Each spring horseshoe crabs (Limulus polyphemus L.) emerge from Delaware Bay to spawn and deposit their eggs on the foreshore of sandy beaches (Shuster and Botton, 1985; Smith et al., 2002a). From mid-May to early June, migratory

shorebirds stopover in Delaware Bay and forage heavily on horseshoe crab eggs that have been transported up onto the beach (Botton et al., 1994; Burger et al., 1997; Tsipoura and Burger, 1999). Thus, estimating the quantity of horseshoe crab eggs in Delaware Bay beaches can be useful

for monitoring spawning activity and assessing the amount of forage available to migratory shorebirds

Botton, Mark L.

Loveland, Robert E.

Michels, Stewart F.

Pooler, Penelope S.

Smith, David R.

Aquatic Commons

698
Each spring horseshoe crabs (Limulus 
polyphemus L.) emerge from Delaware 
Bay to spawn and deposit their eggs on 
the foreshore of sandy beaches (Shuster 
and Botton, 1985; Smith et al., 2002a). 
From mid-May to early June, migra-
tory shorebirds stopover in Delaware 
Bay and forage heavily on horseshoe 
crab eggs that have been transported 
up onto the beach (Botton et al., 1994; 
Burger et al., 1997; Tsipoura and 
Burger, 1999). Thus, estimating the 
quantity of horseshoe crab eggs in 
Delaware Bay beaches can be useful 
for monitoring spawning activity and 
assessing the amount of forage avail-
able to migratory shorebirds. 
We evaluated procedures to estimate 
horseshoe crab egg density by asking 
three questions that address sampling 
at a different spatial scale. 1) How 
many samples of sediment are needed 
Assessment of sampling methods to estimate 
horseshoe crab (Limulus polyphemus L.) 
egg density in Delaware Bay
Penelope S. Pooler
David R. Smith
U.S. Geological Survey 
Leetown Science Center
11700 Leetown Road
Kearneysville, West Virginia 25430
E-mail address (for D. R. Smith, contact author): david_r_smith@usgs.gov
Robert E. Loveland
Department of Ecology and Evolution
Cook College
Rutgers University
New Brunswick, New Jersey 08901
Mark L. Botton
Fordham University
113 West 60th Street 
New York, New York 10023
Stewart F. Michels 
Delaware Division of Fish and Wildlife
P.O. Box 330 
Little Creek, Delaware 19961
Manuscript approved for publication 
12 February 2003 by Scientifi c Editor.
Manuscript received 4 April 2003 at NMFS 
Scientifi c Publications Offi ce.
Fish Bull. 101:698–703 (2003).
for precise estimation of egg density 
within a segment of beach? 2) Does egg 
density within a segment of beach ad-
equately represent egg density across 
a larger stretch of beach? 3) How many 
beach segments should be sampled 
to monitor bay-wide egg density? We 
chose these three questions because 
the objective of egg studies might focus 
on any of these scales. We ask the fi rst 
question to determine the sampling 
effort necessary to detect changes in 
egg density over time within a specifi c 
beach segment. The second question 
allows us to examine the reliability of 
using egg density in a beach segment to 
infer egg density over a larger stretch 
of beach. The third question deals with 
the level of precision in estimates of 
bay-wide egg density and how many 
beaches must be sampled to detect 
bay-wide declines in density over time. 
Understanding the reliability of egg 
density estimates at multiple scales 
will help develop effective monitoring 
programs.
We addressed all three questions 
with respect to eggs found in both 
shallow (0–5 cm) and deep (0–20 cm) 
sediments. Horseshoe crabs are gener-
ally thought to lay most of their eggs at 
a depth of 15–20 cm (Brockmann, 1990; 
Botton et al., 1994). Through processes 
of bioturbation and wave-generated 
sediment activation, horseshoe crab 
eggs are brought onto the beach and 
made available to foraging shorebirds 
(Botton et al., 1994; Kraeuter and Feg-
ley, 1994; Jackson et al., 2002). 
Materials and methods
During May and June 1999, we col-
lected sediment on 16 beaches in 
Delaware Bay (Fig. 1), eight along the 
eastern shore (New Jersey) and eight 
along the western shore (Delaware), to 
estimate egg density. Methods used to 
