Ralston and Tagami: Exploitable biomass of Heterocarpus laevigatus in Hawaiian Is , Part 



497 



purposes of geographically stratifying the analysis. An 

 exception was made for the islands of Maui, Lanai, 

 Kahoolawe, and Molokai (MLKM), which share, in ad- 

 dition to the 915 m (500 fm) contour, a common 366 m 

 (200 fm) isobath. These four islands were, therefore, 

 treated as a single geographic locality. 



Estimates of the amount of suitable shrimp habitat, 

 in hectares (lha = 0.01km"), were obtained by deter- 

 mining the horizontal planar area lying between 

 charted depth contours. A large digitizing tablet was 

 used to calculate all area estimates directly from nau- 

 tical charts (NOAA charts 19016, 19019, and 19022, 

 and Defense Mapping Agency bottom contour charts). 

 These charts included 915m (500 fm) isobaths, but we 

 manually contoured all of the 366 m (200 fm) isobaths 

 using the sounding data provided on each chart. In 

 addition, good detailed bathymetry was available for 

 the islands of Kauai and Niihau, and at these sites the 

 458 m (250 fm), 549 m (300 fm), 640 m (350 fm), 732 m 

 (400 fm), and 824 m (450 fm) isobaths were contoured 

 and digitized as well. 



Each contour was digitized three times by each 

 author, providing a minimum estimate of measurement 

 error in our calculation of habitat areas. These errors 

 were typically small (median CV 0.5%, range 0.1- 

 1.9%). A potentially more serious type of error con- 

 cerns discrepancies between the actual locations of con- 

 tours and their representations on charts. However, 

 we had no information concerning the magnitude of 

 this type of error and, given that measurement errors 

 were negligible, we assumed that our estimates of 

 habitat area were accurate and precise. 



These data were then used to calculate habitat areas 

 for each 92 m (50 fm) depth interval between 366 and 

 915 m (200-500 fm). First, the relative distribution of 

 habitat was calculated from the Kauai and Niihau data. 

 To estimate depth-specific habitat areas for the three 

 remaining sites (Oahu, MLKM, and Hawaii), the com- 

 bined relative proportions of habitat for each depth 

 interval obtained at Kauai-Niihau were applied to 

 the estimates of total habitat area between 366 and 

 915m (200-500fm). In support of this procedure, 

 results in Mark and Moore (1987) indicate that slope- 

 depth relationships among the main islands of the 

 archipelago are, in general, similar. 



Depth-stratified sampling 



For the second phase of the assessment, each of the 

 island areas was targeted for comprehensive trapping 

 surveys to determine abundance patterns (i.e., catch 

 rate) with depth and to estimate standing stocks (Table 

 1). A depth-stratified sampling approach was used. 

 From preliminary data gathered at Kauai and Niihau 

 during the September 1987 cruise, the mean and vari- 



ance in CPUE were calculated for each of the six 92m 

 (50fm) depth intervals lying in the 366-915m (200- 

 500 fm) range. Based on the results of this vertical 

 distribution survey, sampling effort was optimally par- 

 titioned into depth strata by Neyman allocation (Coch- 

 ran 1977), i.e., trap allocations to each depth interval 

 were based on the product of abundance (CPUE • habi- 

 tat area) and the standard deviation of CPUE at that 

 depth. As each cruise progressed, CPUE means and 

 variances \\fere recalculated daily and the trap alloca- 

 tion schedule was updated. 



From the results of the surveys, exploitable biomass 

 was estimated (Eq. 1) for each depth interval at each 

 site visited. This calculation assumes that the catch- 

 ability estimate, which was determined at the deple- 

 tion experiment study site, can be extended to all other 

 localities sampled. An estimate of the variance of the 

 biomass for each stratum was obtained from Eq. 1 

 using the delta method (Seber 1982), resulting in 



A2 A^-CPTJF^ 



VAR[B] = — VAR[CPUE] + VAR[q] 



q2 q4 



if all covariance terms are zero (a reasonable first 

 assumption) and VAR[A] is negligible (see above). Con- 

 fidence intervals were then calculated using the distri- 

 bution of standard normal scores (a = 0.05, Z = 1.96). 



Length-frequency analysis 



The Kaulakahi Channel experimental depletion site was 

 visited on seven separate occasions during May 1986- 

 March 1988 (Table 1). During each visit a length- 

 frequency sample of H. laevigatus was obtained, with 

 the ultimate goal of analyzing the progression of size 

 modes over time (egg bearing is strongly seasonal; 

 Dailey and Ralston 1986, Moffitt and Polovina 1987). 

 Additional length-frequency samples were obtained 

 during the course of the depth-stratified sampling at 

 each of the island sites. 



Mortality and growth parameters were estimated 

 from length-frequency distributions using the regres- 

 sion method of Wetherall et al. (1987). This technique 

 requires an equilibrium population size-structure, an 

 undesirable and restrictive assumption. Even so, data 

 are available to support its use. Dailey and Ralston 

 (1986) present length-frequency data for male and 

 female shrimp sampled during the earliest stages of the 

 fishery (1983-84). The data are very similar to those 

 presented here, suggesting that exploitation has yet 

 to seriously affect size composition. Additionally, the 

 time-invariance of the size-frequency data we collected 

 at the Kaulakahi study site (see below) indicates 

 equilibrium conditions. 



