POLOVINA and RALSTON: MSY FOR DEEP SLOPE FISHES 



ploited biomass per nautical mile of 200 m contour 

 in the subsequent yield estimation, in place of the 

 values computed from the bank CPUE values for 

 the inhabited southern islands (Saipan, Tinian, Rota, 

 and Guam). 



For each species group with values of K, M, t c , 

 and F, the ratio of fishery yield to unexploited 

 recruited biomass {YIBJ can be computed from the 

 Beverton and Holt yield equations (Beddington and 

 Cooke 1983). The product of YIB^ with the species 

 group unexploited recruited biomass estimates 

 (Table 5) results in estimates of equilibrium yield for 

 the seven species for which estimates of K and M 

 are available. For the eighth group, which consists 

 of all other species, the ratio of yield to B^ is taken 

 as the ratio of total yield for the seven species 

 divided by their total B m . For a fixed F, the sum of 

 the equilibrium yield of the eight species groups at 

 a bank is the bank equilibrium yield, and the sum 

 of the equilibrium yields for a species group over 

 all the banks is the species group equilibrium yield. 



The equilibrium yield for the multispecies bottom 

 fish complex fished with handline gear in the 125- 

 275 m depth range for the 22 islands and banks of 

 the Mariana Archipelago increases rapidly as a func- 

 tion of F to a level of about 90 t and beyond that 

 exhibits a gradual increase with increased fishing 

 mortality (Table 7). The MSY estimation approach 

 estimates MSY as the yield from the constant re- 

 cruitment yield curve corresponding to that level of 

 mortality where a marginal increase in one unit of 



Table 7. — Total annual sustainable 

 handline yield in metric tons (t) for a 

 range of fishing mortalities. 



mortality increases the catch by 0.1 of the amount 

 caught by the first unit of F. The value of F 0A for 

 the bottom fish resource in the Marianas is esti- 

 mated to be F = 1.0 and the corresponding annual 

 equilibrium yield is 82 t (Table 7). 



The equilibrium yield value of 82 t, which cor- 

 responds to a fishing mortality of 1.0, is based on 

 the current estimated age of entry to the fishery and 

 not necessarily the age of entry which maximizes 

 the YIR. For a fishery mortality of 1.0, the estimated 

 age of entry which maximizes YIR is computed from 

 the Beverton and Holt equation and compared with 

 the current age of entry for each species (Table 8). 

 With the exception of the jack, Caranx lugubris, the 

 age of entry which maximized YIR is less than the 

 current age of entry (Table 8). Based on the age of 

 entry which maximized the YIR, new levels of sus- 

 tainable yield for each species group as a function 

 of F can be computed as the product of the yield 

 for the current age of entry with the ratio of YIR 

 maximized over age of entry to the YIR for the cur- 

 rent age of entry. The values of F 01 and Y 01 for 

 the ages of entry which maximize the YIR are 1.0 

 and 109 t, respectively (Table 9). An approximate 

 confidence interval (C.I.) for this yield estimate can 

 be obtained from a Taylor series expansion which 

 incorporates the variance estimate for catchability 

 (Polovina 1986a) and a sampling variance of the 

 bank CPUE values (Table 2). The standard error of 

 the yield estimate is 14 t, and thus a 95% C.I. for 

 the yield at F 01 for the archipelago is 81-137 t 

 annually. 



The estimation of MSY based on the relative 

 spawning stock approach requires estimates of the 

 age of sexual maturity (t m ). A relationship express- 

 ing the length at sexual maturity (L m ) as a fraction 

 of the length of the upper one percentile (L max ) for 

 tropical bottom fishes is as follows (Anonymous 

 1977, from Brouard and Grandperrin 1984): 



L m = 0.576 L max . 



1 F 01 and / 01 as defined by Gulland (1983). 



Table 8.— Current age at entry and age at entry which maximizes the yield 

 per recruit (YIR) at F = 1.0. 



Table 9.— Annual sustainable handline 

 yield in metric tons (t) for the age at 

 entry which maximizes the yield per 

 recruit for each species. 



767 



