Shepherd and Idoine Yield- and spawning biomass-per-recruit for Centropristis striata 



333 



120 



0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 

 FISHING MORTALITY 



Figure 6 



Sex composition of total yield for black sea 

 bass Centropristis striata estimated from a dis- 

 tributed delay model with sexual transition 

 (dashed) and without a transitional phase 

 (solid) for varying sizes-at-first-capture (L r ). 



delay model was comparable to traditional methods of estimating 

 yield-per-recruit. The calculated biological reference point of F max 

 from both models was nearly identical (Table 2). 



The addition of the transitional phase into the model had little 

 effect on the estimates of Y/R. The calculated values of Y/R and 

 F maj( were similar for each recruitment size and fishing mortality 

 (Fig. 5, Table 2). Although the effect of including the transition 

 phase on the total yield was negligible, the effect on sex composi- 

 tion of that total yield was substantial. With no transition phase, 

 the proportion of females in the yield was dependent upon the 

 initial sex ratio, in this case 99% female (Fig. 6). If the sexual 

 transformation of females to males was included, the percentage of 

 females to the total yield increased as a function of F and de- 

 creased as a function of size-at-first-capture (Fig. 6). At a recruit- 

 ment size of 16 cm SL (age 2), the percentage of female biomass in 

 the yield went from 21.3% at an F=0.05 to 70.4% at F=1.5, whereas 

 a change in recruitment size to 32cm (age 6) decreased the effect of 

 F, resulting in a percentage range of 17.3-20.3% females for F=0.05 

 and 1.5 respectively. 



The addition of a transitional phase had a significant impact on 

 the estimates of SSB/R from the distributed delay model and sub- 

 sequent estimates of a total female spawning biomass. In the ab- 

 sence of any harvest mortality, maximum SSB/R for a cohort that 

 undergoes a transition was 600.8 g/recruit as compared with 

 2373.3 g/recruit without transition (Fig. 7). Over the life of the 

 cohort, the spawning biomass-at-age increases similarly for the 

 first 2 yr regardless of the form of the delay model (Fig. 8 for size- 

 at-recruitment of 25 cm), at which point the effect of transition 

 begins. At age 2.5, a cohort undergoing transition approaches the 

 maximum contribution to spawning biomass-at-age, while a cohort 

 that does not undergo transition makes its maximum contribution 

 at age 10. 



The inclusion of the transitional term in the model led to lower 

 proportional reductions in SSB/R with increasing F In a model with- 

 out the transitional form (e.g., size-at-first-capture of 25cm [age 4] 

 Fig. 9) at fishing mortality of 1.5, the spawning potential was reduced 

 to 15.2% of maximum spawning potential (%MSP). In a model with 

 the transition term, however, 28.7% of maximum spawning potential 

 was obtained (Fig. 9). The pattern is also obtained at other sizes-at- 

 recruitment. The transitional phase also reduced the sensitivity of 

 SSB/R to changes in F and size-at-recruitment (L c ). Decreasing F 

 from 0.6 to 0.2 (L c =25) increased SSB/R by 107% in the non- 

 transitional model, but only 60.5% in the delay model with transitions. 

 Similarly, an increase in size-at-first-recruitment from 16 to 32 cm 

 (with F=0.6) increased SSB/R by 201.8% in the transitional model but 

 368.9% in the non-transitional version. The inclusion of a transitional 

 phase increased the natural reduction in the number of females in 

 the system, which consequently reduced the maximum SSB/R for the 

 cohort and the relative influence of fishing mortality on SSB/R. 



The sensitivity of estimates of SSB/R to changes in transforma- 

 tion rates was examined. Doubling the transition rate across all 

 lengths decreased the SSB/R by 71%- from 600.8 to 174.6 g/recruit. 

 When the transition rates were doubled over 8 cm length-increments, 

 the impact in SSB/R varied by F and the size-range over which the 

 transformation rate was changed (Fig. 10). Doubling the rate of 