collect sediment and extract horseshoe 
crab eggs are summarized in the pres-
ent study, but are presented in detail 
in Smith et al. (2002b). Beach sediment 
was collected in cores (5 cm diameter) 
within a 3-m wide strip along a 100-m 
segment of beach. Each 3-m wide strip 
was centered on the mid-beach eleva-
tion where a majority of horseshoe 
crab nests occur (Botton et al., 1988). 
The mid-beach elevation is halfway 
between the spring high water level 
and the beach break at the low tide ter-
race. Within each egg-sampling strip, 
40 locations were selected randomly for 
sediment collection. At each location, a 
pair of core samples was taken: one to a 
depth of 5 cm and the other to a depth 
of 20 cm. We sampled eggs on 25–26 
May and 14–15 June 1999, which fol-
lowed the heaviest spawning activity 
in Delaware Bay that year (Smith et 
al., 2002a). We mixed the entire core 
contents thoroughly and then removed 
80-mL aliquots. We ran the aliquots 
699NOTE Pooler et al.: Assessment of sampling methods to estimate egg density of Limulus polyphemus
through a 1-mm sieve to separate eggs and larvae from 
ambient sediments and then counted eggs (dead or live) 
and larvae in each aliquot. Depth of aerobic sand varied; 
thus we measured core volume prior to extrapolating egg 
counts to totals per core and then estimated the total den-
sity of eggs and larvae. The larvae comprised a small frac-
tion of total eggs and larvae, and for the purposes of this 
paper we evaluated the sampling of eggs only.
Question 1: How many sediment cores should be 
sampled per beach segment?
We addressed this question in two steps. First, we deter-
mined the precision of egg-density estimates as a function 
of egg density and sample size. Second, we translated the 
precision of the estimates into statistical power to detect 
change in egg density over time. For simplicity, variance 
of the egg-density estimate was calculated from a random 
sample from an infi nite population. Coeffi cient of variation 
(CV) was calculated as
�� � � �� ���� � � �
where var(y) = variance of eggs among cores; and 
� = egg density. 
We modeled the relationship between egg density and 
variance among cores (i.e. var[y]=f [ � ] to predict coeffi cient 
of variation (CV) for different sample sizes and across 
the observed range of egg densities (i.e. �� � � � �� � � � ). 
Using predicted CVs, we estimated the probability of de-
tecting a change in egg density over time. The probability 
of detecting decline (i.e. statistical power) was calculated by 
using a one-tailed t-test with a type-I error rate of 0.2 and a 
constant rate of annual change for CVs = {0.1, 0.2, 0.3, 0.4} 
with the software program TRENDS (Gerrodette, 1993).
Question 2: Is egg density within a beach segment 
representative of egg densities along a larger 
stretch of beach?
Smith et al. (2002b) modeled the relationship between 
counts of spawning females and egg densities within beach 
segments. Spawning females are counted annually as part of 
a bay-wide survey of spawning activity (Smith et al., 2002a), 
and in 1999, egg sampling was conducted on some of the 
same beaches as the spawning survey (Smith et al., 2002b). 
For eggs that were sampled in May 1999 on six New Jersey 
beaches, the relationship was fairly strong, linear, and pre-
dictive (r2=0.62; Smith et al., 2002b). Although we sampled 
for eggs on only one 100-m segment of beach, we used the 
above relationship to predict egg densities for all 100-m 
segments along the beach where spawning females were 
counted. We limited the predictions to the six New Jersey 
beaches where we felt the relationship between spawning 
females and egg densities was suffi ciently strong (Smith 
et al., 2002b). We compared egg density in the observed 
100-m segment to the distribution of densities predicted in 
all 100-m segments on the beach. If the observed density 
was within the interquartile range of the distribution of 
predicted densities, we concluded that the 100-m segment 
was representative of the larger stretch of beach.
Question 3: How many beaches should be sampled? 
