Smith et al Abundance of Limulus polyphemus in Delaware Bay 



459 



We limited mark-recapture estimates to males be- 

 cause capture probability was not equal for males and 

 females as evidenced by recapture rates. Ratios of males 

 and females captured for the tagging study were used 

 to estimate total abundance with the equation 



estimate harvest rate. To put bounds on the problem, 

 we calculated harvest rate 1) using landings from New 

 Jersey and Delaware and 2) using landings from the 

 Delaware Bay regional states (New Jersey, Delaware, 

 Virginia, and Maryland). 



N=N,JR„^, 



where iV„,= abundance of males; and 



i?„, = the ratio of males to the total captured. 



Abundance of females was estimated by subtraction, 

 i.e., by Nf=N-N,„. 



We used patterns of recaptures among preseason re- 

 leases (released from 26 March to 8 May 2003) versus 

 prepeak releases (released from 28 to 30 May 2003) to 

 test the assumption that tagging did not affect spawn- 

 ing behavior. One approach was to use a contingency 

 table analysis that included a comparison of risks of 

 recapture between animals tagged during preseason 

 and prepeak periods. Another approach was based on 

 the extended likelihood presented above (Z>, ), which 

 included a separate set of recapture probabilities for 

 preseason and prepeak released animals. In this way, 

 the model allowed for a temporary effect on capture 

 probability due to tagging, such as a temporary delay 

 in spawning. We used model comparison techniques 

 (i.e., Akaikes information criteria and likelihood ratio 

 tests) to compare recapture probabilities among pre- 

 season and prepeak released animals (Burnham and 

 Anderson, 1998). 



Results from a telemetry study conducted in 2004 

 provided information on spawning behavior of horseshoe 

 crabs caught and released from boats. In 2004, we at- 

 tached radio transmitters to 60 adult males throughout 

 the Delaware Bay prior to the spawning season. When 

 the animals came on the beach to spawn the signals 

 from the transmitters were recognized by one or more 

 of the 14 fixed station receivers that were arrayed along 

 the shoreline of the bay. In this article, we report the 

 relocation rates (proportion of radio-tagged crabs that 

 were recognized by at least one receiver) from that 

 study because of their relevance to the assumption that 

 tagging does not affect spawning behavior. 



An important application of abundance estimates 

 is in the calculation of harvest rates. We calculated 

 harvest rates by dividing estimated abundance into 

 1) reported landings and 2) projected landings (based 

 on recent regulations). The population that spawns in 

 Delaware Bay disperses widely, some leaving the bay for 

 the ocean. Calculations of harvest rate need to account 

 for these migration patterns because landings from 

 New Jersey and Delaware do not include landings of 

 Delaware Bay spawning animals that were harvested 

 in neighboring states (Virginia and Maryland). How- 

 ever, landings from neighboring states include animals 

 that spawn in embayments other than Delaware Bay. 

 Thus, use of landings from Delaware Bay states alone 

 could underestimate harvest rate and use of landings 

 from Delaware Bay and neighboring states could over- 



Results 



A total of 5398 males and 1823 females were tagged 

 during the preseason period (26 March to 8 May 2003), 

 and 7091 males and 3231 females were tagged during the 

 prepeak period (28 to 30 May 2003; Table 1). Animals that 

 were injured during capture were culled and not tagged. 

 Culling rates were 0.19 during the preseason period, 0.05 

 during the prepeak period, and 0.12 overall. 



During the spawning survey 22,051 males and 6675 

 females were counted in quadrats and examined for 

 tags. Forty-eight tagged animals were recaptured dur- 

 ing the spawning season surveys conducted 29 May, 31 

 May, and 2 June 2003. Nineteen of the recaptures were 

 within quadrats, and 29 were between quadrats. Only 

 three of the recaptured tags were from females. This 

 number is not surprising; tags are difficult to detect 

 on females because the females remain buried during 

 spawning. The between-quadrat recaptures were not 

 used in the estimation because we did not have a cor- 

 responding count of unmarked animals. 



Using the Petersen estimator and all releases, we 

 estimated that there were approximately 14.5 million 

 (SE = 3.2 million) adult male horseshoe crabs in Dela- 

 ware Bay during peak spawning at the end of May 

 2003. Using just the prepeak releases, we estimated 13 

 million adult males (SE = 3.6 million). 



Model comparisons indicated that recapture prob- 

 abilities were time-specific, but the temporary effect on 

 recapture probabilities was not supported by the data 

 (Table 2). The maximum likelihood estimate of male 

 abundance with model 2 (Table 2) was 16.1 million 

 (90% CI: 9.9 to 22.3 million). The difference between 

 the Petersen estimate and the maximum likelihood 

 estimate could have been due to model 2 that allowed 

 for time-specific recapture probabilities, whereas the 

 Petersen estimator did not. The maximum likelihood 

 estimate based on constant recapture probabilities (i.e., 

 model 1 in Table 2), matched the Petersen estimate 

 (14.7 million for model 1 and 14.5 million for the Pe- 

 tersen estimate). 



Sex ratios were different for the preseason and pre- 

 peak spawning periods in a pattern consistent with a 

 sex-specific migration schedule. There was a smaller 

 proportion of adult females in the bay during the pre- 

 season period (0.25) than when spawning activity was 

 near its peak (0.31), which is consistent with the known 

 observation that males migrate earlier than females. 

 Sex ratios observed during the prepeak period were 

 used to estimate abundance in the bay during the peak 

 spawning period. 



The assumption of equal catchability of tagged and 

 untagged animals is an important assumption that af- 



