MOFFITT ET AL.: DISTRIBUTION AND YIELD OF DEEPWATER SHRIMP 



Table 4. — L^ and ZIK estimates for the three 

 major species of Heterocarpus by sex from 

 length-frequency data. 



Table 5.— Catch rates, habitat areas, and unexploited biomass 

 estimates for Heterocarpus laevigatas by location. 



Elefan I (Pauly 1982) to fit the von Bertalanffy 

 growth curve to the time series data for H. laeviga- 

 tus collected at Esmeralda Bank and Pagan Island, 

 the growth constant i^ can be estimated. When ap- 

 plied to the sexes separately, multiple estimates 

 were obtained for each category ranging from 0.19 

 to 0.31 yr"^ The inconsistency of these estimates 

 within area and sex groupings was most likely due 

 to the small sample size. When sexes were pooled, 

 however, K was estimated at 0.30 yr"^ for both 

 areas. Estimates of the age at recruitment and 

 maturity were obtained by solving the von Berta- 

 lanffy equation for the particular carapace lengths 

 estimated above. For female H. laevigatus, with a 

 L^ = 29 mm, the T^ = 2.0 years, and with Ljij = 

 43 mm, the 7^^ = 4.5 years. With a K estimate of 

 0.3 yr-i and ZIK of 2.5, an estimate for Z of 0.75 

 yr"^ is obtained. Because there is no fishery for H. 

 laevigatus in the Marianas, Z is equivalent to natural 

 mortality (M). 



UNEXPLOITED BIOMASS 



Because standard trapping techniques were used 

 throughout our study, CPUE values from various 

 locations could be used as a measure of relative 

 abundance. The unexploited biomass of the H. laevi- 

 gatus resource for each area is then calculated as 

 the product of the area of suitable habitat and rela- 

 tive abundance divided by the coefficient of catch- 

 ability (g = 0.001945 trap-night~^) estimated from 

 the Alamagan Island intensive trapping operation 

 (Ralston 1986). Although the catch rate from the 

 western seamounts is about twice that of the south- 

 ern island chain, the fiftyfold greater area of suit- 

 able habitat around the southern islands more than 

 compensates for the low catch rates in producing 

 a higher biomass estimate for the southern islands 

 (Table 5). 



EQUILIBRIUM YIELD 



With the values for K, L^, M, and Tf., the Bever- 

 ton and Holt yield-per-recruit equation can be used 

 to compute the ratio of equilibrium yield to unex- 

 ploited recruited biomass (Y/B) as a function of 

 fishing mortality (F) (Polovina and Ralston 1986). 

 Because the shrimp resource in the Marianas is not 

 fished, the estimates of the biomass for each bank 

 represent the unexploited trappable biomass (B), 

 and hence, the product of Y/B and B gives the equi- 

 librium yield as a function of F (Table 6). As F in- 

 creases, the equilibrium yield increases rapidly for 

 low levels ofF. The relationship between F and the 

 equilibrium yield estimated from the Beverton and 

 Holt yield-per-recruit equation assumes that recruit- 

 ment is unchanged as F increases and does not take 

 into account any economic considerations. Ideally 

 a spawner-recruit relationship is needed to account 

 for changes in yield because of the changes in re- 

 cruitment which might occur as F increases. How- 

 ever, in the absence of a knowledge of the spawner- 

 recruit curve, two approaches can be used to 

 estimate recommended yield. One approach esti- 



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