Jacobson and Cadrin: Stock rebuilding time isopleths and constant f stock rebuilding plans for overfished stocks 



533 



CM 

 O 



O 

 O 



o 

 o 



o 



CNJ 

 O 



o 

 o 



o 

 o 



Gamma 

 Bootstrap 

 Normal 

 LognormaL 



Q99% 



Q90% 



Mode 



0.00 0.25 0.50 0.00 0.25 0.50 



Relative biomass (Sq/K) 



Figure 11 



Mean, median, mode, Qiq,-,, Qgo^-,. and Qggr-, 75-year stock-rebuilding time 

 isopleths for cowcod rockfish, simulated with model type 3 (no uncer- 

 tainty about Fysy and uncorrelated r^ values). Stochastic r^, values were 

 from a gamma distribution (same as Figs. 7 and 9>. normal distribution, 

 lognormal distribution or bootstrap of observed r values. All distribu- 

 tions had the same mean and variance. 



Developing, monitoring, and 

 evaluating stock-rebuilding programs 



Once the management goal, desired probability of achiev- 

 ing the stock- rebuilding goal, and the time frame for 

 rebuilding are identified (e.g.lO-yr median rebuilding time 

 to a B^j^y target), the simplest way to use stock-rebuilding 

 time isopleths in designing a rebuilding plan is to choose 

 a constant-Fg level from the appropriate rebuilding time 

 isopleth, based on a current estimate of Bq. Cadrin (1999) 

 has provided an example of this approach. 



Stock-rebuilding time isopleths can be used to monitor 

 the progress of any rebuilding plan although interpreta- 

 tion is clearest with constant-F values (Cadrin, 1999). 

 For example, the point defined by current biomass and F 

 for Georges Bank yellowtail flounder in the second year 



(1997) of a hypothetical five-year rebuilding plan begin- 

 ning in 1996 should lie near or within the 3-year rebuild- 

 ing time isopleth (Fig. 1). If the point lies far outside the 

 3-year isopleth, then managers could be sure that the 

 rebuilding plan was behind schedule. 



Evaluating harvest control rules 

 as stock-rebuilding programs 



It may be necessary to evaluate harvest control rules that 

 allow F to vary with biomass (e.g. the common harvest 

 control rule in Fig. 1) as a rebuilding plan. Rebuilding 

 isopleths provide guidance in this situation because they 

 can be used to reject some harvest control rules based on 

 a single necessary criterion. However, the test is weak 

 because a harvest control rule that passes the test may or 



