Thompson Variations on a simple dynamic pool model 



723 



biased estimate of F MSY - One way to compare the two 

 types of curve is to require that they intersect at iv r 

 and that they imply the same pristine biomass-per- 

 recruit level. In the base model, stock biomass per 

 recruit is obtained by multiplying Equation 2 through 

 by w r /b(F',a r ). When Equation 22 or 23 is used to rep- 

 resent growth, stock biomass per recruit is given by 

 Appendix Equation 5 or Appendix Equation 11. When 

 growth curves are forced to intersect at w r and pris- 

 tine biomass per recruit levels are equated, the follow- 

 ing parametrization is defined: 



zr = u 





(-ini)e kK K 



):K' + 1 



1. 



(24i 



where (p is the binomial coefficient (Appendix) and 

 K" is the estimated value of K" used to define the 

 linear growth relationship (assuming that M and a r 

 are the same under both weight-at-age relationships, 

 K" is distinguished from K" by the fact that the age 

 intercepts of the two curves differ — Equation 3). 



Substituting Equation 24 for K" in Equation 6 gives 

 F' MSY in the base model when the linear growth func- 

 tion is fit in the manner described above. This F' MSY 

 value can be either higher or lower than the value 

 given by the solution derived in the Appendix. For the 

 case where n=3. Figure 3 shows the range of +/- l(Kr 

 bias for four values of K", along with the loci of zero 

 bias. Note that at low values of K" (e.g., 0.5), the two 



