519 



Abstract— Stock-rebuildinR time iso- 

 |)li'ths relate constant levels of fishing; 

 mortality iF), stock biomass, and man- 

 agement goals to rebuilding times for 

 overfished stocks. We used simulation 

 models with uncertainty about Fj^f^y 

 and variability in annual intrinsic 

 growth rates (r^ ) to calculate rebuilding 

 time isopleths for Georges Bank yellow- 

 tail flounder, Limanda ferruginea, and 

 cowcod roekfish. Sebastes levis, in the 

 Southern California Bight. Stock-re- 

 building time distributions from sto- 

 chastic models were variable and right- 

 skewed, indicating that rebuilding may 

 take less or substantially more time 

 than expected. The probability of long 

 rebuilding times increased with lower 

 biomass, higher F, uncertainty about 

 F^igy. and autocorrelation in r^ values. 

 Uncertainty about Fysi- had the great- 

 est effect on rebuilding times. Median 

 recovery times from simulations were 

 insensitive to model assumptions about 

 uncertainty and variability, suggesting 

 that median recovery times should be 

 considered in rebuilding plans. Iso- 

 pleths calculated in previous studies 

 by deterministic models approximate 

 median, rather than mean, rebuild- 

 ing times. Stochastic models allow 

 managers to specify and evaluate the 

 risk (measured as a probability) of not 

 achieving a rebuilding goal according 

 to schedule. Rebuilding time isopleths 

 can be used for stocks with a range of 

 life histories and can be based on any 

 type of population dynamics model. 

 They are directly applicable with con- 

 stant F rebuilding plans but are also 

 useful in other cases. We used new 

 algorithms for simulating autocor- 

 related process errors from a gamma 

 distribution and evaluated sensitivity 

 to statistical distributions assumed for 

 r^,. Uncertainty about current biomass 

 and fishing mortality rates can be con- 

 sidered with rebuilding time isopleths 

 in evaluating and designing constant-F 

 rebuilding plans. 



Stock-rebuilding time isopleths and 

 constant-F stock-rebuilding plans 

 for overfished stocks 



Larry D. Jacobson 



Steven X. Cadrin 



Northeast Fisheries Science Center 



National Marine Fishenes Service 



166 Water Street 



Woods Hole, MA 02543 



Email address (lor L D Jacobson) Larry JacobsomgiNOAA gov 



Manuscript accepted 12 Febraury 2002. 

 Fish. Bull. 100:519-536 (2002). 



Stock-rebuilding plans proposed for 

 overfished stocks are best evaluated by 

 stock-specific simulation analysis (e.g. 

 PFMC^). However, general approaches 

 are also valuable because many stocks 

 are overfished (NMFS, 1999) and 

 default or generic rebuilding plans can 

 be used without extensive analyses for 

 each species (e.g. PFMC'^; Applegate et 

 al.'^). In this article we show how stock- 

 rebuilding time isopleths can be used 

 to design, evaluate, and monitor prog- 

 ress of "constant F" and other types 

 of rebuilding plans. Constant-F stock- 

 rebuilding plans maintain fishing mor- 

 tality at a fixed level until the stock is 

 rebuilt, and are relatively simple and 

 easy to analyze. The isopleth approach 

 is easy to use as both a general and 

 stock-specific tool. 



The U.S. Sustainable Fisheries Act 

 (SFA) mandates rebuilding plans for 

 overfished stocks (DOC, 1996, 1998). 

 Federally managed stocks are consid- 

 ered overfished when stock biomass is 

 less than the biomass threshold (fiT-zir,.,/,. 

 gij) defined in the Fishery Manage- 

 ment Plan (FMP). National Standard 

 1 (DOC, 1998) for the SFA indicates 

 that fi7-/,res/,o/rf should be the greater 

 of one-half of fi,vf.sy *'-he theoretical 

 biomass level for maximum sustained 

 yield, MSY) or the minimum biomass 

 from which rebuilding to B^j^y could 

 be expected to occur within ten years 

 if the stock is exploited at Frhreshoid- 

 Typically, Fj,^,„;,„w = ^w.^j- (the theo- 

 retical fishing mortality rate for MSY) 

 when current biomass is at or above 



^Threshold' and F7.^„,,;,„w < P'msy at lower 

 biomass levels. A common approach 



(Fig. 1, and Thompson, 1999) reduces 

 ^Threshold from the F^i^Y level linearly to 

 zero as biomass declines from B7'/,„.,/,oW- 

 In cases where Bg^gy, and F^^gy can not 

 be estimated, reasonable proxy values 

 (e.g. one-half unfished biomass or F^ ,) 

 are typically used instead. 



The goal for most rebuilding plans 

 under the SFA is to achieve the target 

 biomass level iB^jgy or an acceptable 

 proxy level) in ten years or less. Even 

 with zero fishing mortality, ten years 

 may not be sufficient to rebuild some 

 overfished stocks. In such cases, the 

 Guidelines for National Standard 1 al- 

 low a rebuilding time period no longer 

 than one mean generation time (Re- 

 strepo et al., 1998) plus the expected 

 time to recovery in the absence of fish- 

 ing mortality (DOC, 1998). 



' PFMC (Pacific Fishery Management Coun- 

 cil). 1999. The coastal pelagic species 

 fishery management plan, Amendment 8, 

 405 p. Pacific Fishery Management Coun- 

 cil, 7700 NE Ambassador Place, Portland, 

 OR, 97220-1384. 



- PFMC (Pacific Fishery Management Coun- 

 cil). 1999. Status "of the Pacific Coast 

 groundfish fishery through 1999 and rec- 

 ommended acceptable biological catch for 

 2000 stock assessment and fishery evalua- 

 tion, 230 p. Pacific Fishery Management 

 Council, 7700 NE Ambassador Place, Port- 

 land, OR, 97220-1384. 



3 Applegate, A., S. Cadrin, J. Hoenig, C. 

 Moore, S. Murawski, and E. Pikitch. 

 1998. Evaluation of existing overfishing 

 definitions and recommendations for new 

 overfishing definitions to comply with the 

 Sustainable Fisheries Act, 179 p. New 

 England Fishery Management Council, 

 50 Water Street, Mill 2, Newburyport, MA 

 01950. 



