Shepherd and Idoine Yield- and spawning biomass-per-recruit for Centropnstis striate 



331 



B 



FEMALE 



TRANSITIONAL 



MALE 



TRANSITIONAL 



FEMALE 



10 20 30 40 50 



STANDARD LENGTH (cm) 



10 20 30 40 50 



STANDARD LENGTH (cm) 



Figure 3 



(A) Calculated values of number of substages, k, and (B) mean transit times, D, for 

 female, male, and transitional stages of black sea bass Centropnstis striata. 



16 



£° 



< 

 DC 



°-o 



z 



1° 



3° 



cc 



10 15 20 25 30 35 40 

 STANDARD LENGTH 



Figure 4 



Transformation rates-at-length of female black sea bass 

 Centropristis striata used in the delay model. 



estimated per length category for each sex, with sex 

 determined at the time of capture. Delay and variance 

 estimates were extrapolated with a linear regression 

 between the largest length categories in the dataset 

 and maximum potential length (Fig. 3). Maximum 

 lengths were 49cmSL for females, 39 cm SL for 

 transitionals, and 60 cm SL for males. D and S 2 for 

 each length-interval in the transitional category were 

 estimated by using the mean values of females and 

 males. Transformation rates-at-length were estimated 

 from a composite of the frequency of transitional-stage 

 fish recorded in field observations (Fig. 4) (Mercer 1978, 

 Low 1981, Wenner et al. 1986). Transformations be- 



gan at 8 cm, and individual fish 

 were allowed to exist in a transi- 

 tional state for 1 cm. Sex-specific 

 length- weight equations (Mercer 

 1978) used to convert standard 

 length (cm) to weight in grams 

 were 



males: wt=0.01773 SL 3 1525 



females: wt=0.02810 SL 30104 

 transitional: wt=0.02120 SL 30991 



Annual instantaneous natural 

 mortality (M) for both the Y/R 

 and SSB/R calculations was mod- 

 eled as a length-dependent rate 

 equal to 0.3 at lengths 1-10 cm 

 and 0.2 at 11 cm-max. length. In- 

 stantaneous fishing mortality (F) 

 was varied between 0.0 and 1.50 

 in both calculations. Mortality 

 rates were applied over time- 

 intervals of Id (t= 1/365). 

 Length-at-first-capture (L c ), which was modeled as 

 knife-edge recruitment, varied between 16 and 

 32 cm SL. Increments were equivalent to annual mean 

 lengths at successive ages, as determined from the 

 delay model. The effect of harvesting was examined by 

 incorporating an additional mortality term at each 

 length category beyond the size-at-recruitment. 

 Maturity-at-length data were collected during NEFSC 

 bottom-trawl surveys between 1982 and 1990 (O'Brien 

 et al. 1993). The initial cohort in the model consisted 

 of 2000 fish divided according to a sex ratio of 99:1 

 female to male (Mercer 1978, Wenner et al. 1986). Pre- 

 cision of rounded values in the computer program re- 

 sulted in the net loss of some individuals; therefore, 

 the number of recruits used in the per-recruit calcula- 

 tions was the sum of individuals accounted for at the 

 end of the run rather than the initial input value. The 

 yield model was run for 25 yr or until the number of 

 remaining fish in the cohort was <1; and the spawning 

 biomass model (females only) was run for 11 yr or un- 

 til the cohort was reduced to <1 fish. The Y/R and 

 SSB/R models were developed as separate computer 

 programs written in ANSI standard FORTRAN. 

 The Y/R estimates from the distributed delay model 

 were compared with results from a Thompson-Bell 

 (T-B) Y/R model. Lengths-at-annual-intervals for males 

 and females were derived from execution of the delay 

 model without a transitional phase and converted to 

 grams using the appropriate length-weight equations. 

 The mean of the male and female weights-at-age served 

 as input to the T-B Y/R model. M was set equal to 0.3 

 for age 1, and 0.2 thereafter. The traditional SSB/R 