Using the observed variation in egg density among the 16 
beaches sampled in 1999, we predicted the CV for bay-wide 
egg density estimates as a function of the number of   beaches 
sampled and under a stratifi ed sampling design where the 
two strata were New Jersey and Delaware. We could not 
evaluate CV across a range of bay-wide densities because 
the 1999 results provided only one datum point, and we 
expected variation among beaches to be a function of egg 
Figure 1
Delaware Bay beaches (•) where horseshoe crab eggs were sampled 
in May and June 1999.
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
DELAWARE
Broadkill
Prime Hook
Fowler
Slaughter
Big Stone
North Bowers
Kitts Hummock
W oodland NEW  JERSEY
North
Cape May
South Cape
Shore Lab
Highs
Kimbles
Reeds
Fortescue
Sea Breeze
Raybins
39°00' 39°00'
75°30'
75°30'
75°00'
75°00'
10 0 10 20 Kilometers
N
EW
S
700 Fishery Bulletin 101(3)
Table 1
Mean eggs per core and standard errors (SE) for horseshoe crabs (Limulus polyphemus) at 16 beaches sampled in Delaware Bay 
that were sampled in May and June 1999. Cores were 5 cm in diameter. At 40 random locations on each beach, a pair of sediment 
cores were sampled: one core at 5 cm depth (shallow sediment) and another at 20 cm depth (deep sediment).
No. of eggs per core on 25–26 May 1999 No. of eggs per core on 14–15 June 1999
  Shallow  Deep  Shallow  Deep
State Beach sediment SE sediment SE sediment SE sediment SE
Delaware Broadkill 0.0 0.00 1.5 1.47 1.2 0.36 101.7 60.42
Prime Hook 0.2 0.08 81.9 76.17 7.4 2.06 223.9 112.14
Fowler 0.1 0.05 1.8 0.65 2.7 1.22 211.3 116.56
Slaughter 11.7 2.69 814.8 186.04 41.7 5.35 664.5 97.81
Big Stone 0.1 0.05 11.3 5.09 0.7 0.53 24.2 14.27
North Bowers 23.0 6.49 950.3 234.18 105.1 23.54 400.4 70.81
Kitts Hummock 26.4 8.23 325.1 78.63 15.2 5.49 124.8 43.94
Woodland 0.5 0.17 0.1 0.06 7.0 3.68 60.9 29.75
New Jersey North Cape May 0.3 0.25 0.0 0.00 0.5 0.33 0.7 0.37
South Cape Shore Lab. 25.5 0.86 1085.4 140.29 4.5 0.81 1399.2 144.03
Highs 2.1 0.71 1128.6 96.99 4.4 0.94 1456.8 173.80
Kimbles 9.7 4.80 1561.3 286.32 1.7 0.55 1008.0 105.63
Reeds 2.0 0.52 540.4 79.90 18.2 2.52 468.0 62.67
Raybins 3.5 1.91 65.8 43.88 0.1 0.06 6.7 4.57
Fortescue 2.0 0.43 645.9 108.71 20.6 3.85 465.7 193.64
Sea Breeze 27.5 7.95 347.3 94.70 0.2 0.09 3.1 2.01
density. However, we examined the probability of detecting 
a percentage change in bay-wide egg density over time as a 
function of the number of beaches sampled by using the 1999 
bay-wide egg density as the initial value in the time series.
Results
When the objective is to monitor egg density within a seg-
ment of beach, a sample size of 40 sediment cores is suf-
fi cient for detecting substantial changes in egg density in 
the top 20 cm of sediment, but >40 cores would be needed to 
monitor egg density in the top 5 cm of sediment. Distribu-
tions of egg densities were skewed right with median densi-
ties of 3 and 275 eggs per core for shallow and deep cores, 
respectively (Table 1). A sample size of 40 cores resulted in 
a CV of 0.26 for a median density of eggs 0–20 cm deep (Fig. 
2B). In contrast, about 100 cores would need to be sampled 
to bring the CV down to 0.3 when sampling shallow sedi-
ment and when egg density was at the median (Fig. 2A). A 
CV of 0.3 corresponds to a 75% chance of detecting a 50% 
decline in egg density over 5 years (Fig. 3A) and an 80% 
chance of detecting a 40% decline over 10 years (Fig. 3B). 
A sample size of 60 shallow cores would result in CV of 0.4 
for median egg density (Fig. 2A), which would be suffi cient 
for monitoring over 10 years, but not over 5 years. A CV 
of 0.4 would lead to a better than 85% chance of detecting 
a 50% decline in density over 10 years (Fig. 3B). Precision 
and power would improve when sampling higher densities 
of eggs (Fig. 2).
At most beaches, observed egg densities within a 100-m 
segment of beach were not representative of egg densities 
throughout a larger beach. On only two of the six New Jer-
sey beaches examined (South Cape Shore Lab and Reeds) 
