Jacobson and Cadrin: Stock-rebuilding lime isopleths and constants stock-rebuilding plans for overfished stocks 



529 



o 

 o 



o 

 o 



IVIodel 1 

 Model 2 

 Model 3 

 Model 4 

 Model 5 

 Model 6 



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 (BiyK) 



Figure 7 



Isopleths for mean, median, mode, Qior,, Q90.-. and Q99,. 75-year stock- 

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

 rocktish in the Southern California Bight. Isopleths for all statistics 

 and one type of model are shown in each panel. Model types 2, 4, and 6 

 include uncertainty in F^^^- 



isopleths from deterministic model type 1 were quite dif- 

 ferent from isopleths (other than for median rebuilding 

 times) from stochastic models. 



Rebuilding time isopleths can be used with any type of 

 population dynamics model. We used the logistic popula- 

 tion growth model in this paper because it is clearly linked 

 to Sj^jsy and F^^y, incorporates density dependence, is easy 

 to apply to a wide range of stocks (with varying amounts of 

 information), and computationally efficient. However, re- 

 building time isopleths could have been calculated by us- 

 ing Cadrin's'' age-structured model for Georges Bank yel- 

 lowtail flounder or Butler et al.'s'' biomass dynamic model 

 for cowcod rockfish. Age-structured models might be best 

 for calculating rebuilding time isopleths if the rebuilding 

 time frame is relatively short and estimates of abundance 

 are available for several incoming year classes because 



age-structured models account for transient conditions 

 (e.g. recruitment and growth patterns) that are important 

 in the short term. 



Age-based projections were used to test the expected 

 performance of rebuilding targets for six New England 

 groundfish stocks (NDWG**). The original rebuilding 

 targets were derived from five-year rebuilding time iso- 

 pleths calculated with a deterministic logistic growth 

 models, but the targets incorporated estimation uncer- 

 tainty by assuming the tenth percentile of the estimate 



8 NDWG (Northern Demersal Working Group). 2000. Assess- 

 ment of 11 northeast groundfish stocks through 1999. North- 

 east Fisheries Science Center Reference Document 00-05, 175 p. 

 Northeast Fisheries Science Center, 166 Water Street, Woods 

 Hole, MA, 02543. 



