



Sy/(l-a). 



Beverton and Holt 

 Substituting Equation A. 3 into Equation A.l gives 



(A.3) 



R- 



aSa 



-s/s„ 



aS, 







Ricker 



Beverton and Holt 



(A.4) 



l-Ka-l)S/S„ 