did the observed egg density fall within the interquartile 
range of beach-wide densities (Fig. 4). On three beaches 
the observed egg density was greater than all predicted 
densities, and on one beach observed egg density was less 
than all predicted densities. 
With egg density at the 1999 level and sampling at 16 
beaches (i.e. eight beaches per state) distributed throughout 
the bay, the CV for densities of eggs in 0–20 cm of sediment 
was 0.26 in May and 0.29 in June (Fig. 5). For densities of 
shallow eggs, the CV was 0.33 for egg densities in May and 
0.43 in June. Variability in egg densities among beaches was 
greater for sampling in June 1999 than in May 1999. 
Discussion
Eggs in shallow sediment (0–5 cm) consistently yielded 
lower densities and higher variability than eggs in deep 
sediment (0–20 cm). A sample size of 40 sediment cores was 
suffi cient for estimating and monitoring density of eggs 
0–20 cm deep within a 100-m beach segment. However, a 
larger sample size (≥60 sediment cores) would be needed 
for estimating and monitoring density of eggs 0–5 cm deep 
within a segment of beach. 
Because egg density in a 100-m segment of beach is not 
necessarily representative of the larger surrounding beach, 
701NOTE Pooler et al.: Assessment of sampling methods to estimate egg density of Limulus polyphemus
Figure 2
The relationship between density and coeffi cient of variation (CV) for (A) shallow 
sediment (0–5 cm) and (B) deep sediment (0–20 cm). Curves in each fi gure depend 
on sample size: circle is n = 20, triangle is n = 40, square is n = 60, diamond is 
n = 80, and × is n = 100. Vertical lines represent median egg densities that we 
observed in 1999. 
0 20 40 60 80 100
0.0
0.2
0.4
0.6
0 500 1000 1500
n = 20
n = 40
n = 60
n = 80
n = 100
Density of eggs per core
P
re
di
ct
ed
 c
oe
ffi 
ci
en
t o
f v
ar
ia
tio
n
it is important to realize that if sampling is restricted to 
a short segment of beach, then the scope of inference is 
strictly limited to that segment. If a reliable estimate of 
egg density along a beach is required, then it will be nec-
essary to take samples along the entire beach. Because of 
the logistics of sampling sediment it would be diffi cult to 
sample throughout a long stretch of beach in one stage of 
sampling. However, a two-stage sampling design could be 
considered in which beach segments are selected at the 1st
stage and sediment cores within segments are selected at 
the 2nd stage. 
Consistent with our fi ndings on sampling within a beach, 
bay-wide egg density can be more precisely estimated for 
eggs 0–20 cm deep than for eggs 0–5 cm deep. A stratifi ed 
A B
0.3 0.4 0.5
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.3 0.4 0.5
CV = 0.1
CV = 0.2
CV = 0.3
CV = 0.4
Rate of decline over fi ve years
P
ro
ba
bi
lit
y 
of
 d
et
ec
tin
g 
de
cl
in
e
Figure 3
Probability of detecting a decline (i.e. statistical power) for various magnitudes 
of decline and for annual surveys over fi ve (A) and 10 (B) years. Statistical power 
was calculated for a one-tailed t-test with a type-I error rate of 0.2, and a constant 
annual rate of change. 
Rate of decline over ten years
A B
702 Fishery Bulletin 101(3)
Figure 5
Predicted coeffi cient of variation (CV) shown for the pos-
sible range of number of beaches sampled per state. This 
fi gure is based on the observed levels of bay-wide density 
during the two sampling periods in 1999. Curves are based 
on egg densities found at different depths and time periods: 
triangle is shallow sediment in June, circle is shallow sedi-
ment in May, diamond is deep sediment in June, and square 
is deep sediment in May. Shallow sediment is 0 to 5 cm deep, 
and deep sediment is 0 to 20 cm deep.
5 7 10 12 15 17 20 22
0.1
0.2
0.3
0.4
0.5
Number of beaches sampled per state
P
re
di
ct
ed
 c
oe
ffi 
ci
en
t o
f v
ar
ia
tio
n
random sample of eight beach segments per state would 
result in CV ≤0.3 for estimates of egg densities 0–20 cm 
deep. If this level of effort were maintained, it would be 
suffi cient to detect biologically signifi cant declines in egg 
