POLOVINA and RALSTON: MSY FOR DEEP SLOPE FISHES 



equilibrium yield (Y) can be expressed as 



oo 



Y = R F J exp {-tM - (t - t c ) F) w(t) dt, 



where w(t) = W^ (1 - exp(-Kt)) b , and where W^ 

 is the asymptotic weight and b is the exponent of 

 the length-weight relationship. The unexploited 

 recruited biomass (B ) can be expressed as 



B 



= R J w(t) exp ( -Mi) dt. 



The ratio of equilibrium yield to unexploited re- 

 cruited biomass (Y/BJ) is then independent of W x 

 and R, depending only on K, M, t c , F, and b. Tables 

 and computational formulae are readily available to 

 evaluate these integrals for Y and 5 m as functions 

 of t c and F (Beverton and Holt 1966; Beddington 

 and Cooke 1983). Upon estimation of B^, the equi- 

 librium yield is estimated for a given level of F as 

 the product of YIB and B . 



* oo oo 



If a stock is unfished, B m can be estimated by 

 mapping the relative abundance of the stock in 

 terms of CPUE from a systematic survey and then 

 converting estimates of relative abundance into 

 biomass with an estimate of catchability. There are 

 a number of methods which have been used to esti- 

 mate catchability (Ricker 1975). For work on Pacific 

 island fishery resources, an intensive fishing ap- 

 proach, which fishes a small isolated location heavily 

 and regresses CPUE on cumulative catch (Leslie 

 model), has been used successfully to estimate catch- 

 ability for bottom fishes and shrimp (Polovina 1986a; 

 Ralston 1986). If only one estimate of catchability 

 is obtained, then the standing stock per unit of area 

 is determined as the ratio of CPUE to catchability 

 in the appropriate units of weight or numbers. If 

 several estimates of catchability are available corre- 

 sponding to different levels of CPUE, then it might 

 be appropriate to fit a more general power function 

 relationship between CPUE and standing stock 

 (Bannerot and Austin 1983). 



The product of YIB^ and B^ as a function of F 

 is the equilibrium yield based on the assumption of 

 constant recruitment. While this assumption will be 

 valid for low levels of exploitation, there will come 

 a point as F increases that recruitment will begin 

 to decline and sustainable yield may thus be less than 

 the yield predicted under the assumption of constant 

 recruitment. Estimating MSY yield as the maximum 

 equilibrium yield obtained over all F from the prod- 



uct of Y/B^ and B^ may, therefore, overestimate 

 the actual MSY. There are two adjustments which 

 have been proposed to estimate MSY in the absence 

 of detailed knowledge of the spawner-recruit rela- 

 tionship. One approach is to estimate MSY from the 

 constant recruitment yield curve as that yield cor- 

 responding to that level of F where the addition of 

 one unit of mortality increases the yield by 10% of 

 the amount caught by the first unit of F (Gulland 

 1983, 1984). This level of mortality and correspond- 

 ing yield have been denoted as F 01 and Y 0A , 

 respectively. A second approach to estimating MSY 

 from the constant recruitment yield curve is to use 

 the Beverton and Holt equation to calculate the ratio 

 of the spawning stock biomass under exploitation 

 (S) to the spawning stock biomass in the absence 

 of exploitation (S ) and to use this ratio as an in- 

 dicator of the sustainability of a yield for a given 

 combination of F and t c . For simplicity, we assume 

 that the age of sexual maturity (t m ) is identical for 

 both sexes. Then the unexploited spawning stock 

 biomass (5 ) is 



S = R J exp(-Aft) w(t) dt, 



and 



S = R J exp(-M - (t-t c ) F) w(t) dt. 



Thus, the ratio of S/S depends only on M, K, t c , t m , 

 andF. 



It has been suggested that the spawning stock 

 biomass of a species should not be reduced below 

 20% of its unexploited level if a substantial reduc- 

 tion in the recruitment is to be avoided (Beddington 

 and Cooke 1983). Thus, the estimate of MSY is 

 determined as the maximum yield from the constant 

 recruitment curve subject to the constraint that F 

 does not exceed the level which reduces the relative 

 spawning stock biomass below 0.20 of S . 



ASSESSMENT OF SNAPPERS AND 

 GROUPERS IN THE MARIANAS 



The Mariana Archipelago consists of a chain of 

 islands and banks on a north-south axis beginning 

 with Galvez Banks and Santa Rosa Reef at the 

 southern end and extending northward to Farallon 

 de Pajaros (30 nmi north of Maug Island). A chain 

 of seamounts also runs on a north-south axis 



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