Factors Affecting Horseshoe Crab Limulus polyphemus Trawl Survey Design

Trawl study

This study was conducted in the Atlantic Ocean in the vicinity of Delaware Bay, which is considered the center of horseshoe crab abundance (Shuster 1982; Botton and Ropes 1987). The study area extended from north of Cape May, New Jersey, to south of Ocean City, Maryland, and from shore out to 22.2 km (Figure 1). Because horseshoe crab abundance apparently decreases with depth (Botton and Haskin 1984; Botton and Ropes 1987), the area was split into an inshore zone from 0 to 5.6 km (0–3 nautical miles) and an offshore zone from 5.6 to 22.2 km (3–12 nautical miles).

Commercial fishers to whom we talked stated that topography affected horseshoe crab catches and that catches were greater in troughs than in nontrough areas. For this study, troughs were defined as at least 2.4 m deep, no more than 1.8 km wide, and more than 1.8 km long. These characteristics were common for troughs identified as important by the commercial fishers. Troughs were delineated by eye on NOAA (National Oceanic and Atmospheric Administration) charts of the area (1:80,000 scale). The study area was divided into cells of 1′ of latitude by 1′ of longitude. Cells through which the trough axis passed were considered troughs and were treated separately from nontrough cells.

Fishers also reported that catches were greater at night than during the day, so cells were sampled in both day and night in haphazard order. The second tow (day or night) in a cell was made at least 24 h after but within 4 d of the first tow and approximately parallel to but not intersecting the first track, which presumably prevented the first tow from influencing the number of horseshoe crabs available to the second tow. Twelve randomly selected cells were sampled in each of the four combinations: inshore-trough, inshore-nontrough, offshore-trough, and offshore-nontrough.

Sampling was conducted from a chartered 16.8-m-long commercial fishing vessel. For capturing horseshoe crabs, commercial fishers typically use a flounder trawl equipped with a Texas sweep. This modified ground gear consists of a chain line instead of footrope (Figure 2). The net ropeline is attached behind the sweep chain, and several rows of weight chain are also attached to the sweep chain. The chain sweep is considered more effective in digging crabs out of the bottom than ground gear typical of most trawls. We used a two-seam flounder trawl with an 18.3-m headrope and a 24.4-m footrope, rigged with a Texas sweep of 13-mm link chain and a tickler chain. The net was attached to the trawl doors by 91-m ground cables wrapped in 5.1-cm rubber cookies. The net consisted of 14-cm stretched mesh polypropylene throughout and chafing gear on the bag. Trawls were towed for 15 min (bottom time) at 4.6–5.6 km/h, except that one tow in the Delaware Bay shipping channel was reduced to 7.5 min because of an approaching cargo ship. Data from that tow were doubled to equate catches with the standard tows.

This study was conducted in the fall to obtain information on primiparous horseshoe crabs (i.e, those which are mature but have not spawned yet). Their identification requires that horseshoe crabs have recently undergone a terminal molt, which fishers reported occurs in the late summer and fall in the Delaware Bay area. For each trawl catch, horseshoe crabs were culled out, and all or a subsample were examined, depending on the size of the catch. Examined horseshoe crabs were measured for prosomal width and identified to sex and maturity. Maturity classifications were immature, primiparous, and multiparous (those that had spawned at least once; Table 1). Large catches were subsampled for 50 large horseshoe crabs (>150 mm prosomal width) because of limited available time, but we retained all small (<150 mm), soft, and shedding horseshoe crabs. When subsampling, the catch was emptied on the deck, and the 50 large crabs were selected beginning at the port (left) side and continuing to the starboard side; any other large horseshoe crabs were counted by sex and released. The resulting characteristics of the large horseshoe crabs in the subsample were extrapolated to all large horseshoe crabs in that tow.

Table 1. Criteria used for classifying horseshoe crab gonadal maturity stage

Analysis of trawl study

A split-plot analysis of variance (ANOVA) design was used to test for factors that significantly affected horseshoe crab catches. Time of day (night, day), depth (inshore, offshore), and topography (trough, nontrough) were main effects in the model (Snedecor and Cochran 1980; Steel and Torrie 1980). For the analyses, cell within depth × topography was used as the whole-plot error term for testing the significance of the depth and topography main effects and the depth × topography interaction. The ANOVA mean square error was used to test time, time × depth, time × topography, and time × depth × topography. All interactions were retained in the model because two-factor interactions were expected and of interest, and their interpretation would be affected by a significant three-factor interaction. Catch sizes were not normally distributed, so the number of horseshoe crabs per standard tow (Y) was transformed as X = log₁₀(Y + 1) (Snedecor and Cochran 1980; Gunderson 1993). Variances among treatments remained unequal after transformation, so actual significance levels of the tests were slightly higher than the specified level of α = 0.05 (Neter et al. 1985). Analyses were conducted for all horseshoe crabs combined and separately for immature and mature (primiparous and multiparous combined) females and males.

