Jacobson and Cadnn: Stock rebuilding time isoplelhs and constant f stock rebuilding plans for overfished stocks 



531 



O 



O 



o 



o 

 o 



CN 



o 



ra O 

 S O 



O 

 O 



Mean 

 Q10% 



Median 



Q90% 



Q99% 



Mode 



Model Type 1 



// / / 



/ / Model Type 2 



Model Type 3 



/ // y 



/ '/ / ' 



// ^ ' 



' ^ ^ Model Type 4 



0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 



Relative biomass [B^K) 



Figure 9 



Isopleths for mean, median, mode, Q,orj, Qgo^j, and Q^^,,, 75-year stock- 

 rebuilding times simulated with six model types (Table 1 ) for cowcod rock- 

 fish in the Southern California Bight. Isopleths for one statistic and all 

 six model types are shown in each panel. Model types 2, 4, and 6 include 

 uncertainty in f^gj-. Isopleths of mean and modal rebuilding times in 

 results for models with uncertainty in F_„>,.j. (model types 2, 4, and 6) may 

 be distorted (flat) at relatively high fishing mortality levels because fish- 

 ing mortality exceeds the simulated true F^^gy '" some simulations so that 

 the simulated stock may never rebuild. 



and Stefansson^ and Patterson (1999J used more complex 

 simulation models with success. 



Distributional assumptions 



Simulation analyses (Figs. 10-11) indicate that the 

 choice of statistical distribution for simulating process 

 errors in model parameters (e.g. r^) may be important, 



^ Bell, E. D., and G. Stefansson. 1998. Performance of some 

 harvest control rules. NAFO (North Atlantic Fisheries Orga- 

 nization! SCR Doc. 98/7, 1-19. Northwest Atlantic Fisheries 

 Organization, 2 Morris Drive, P. O. Box 638, Dartmouth, Nova 

 Scotia, B2Y 3Y9, Canada. 



particularly when rebuilding times are long (e.g. those for 

 cowcod rockfish) due to low stock productivity, low stock 

 biomass, unproductive stock dynamics, or autocorrelation 

 in process errors. The choice of statistical distributions for 

 simulating r^, involves choosing between theoretical distri- 

 butions supported by theory (e.g. autocorrelated gamma 

 distribution with negative values bounded below at -M) or 

 bootstrap distributions of observed values. The program- 

 ming and work required to experiment with alternative 

 distributions is not overwhelming and we recommend 

 sensitivity analyses in cases where distributional assump- 

 tions may be important. 



Theoretical distributions for stochastic parameters are 

 flexible because many types of distributions are available, 

 most can be modified to include autocorrelation, most can 