density over a 5- or 10-year period. However, greater effort 
would be required to monitor change in egg densities 0–5 
cm deep. According to results from the May samples, to 
estimate egg densities in shallow sediment with CV ≤0.3, 
a stratifi ed random sample of 10 segments per state would 
be required. 
Sampling eggs is a costly process; therefore sampling 
effi ciency and reducing sample size are important consider-
ations. Although sediment can be collected quickly, the pro-
cess of extracting and enumerating eggs from the sediment 
can be time consuming. Quantifying the eggs in surface 
sediments to assess shorebird forage biomass is likely to be 
the main objective of many egg sampling studies because 
horseshoe crab spawning activity can be assessed by other 
methods, such as through counts of spawning horseshoe 
crabs (Smith et al., 2002a). However, a primary fi nding 
in the present study is that estimating eggs in 0–5 cm 
of sediment will be more costly than estimating eggs in 
0–20 cm of sediment. In the future, alternatives in survey 
design, such as stratifi cation of the beach foreshore, should 
be considered to reduce the amount of sediment that needs 
to be collected for precise estimates of horseshoe crab egg 
density.
Acknowledgments
This work was funded through the USGS/State Partner-
ship Project (no. 99HQAG0050). Additional funding was 
provided through the New Jersey Endangered & Nongame 
Species Program.
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1988. Beach erosion and geochemical factors: infl uence on 
spawning success of horseshoe crabs (Limulus polyphemus) 
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Bay, and its relationship to beach characteristics and 
abundance of horseshoe crab (Limulus polyphemus) eggs. 
Auk 111:605–616.
Brockmann, H. J. 
1990. Mating behavior of horseshoe crabs, Limulus 
polyphemus. Behaviour 114:206–220.
Burger, J., L. Niles, and K. E. Clark. 
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migrant shorebirds on Delaware Bay. Biol. Conserv. 79:
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Figure 4
Density curves of predicted egg densities on 100-m beach 
segments at six New Jersey beaches. An arrow represents 
the egg density in the observed 100-m segment. These 
density curves were generated by dividing the area sur-
veyed for spawning females into 100-m segments and 
using the observed relationship between egg densities 
and spawning females to predict egg density for each seg-
ment. The beaches shown are (A) Fortescue, (B) Highs, 
(C) Kimbles, (D) North Cape May, (E) Reeds, and (F) South 
Cape Shore Laboratory. 
0 15000 30000 45000 60000 0 15000 30000 45000 60000
Predicted density of egg cores
A B
C D
E F
703NOTE Pooler et al.: Assessment of sampling methods to estimate egg density of Limulus polyphemus
Gerrodette, T. 
1993. TRENDS: software for a power analysis of linear 
regression. Wildl. Soc. Bull. 21:515–516.
Jackson, N. L., K. F. Nordstrom, and D. R. Smith. 
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estuaries. J. Coast. Res. 36:414–424.
Kraeuter, J. N., and S. R. Fegley.
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(Limulus polyphemus) during their spawning season. Es-
tuaries 17:288–294.
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crabs, Limulus polyphemus (L.), in Delaware Bay. Estu-
aries 4:363–372. 
Smith, D. R., P. S. Pooler, B. L. Swan, S. F. Michels, W. R. Hall, 
P. J. Himchak, and M. J. Millard. 
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(Limulus polyphemus) spawning in Delaware Bay: implica-
tions for monitoring. Estuaries 25:115–125.
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Tsipoura, N., and J. Burger. 
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Assessment of sampling methods to estimate horseshoe crab (Limulus polyphemus L.) egg density in Delaware Bay

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Assessment of sampling methods to estimate horseshoe crab (Limulus polyphemus L.) egg density in Delaware Bay

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