862 



Fishery Bulletin 101(4) 



by the following double-logistic equation: 



5,, „ = S[ ^, / max 5' ,,. 



I 1 



(1) 



5,' =- 



\ + e 



■6f(u-iiy^+y, I 



l + e 



-Slti^-a) 



where S^^ = the selectivity on fish of age a during 



yeary; 

 a^Q, oIq, 5j, ^2 = the parameters of the double-logistic 

 equation; 

 7 = the deviation from the average selectiv- 

 ity pattern in yeary: 



Yy = Ps rv-l + ^v 



el ~ N(0;a;), 



pg = the interannual correlation in the de- 

 viation from average selectivity; and 



Gg = a measure of the standard deviation of 

 the interannual deviations from aver- 

 age selectivity. 



Recruitment is assumed to be governed by a Beverton-Holt 

 stock-recruitment relationship: 



' 4/i + (5/i-l)(B, /B„-l) 



E^~N{0-ol). (2) 



where Rq = the "virgin recruitment" (the number of zero- 

 year-olds at the pre-exploitation equilibrium 

 level); 



By - the spawning output at the start of year y; 

 h = the"steepness"of the stock-recruitment rela- 

 tionship (the fraction of virgin recruitment 

 expected at 0.2B„); and 



a^ - the standard deviation of the logarithms of 

 the random fluctuations in recruitment about 

 its expected value. 



The biological parameters of the operating model are set 

 to those for widow rockfish (Fig. lA), and the catches for 



the 40 years prior to the year in which the management 

 procedure is first applied (referred to as "projection year 1") 

 are set to the actual catches for widow rockfish (Fig. IB). 

 The baseline values for the parameters /;, (T^, pg, and Og 

 (Table 1) are educated guesses. The baseline choice for 

 steepness, /;, is lower than the posterior mean for this 

 quantity (0.65) obtained by Dorn (2002) because, increas- 

 ingly. West Coast rockfish are being found to be less pro- 

 ductive than initially anticipated (e.g. lanelli, 2002). The 

 value assumed for the extent of variation in recruitment, 

 a^, although based on the collection of estimates of this 

 parameter by Beddington and Cooke (1983), is neverthe- 

 less also largely an educated guess. Sensitivity to the 

 values for both h and a^j is explored. 



The biomass at the start of year 1 is assumed equal to 

 Bq, which is defined as the mean of the distribution for 

 the unfished biomass which would arise given variability 

 in recruitment about its expected value. However, this 

 specification has little impact on the results. For example, 

 the alternative that is defined to be the median of the 

 distribution for the unfished biomass would only change 

 B„ by about 5%. 



The value for Bg for each simulation is selected so that 

 the spawning output at start of year 41 (projection year 1) 

 equals a prespecified fraction of Bq (baseline fraction 



