528 



Fishery Bulletin 100(3) 



^ o 



o 



<M 



O 



o 



Median 



Model 1 

 Model 2 

 Model 3 

 Model 4 

 Model 5 

 Model 6 



Q10% 



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 (Bo/K) 



Figure 6 



Isopleths for mean, median, mode, Qm,,, Qgo-j. ^nci Qggr,, ten-year stock- 

 rebuilding time.s simulated with six model types (Table 1) for Georges 

 Bank yellowtail flounder Isopleths for all statistics and one type of 

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

 tainty in F,,,.,.. 



error) in a high proportion of cases (Figs. 8-9). Fortunately, 

 process errors and autocorrelation may reduce this prob- 

 lem because stock growth rates increase in some years so 

 that the true Fj^^gy exceeds the manager's estimate. 



Stock-rebuilding times calculated with deterministic 

 models approximate median rebuilding times from sto- 

 chastic models. For example, rebuilding times in Cadrin 

 (1999) calculated with a deterministic model for Georges 

 Bank yellowtail flounder are very close to median rebuild- 

 ing times from our stochastic models. From our results, 

 we hypothesize that rebuilding time isopleths for other 

 species (Applegate et al.'^) based on Cadrin's ( 1999) deter- 

 ministic model should also be viewed as approximations to 

 isopleths for median rebuilding times. 



Our simulation analyses indicate that rebuilding times 

 for overfished stocks (with a range of life history charac- 



teristics, initial biomass levels and fishing mortality rates) 

 tend to be skewed and can be highly variable (Figs. 4-5). 

 Hence, rebuilding in any specific case may be quicker or 

 take much longer than expected, particularly if expecta- 

 tions are based on deterministic models that approximate 

 median rebuilding times. For example, probabilities of re- 

 building times twice as long as the goal for Georges Bank 

 yellowtail flounder (10 yr) and cowcod (75 yr) were 4% and 

 8'7( and probabilities of rebuilding times half as long were 

 40% and 1%. 



Modeling choices 



Stochastic models are necessary when estimates of mean 

 rebuilding times or quantiles other than the deterministic 

 approximation to the median are needed. Rebuilding time 



