534 



Fishery Bulletin 100(3) 



may not be sufficient as a rebuilding plan. In this context, 

 it is important to remember that rebuilding time isopleths 

 are constructed based on the assumption of constant fish- 

 ing mortality rates during the rebuilding program. More 

 complicated rebuilding plans, that allow F to vary accord- 

 ing to changes in biomass or other factors, are best evalu- 

 ated by stock-specific simulations. 



The test is based on the notion that control rules that al- 

 low F levels above the stock-rebuilding time isopleth for bio- 

 mass levels above Bq are unlikely to rebuild the stock with 

 desired probability in the desired time frame. Therefore, as 

 a minimum requirement for meeting rebuilding time goals, 

 harvest control rules used as rebuilding plans should lie on 

 or under the corresponding rebuilding time isopleth for all 

 biomass levels above Bq. Consider a hypothetical overfished 

 stock for which there is a ten-year median rebuilding time 

 goal. Assume that a harvest control rule proposed as a 

 rebuilding plan has the typical shape (i.e. F increases or 

 stays the same as biomass increases, as in Fig. 1). If the 

 control rule lies above the isopleth for some critical biomass 

 level between B^^ and B^/s-y then the rule will allow fishing 

 mortality rates that are generally too high to meet manage- 

 ment goals once biomass reaches the critical level. 



The example of Georges Bank yellowtail flounder 



Georges Bank yellowtail flounder (Fig. 1) can be used to 

 illustrate how rebuilding time isopleths might have been 

 used to evaluate stock-rebuilding plans for hypothetical 

 implementation during 1996 and how stock-rebuilding 

 time isopleths can be used to monitor progress in rebuild- 

 ing overfished stocks. The discussion is hypothetical, 

 however, because the examples evaluate management 

 approaches that have not been used in rebuilding the 

 stock. In reality, managers kept F for Georges Bank yel- 

 lowtail flounder during 1996-99 nearly constant at a level 

 well the below the 10-year isopleth, and the Georges Bank 

 yellowtail flounder stock was almost rebuilt to the Bj^jgy 

 target level in 1999 after only four years (Fig. 1). 



Based on this example, the hai-vest control rule in Figure 

 1 would have been marginal for use in a hypothetical medi- 

 an ten-year stock-rebuilding plan for Georges Bank yellow- 

 tail flounder starting in 1996, because the rule lies slightly 

 above the 10-year isopleth for biomass levels of 47*7^ B^jgy. 

 The harvest rule might have been rejected outright as a 

 five-year rebuilding plan because the rule lies well above 

 the 5-year rebuilding time isopleth. The rebuilding trajec- 

 tory for Georges Bank yellowtail flounder (Fig. 1) shows 

 that the five-year rebuilding plan, which began in 1996, 

 was on schedule during 1996-98 because fishing mortality 

 and estimated biomass were within the 5-year, 4-year, and 

 3-year isopleths during successive years. 



The Georges Bank yellowtail flounder example provides 

 an important final lesson about uncertainty in actual re- 

 building times, even if statistical distributions of potential 

 rebuilding times are characterized accurately. During 

 1996-99, the stock was managed at a relatively constant 

 F level that was well above the entire 4-year median 

 rebuilding time isopleth (Fig. 1). Despite the relatively 

 high F level, Georges Bank yellowtail flounder reached a 



biomass level near fi^gy in 1999, after four years. We attri- 

 bute this fortunate chain of events to stochastic variation 

 in process errors stemming primarily from recruitment 

 and growth of the strong 1997 year class (Cadrin'^). 



Acknowledgments 



We thank P. Rago, D. Hart, M. Sissenwine (National Ma- 

 rine Fisheries Service, Woods Hole, MA), M. Prager 

 (National Marine Fisheries Service, Beaufort, NC), and 

 three anonymous reviewers for information and advice. 

 S. Murawski suggested sensitivity analyses. J. Boreman, 

 S. Murawski, and F. Serchuk (National Marine Fisheries 

 Sei-vice, Woods Hole, MA) made editorial suggestions. 



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