Annual trawl survey protocol design

With the information gathered during this study, it is possible to design an annual trawl survey to target the entire horseshoe crab population available or any of the demographic components. Differences in stratum variances among the various maturity and sex categories led to different survey effort allocation schemes.

Of the possible maturity and sex categories, we focused on the two most important for the stock assessment model: (1) all horseshoe crabs combined and (2) all mature female horseshoe crabs (primiparous and multiparous). A survey designed to monitor the relative abundance of the entire horseshoe crab population could provide information on the demographic composition, including sex ratios and approximate age structure, as well as relative abundance of the components available to the trawl gear. In contrast, for stock assessment purposes the HCTC recommended focusing on the mature female horseshoe crabs, which were required as input into the modified catch survey model. We developed the protocols for both surveys using the methods described below.

The data from this study were applicable to a stratified random survey design because the main effect treatments of depth and topography were assigned to nonoverlapping cells and sampling sites were randomly and independently selected in each treatment (Cochran 1977). The survey design used the treatment combinations as strata, with equal effort allocation of 12 sampling sites randomly selected in each stratum. Day and night sampling were analyzed separately.

Horseshoe crab relative density was estimated using tow distance and approximate net width to calculate the swept area. For all but three tows, tow distances were determined from beginning and ending positions recorded using Loran C. These are minima, because wind and current effects on the vessel caused deviations from the intended straight paths. Distances for the other three tows were estimated as the simple mean distance across all tows (1,209 m) because of a malfunction in the Loran receiver. Net width was approximated as half of the mean of the headrope and footline lengths (Fridman 1986). We assumed all fishing was done only by the net. No information is available on the efficiency of the ground cables for horseshoe crabs, but we assumed that horseshoe crabs were not effectively herded by them.

In each stratum, mean relative density (crabs/km²) and variance were calculated assuming a Δ-distribution (Aitchison and Brown 1957; Pennington 1983). The Δ-distribution is applicable to skewed data that are log-normally distributed and include a portion of zero-catches (Pennington 1983; Smith 1988; Pennington 1996). Efficiency of the Δ-distribution estimators relative to the normal distribution sample estimators depends on the sample size, number of nonzero catches, variances, and magnitude of skewness (Smith 1988; Conquest et al. 1996).

Stratum and total areas were substituted for stratum and total cell numbers for determining stratum weights. Longitudinal distances (and to a minor degree latitudinal distances), and therefore cell areas, differ by latitude, so cell areas were calculated separately for each minute of latitude. The total number of cells in each stratum and the number sampled were determined for each latitude to calculate stratum and total areas. Because cell areas are not constant, stratum weights derived from areas differ slightly from stratum weights calculated from numbers of cells.

To evaluate the efficiency of the sampling design, the observed variances (with equal effort allocation in a stratified random sampling design) and estimated variances (assuming proportional and optimum effort allocation in stratified random sampling designs) were compared with variance estimates assuming a simple random sampling design (Cochran 1977:99). Optimum effort allocation as used here refers to variance-minimizing allocation, without regard to cost.

The required sample sizes for different levels of precision were determined from the estimated variances derived from target coefficients of variation (CV, defined as 100·SD/mean) assuming optimum effort allocation in a stratified random sampling design (Cochran 1977). Sample sizes were examined using a coefficient of variation of 20% as a reference level, and compared against varying values of the CV.

Separate sample size calculations were made for all horseshoe crabs and for mature females to compare sampling design efficiencies and effort allocations. These considerations may vary greatly depending on the target category of a survey.

All horseshoe crabs combined

The ANOVA for all horseshoe crabs combined indicated that depth was a significant factor in determining catch size (P < 0.01; Table 2). Topography (P < 0.01) and time of day (P < 0.01) were also significant factors, but there was a significant interaction between them (P < 0.01). Differences between day and night catches in troughs were not significant (P = 0.12), but time of day was significant in nontrough areas (P < 0.01; Table 2).

Table 2. Analysis of variance F-values for all horseshoe crabs combined, mature (primiparous and multiparous) females and males, and immature females and males. The analyses of variance used a split-plot design; depth (DEPTH : inshore versus offshore) and topography (TOPO : trough versus nontrough) were whole-plot factors and time of day (TIME : day versus night) was a split-plot factor. Some main effects are not interpretable because of interactions or absence of horseshoe crabs within treatments. Also presented are unsigned t-values of relevant tests of treatment means. Asterisks indicate significance at α = 0.05

Mature females

Mean catches of mature females were greater inshore than offshore (P < 0.01; Table 2). Topography (P < 0.01) and time of day (P < 0.01) were also significant factors but with a significant interaction (P = 0.03). Differences between day and night catches in troughs were not significant (P = 0.11), but the differences were significant in nontrough areas (P < 0.01; Table 2).

