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Fishery Bulletin 100(3) 



1.0 

 0.5 

 0.0 



1.0 



0.5 



0.0 



6 12 18 24 30 



1.0 

 0.5 

 0.0 



12 



18 24 



30 



Rebuilding time (yr) 



Figure 4 



Distribution of simulated recovery times for Georges Bank yellowtail flounder from six types 

 of logistic population growth models (type 1 deterministic, others stochastic, see Table 1) with 

 Fyi,.,— 0.30/yr, CV for uncertainty in F^/^^— zero or 20"-?^, variance for production process errors zero 

 or 0.037. and autocorrelation in process errors p=zero or 0.33. Results are for 2000 model runs 

 starting from an initial biomass of B/S,,,,.)- =0.19 and constant F=0.18/vr. 



was more asymmetry and separation between isopleths 

 (Figs. 6-7) for model type 2 (no process errors and with 

 uncertainty about F^^y'' than for model type 3 (uncorre- 

 lated process error with no uncertainty about ^v/sy'- 



The fishing mortality rate that gave a median recovery 

 time often years for yellowtail flounder (or 75 years for 

 cowcod rockfish) was generally higher than the fishing 

 mortality rate that gave a corresponding mean recovery 

 time from the same initial biomass level (Figs. 8-9). Simi- 

 larly, the F that gave a mean recovery time of ten or 75 

 years was generally higher than the F that gave the corre- 

 sponding Qgg,- recovery time. There were some exceptions 

 for cowcod at high F and initial biomass levels in runs 

 with uncertainty in F^gy (run types 2, 4, and 6) due to a 

 few runs with very long rebuilding times. The very long 

 rebuilding times in runs for cowcod with uncertainty were 

 due to F in excess of the simulated true F^f^y- 



Isopleth shape may be important in interpreting simu- 

 lation results. For example, isopleths for 10-year median 

 rebuilding times in all models for yellowtail flounder were 

 steep for F in the range 0-0.2/yr (Figs. 8-9). Therefore, 

 according to example model results, the probability of 

 recovery in ten years is at least 50'7f for Georges Bank 



yellowtail flounder at biomass values >0.05 A', as long as 

 fishing morality rates are less than 0.2/yr. 



Seventy-five year stock-rebuilding time isopleths for cow- 

 cod rockfish were sensitive to assumptions about the distri- 

 bution of production process errors but 10-year isopleths for 

 yellowtail flounder were not (Figs. 10-11). We hypothesize 

 that differences among statistical distributions r^, assumed 

 in simulations were magnified for cowcod by long (e.g. 75 yr) 

 rebuilding times (see "Discussion" section). 



Rebuilding isopleths for cowcod based on i\, values from 

 a gamma distribution had higher F, at a given biomass, 

 than rebuilding isopleths based on the distribution of ob- 

 served !\, values (Fig. 11). In other words, results based on 

 the gamma distribution suggest a more productive cowcod 

 stock, presumably because the distribution of r^, values for 

 cowcod had more mass than the gamma distribution over 

 low r^ values (<0.03/yr, Fig. 3). 



Discussion 



Managers should consider using median rebuilding time 

 goals, in addition to mean or other quantiles, in develop- 



