NOTE Pooler et al.: Assessment of sampling methods to estimate egg density of Limulus polyphemus 



699 



Figure 1 



Delaware Bay beaches ( • ) where horseshoe crab eggs were sampled 

 in May £ind June 1999. 



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 infinite population. Coefficient of variation 

 (CV) was calculated as 



CV = Vvar(.v)/H/y, 



where var(jy) = variance of eggs among cores; and 

 y = egg density. 



We modeled the relationship between egg density and 

 variance among cores (i.e. var[y]=/'[ y] to predict coefficient 

 of variation (CV) for different sample sizes and across 

 the observed range of egg densities (i.e. CV = ■]f\y\l n jy). 

 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 ^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 (Gterrodette, 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 (/•2=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 sufficiently 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 stratified sampling design where the 

 two strata were New Jersey smd 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 