Mature males

Depth was also a significant factor affecting catch sizes of mature male horseshoe crabs (P < 0.01; Table 2). Topography (P < 0.01) and time of day (P < 0.01) were significant factors, but there was a significant time × topography interaction (P = 0.01). Time of day affected catches in nontrough areas (P < 0.01) but not in troughs (P = 0.08; Table 2).

Immature females

Immature females were captured only once in the day-offshore-nontrough treatment, limiting the interpretation of main effects and interactions. Time of day in nontrough areas, time offshore, and topography offshore were also not considered as valid comparisons. Nighttime catches were greater than daytime catches in troughs (P = 0.01) and inshore (P < 0.01; Table 2). Catches in troughs were greater inshore than offshore (P = 0.05), and topography had no significant effect on catches inshore (P = 0.25).

Immature males

Immature males were completely absent from the day-offshore-nontrough treatment, affecting the interpretation of main effects and interactions. As with immature females, time of day in nontrough areas, time offshore, and topography offshore were not considered as valid comparisons. Nighttime catches were greater than daytime catches in troughs (P < 0.01) and inshore (P < 0.01; Table 2). Catches in troughs were greater inshore than offshore (P = 0.01), and topography was not significant inshore (P = 0.63).

All horseshoe crabs combined

A stratified sampling design was more efficient for a survey of all horseshoe crabs available to the gear than a simple random design. Variances were largest assuming simple random sampling (Table 3). Proportional allocation of effort in a stratified random survey design was slightly more efficient than the simple random design. Efficiency of the equal effort allocation used in this study was intermediate between those of proportional and optimum allocations. The efficiency of the original design was lower for nighttime than for daytime sampling, but nighttime sampling produced a lower CV than day sampling (Table 3).

Table 3. Variances of the stratified mean (in thousands) and coefficients of variation (in percent) for evaluating the efficiency and precision of the sampling design for all horseshoe crabs and for mature females by day versus night sampling. Calculated variances are for equal allocation in all strata (the original sampling design; V_eq), proportional allocation (V_prop), and optimum allocation (V_opt) in stratified random survey designs and for a simple random sampling design (V_ran). The efficiencies of the various allocation schemes in stratified random sampling are determined by comparing the calculated variance against the variance for a simple random design (i.e. V_eq /V_ran)

The sample size requirement and effort allocation depended on time of day. To attain a fixed CV of 20%, nighttime sampling required 53 stations with optimum effort allocation, whereas daytime sampling required 81 stations (Table 4). Sampling effort increased dramatically for target CVs less than about 20% (Figure 3). At sample sizes less than about 25 stations, the relationship became flat, so by random error, the observed mean catch could be too imprecise to be useful. For optimum effort allocation, daytime sampling placed 54% of the stations in the inshore nontrough stratum and only 4% of the effort in the offshore nontrough stratum (Table 4). In contrast, nighttime sampling placed 31% and 44% of effort in these strata, respectively.

Table 4. Sample sizes for horseshoe crabs required to attain a coefficient of variation of 20%, assuming optimum allocation of effort in a stratified random sampling design, by demographic group. Effort allocation by stratum is presented separately for day and night surveys. Sampling fractions (in percent of total effort) are given in parentheses below stratum sample sizes. Stratum weights in percent are presented for comparison. Strata are as follows: I–NT = inshore, nontrough, I–TR = inshore, trough, O–NT = offshore, nontrough, and O–TR = offshore, trough; SUM is the total number of samples

Mature females

The pattern of sampling design efficiency for mature female horseshoe crabs was similar to that for all horseshoe crabs. Sample variances were largest assuming simple random sampling (Table 3). Proportional allocation of effort in a stratified random survey design was more efficient than a simple random design. Efficiency of the equal effort allocation used in this study was intermediate between efficiencies of proportional and optimum effort allocation. As observed for all horseshoe crabs, the efficiency of the original design was lower for nighttime than for daytime sampling, but precision was greater at night.

The sample size requirements for mature females were smaller than for all horseshoe crabs combined. To attain a CV of 20%, nighttime sampling required 38 stations with optimum allocation of effort, whereas daytime sampling required 57 stations (Figure 3; Table 4). Compared with the effort allocation for all horseshoe crabs, both daytime and nighttime sampling for mature females placed less effort in the inshore nontrough stratum and more effort in the inshore trough stratum (Table 4). However, the relative orders were similar.

In all except the inshore-trough stratum, the sampling effort by stratum was greater for all horseshoe crabs than for only mature females for the same level of precision. Therefore, the sampling effort for a survey designed to sample all horseshoe crabs with a CV of 20% would be more precise for the mature female component, even though effort allocation would deviate from optimal.