NOTE Hata and Berkson: Abundance of Limulus polyphemus in the Delaware Bay area 935 



stead of rope, which runs from wing to wing of the 

 net (Fig. 2). The net ropeUne is attached behind the 

 sweep chain. In addition, usually three rows of weight 

 chain are attached behind the sweep chain. The chain 

 sweep is considered more effective in digging crabs 

 out of the bottom than the typical ground gear of 

 most research trawls. We used a standard two-seam 

 flounder trawl with an 18.3-m headrope and 24.4-m 

 footrope. The net consisted of 14-cm stretched mesh 

 polypropylene throughout and was equipped with 

 chafing gear on the bag. The net was attached to the 

 trawl doors by 91-m ground cables wrapped in rubber 

 cookies. Tow duration was usually 15 minutes (bottom 

 time), except for one tow in the Delaware Bay ship- 

 ping channel, which was reduced to 7.5 minutes. We 

 assumed that density was not affected by tow dura- 

 tion (e.g. gear saturation was not a factor). 



All horseshoe crabs were culled from the catch, 

 and either all or a subsample were examined. For 

 subsamples of a large catch, 50 crabs greater than 

 150 mm prosomal width were examined, as well as 

 all small, soft, and shedding crabs. Horseshoe crabs 

 that were not examined were counted separately by 

 sex. Examined crabs were measured for prosomal 

 width and identified to sex and maturity. Maturity 

 classifications were as follows: immature; primipa- 

 rous (mature horseshoe crabs that had not spawned 

 yet); and multiparous (crabs that had spawned at 

 least once (Table 1| ). When catches were subsampled, 

 characteristics of examined crabs were extrapolated 

 to all crabs in that tow. Abundance was estimated for 

 each demographic group as well as for the total. 



Tow distances were determined for most tows 

 from beginning and ending positions and recorded 

 by using Loran C. These are minima because they 

 do not consider any deviations from a straight path. 

 Distances were not recorded for three tows; therefore they 

 were estimated as the mean distance of all other tows. Net 

 width was estimated as half of the mean of the headrope 

 and footline lengths (Fridman, 1986). The tow distance and 

 net width were used to calculate the swept area to deter- 

 mine the density of horseshoe crabs. We assumed that the 

 ground cables and trawl doors were not effective in catch- 

 ing crabs; therefore all fishing was done only by the net. 

 No information is available on the efficiency of the ground 

 cables or doors for horseshoe crabs, but we do not believe 

 horseshoe crabs are mobile enough, nor swim fast enough, 

 to be effectively herded by them. 



The mean density (crabs/km^) and variance in each 

 stratum were calculated by assuming a zl-distribution 

 (Aitchison and Brown, 1957; Pennington, 1983), and these 

 estimates were combined by using formulas for a stratified 

 random design (Cochran, 1977). The /i-distribution model 

 is applicable to skewed data that consist of a portion of zero 

 catches when the frequency of nonzero catches follows a 

 lognormal distribution (Pennington 1983; Pennington 

 1996). With such skewed data, the estimator of the mean as 

 defined for the 4-distribution model is more efficient than 

 the sample mean estimator derived from the normal distri- 

 bution (Smith, 1988). Areas by stratum and total area were 



substituted for the numbers of grids per stratum and total 

 number of grids for determining stratum weights (Table 2). 

 Latitudinal and longitudinal distances, and therefore grid 

 areas, differed by latitude; therefore grid areas were cal- 

 culated separately for each minute of latitude. The total 

 number of grids in each stratum was determined for each 

 latitude to calculate the area by stratum and the total area. 

 Ninety-five percent confidence intervals of the stratified 

 mean density and population total were calculated by us- 

 ing the effective degrees of freedom (Cochran, 1977). Mean 

 densities, totals, and confidence limits for demographic 

 groups did not sum to the values calculated by using all 

 horseshoe crabs combined because the stratum mean cal- 

 culated by the 4-distribution is a function of the stratum 

 variance, which varies by demographic group. 



Results 



The mean abundance estimate for all crabs within the 

 study area based on day sampling was 6.81 million crabs 

 within the 2912-km2 study area (Table 3). The mean abun- 

 dance estimate for all crabs based on night sampling was 

 11.40 million crabs in the study area (Table 3). 



