134 



Fishery Bulletin 89(1). 1991 



12 14 B ffl 20 22 24 26 28 30 32 34 36 38 40 42 ' 44 46 48 50 52 54 



12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 



5 : 



UJ ' 



o  



UJ 



16 18 20 22 24 25 28 30 32 34 36 38 40 



D 



I ll 



28 30 32 34 36 38 40 42 



16 18 20 22 24 



28 30 32 34 36 38 40 42 



BIOMASS (THOUSANDS) 



F = 0, years 1-14; F = 0.06. vears 

 A 15-50, with slocking of 5 million 

 per year for 6 years 



F = 0, years 1-21; F = 0.06, years 



22-SO 



F = 0.03. years 1-16; F = 0.06, 

 Q years 17-50, with slocking of 5 

 million per year for 10 years 



n F = 0.03. vears 1-35; F = 0.06, 

 U years 36-50 



F = 0.06, years 1-50, with slock- 

 E Ing of 5 million per year for 12 

 years 



C F = 0.06. years 1-50 



Figure 6 



Biomass distributions of Pacific ocean 

 perch 20 years after the onset of 

 hatchery releases (from 100 simula- 

 tions), with and without stocking, for 

 three management strategies. 



after the start of stocking; (2) divide this increase in 

 yield (the result from step 1) by the total number of 

 juveniles stocked to obtain the increase in yield per 

 stocked juvenile; (3) multiply the result of step 2 by the 

 unit value of the yield to the fishery to compute the 

 value to the fishery per stocked juvenile; and, finally, 

 (4) discount this yield cumulated over n years to a pres- 

 ent value by dividing the result of step 3 by (1.03)". 

 Using this approach, based on a wholesale value for 

 Pacific ocean perch of $0.67 per kg (National Marine 

 Fisheries Service 1989), the break-even cost per juve- 

 nile ranges from $0.04 to $0.16. For example, under 

 the scenario where the fishery is closed until B MSY is 

 reached, if hatchery juveniles can be stocked at a cost 

 of $0.16 per juvenile, then hatchery releases result in 

 increasing the value of the catches over the nonstocked 

 strategy equivalent to a 3% annual return on stocking 

 costs for the first 20 years after stocking (Table 4). 

 However, under the scenario where F = 0.06 from the 

 beginning of the recovery period, the break-even cost 

 of a hatchery-released juvenile cannot exceed $0.04 if 

 the release program is to achieve a 3% annual return 

 over the first 10 years and $0.08 over a 40-year period. 



Looking at just the cumulative yields does not show 

 all of the benefits of stocking, since some of the re- 

 leased juveniles contribute to an increase in standing 

 stock. When the contribution of the released juveniles 

 to both the fishery and standing stock is considered, 

 the relative benefit is the same for all three stocking 

 and harvesting strategies (Table 5). 



A delay-difference model very similar to the model 

 used in this analysis, but with a Cushing rather than 

 Ricker recruitment function, has been fit to data on the 

 Pacific ocean perch fishery in waters off Washington 

 and Oregon (I to et al. 1987). When the Cushing recruit- 

 ment function is used in our model, the estimates of 

 MSY, F MSY and B MSY change, but the relative con- 

 tribution of hatchery releases to biomass and yield is 

 unchanged (Table 5). Further, based on simple sensitiv- 

 ity analyses, the relative benefits of hatchery releases 

 by increasing biomass and yield apparently are most 

 sensitive to the ratio of natural mortality to growth 

 (Table 5). Thus, as in the yield-per-recruit model, the 

 relative benefits of hatchery releases are inversely pro- 

 portional to the ratio of mortality to growth. 



