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



523 



r = G„ + R-M 



(7) 



where G^ = the instantaneous rate of somatic gi'owth; 

 and 

 R^ = an instantaneous rate for recruitment (in 

 units of biomass). 



Somatic growth and recruitment may be density depen- 

 dent but are usually positive (G,>0 and i?,>0). Thus, r^=-M 

 is possible in the extreme case of zero growth and zero 

 recruitment. 



Production process errors were simulated by drawing 

 random numbers from a three-parameter gamma prob- 

 ability distribution (Johnson et al., 1994, Appendix 1). 

 Runs with autocorrelated process errors used one of two 

 algorithms based on gamma distributions with adjusted 

 parameter estimates (Appendix 2). 



assumed M=0.2 /yr), relatively productive (r=0.58-0.65) 

 stock with some autocorrelation (p =0.33-0.34) in pro- 

 duction process errors (Table 2). Empirical, and gamma 

 distributions fit by maximum likelihood and the method 

 of moments had similar means and variances (Table 2). 

 Surplus production and biomass are related for Georges 

 Bank yellowtail flounder, with P^ reduced at the low B^, 

 levels (Fig. 2A). Variability in estimated r^, values indicate 

 autocorrelation in process errors (Fig. 2B). The distribu- 

 tion of r^, values (Fig. 2C) was skewed to the left and there 

 were no negative values. Gamma distributions fitted by 

 maximum likelihood and the method of moments (Appen- 

 dix 1) were similar in shape (Fig. 2C). In simulations for 

 yellowtail flounder, we used F^^^.j^0.30 (from ASPIC) with 

 CT;^ = 0.037andp = 0.33. 



Cowcod rockfish 



Georges Bank yellowtail flounder 



Cadrin'' used virtual population analysis (VPA, cali- 

 brated by using survey data) to estimate stock biomass 

 for Georges Bank yellowtail flounder during 1973-98. In 

 the same assessment, a surplus production model (ASPIC 

 [stock-production model incorporating covariates], Prager, 

 1994) was used to estimate 7^=93,700 metric tons (t) 

 (80'7r bootstrap confidence interval 87,700-97,000 t) 

 and F,^^^.5— 0.30/yr (80% bootstrap confidence interval 0.27- 

 0.32/yr'). 



Cadrin's stock assessment^ and our production calcula- 

 tions indicate that Georges Bank yellowtail flounder is 

 a moderately long-lived (maximum observed age 14 yr. 



Cadrin, S. X. 2000. Georges Bank yellowtail flounder In 

 Northern demersal working group: assessment of 11 northeast 

 groundfish stocks through 1999. In Northeast Fisheries Science 

 Center Reference Document 00-05, p. 45-64. Northeast Fisher- 

 ies Science Center 166 Water Street, Woods Hole, MA, 02543. 



Butler et &\.^ (see also Butler et al.') estimated A:=3400 t 

 (95% CI 2800-4000 t) with a delay-difference biomass 

 dynamic model for cowcod rockfish in the Southern Cali- 

 fornia Bight. Annual biomass estimates from the same 

 source were used to calculate surplus production during 

 1951-97 when the stock was fished down from about 3200 t 

 to 240 t (about 1% of virgin biomass). 



Butler et al.^ and our production calculations indicate 

 that cowcod rockfish are a long-lived (maximum observed 



^ Butler, J. L., L. D. Jacobson, J. T. Barnes, and H. G. Moser 

 2002. Manuscript in revew. Biology and population dynam- 

 ics of cowcod rockfish iSebastes leuis) in the southern California 

 Bight. 



' Butler, J. L., L. D. Jacobson, J. T. Barnes, H. G. Moser, and R. 

 Collins. 1999. Stock assessment of cowcod. In Appendix 

 to the state of the Pacific Coast groundfish fishery through 

 1999 and recommended acceptable biological catch for 2000 

 stock assessment and fishery evaluation, p. Vi-113 (section 

 5). Pacific Fishery Management Council, 7700 NE Ambassa- 

 dor Place, Portland, OR, 97220-1384. 



