458 



Fishery Bulletin 104(3) 



Fig. 1). The design of the spawning survey is described 

 in Smith et al. (2002). 



Mark-recapture methods 



We took two approaches to estimate abundance. The 

 first was an application of Chapman's modification of the 

 Petersen estimator (Borchers et al., 2002). We applied 

 the Petersen estimator separately for each of the two 

 release periods and the three spawning survey dates. 

 In addition, we combined the releases and recaptures 

 for a pooled Petersen estimate. 



The second approach was based on an extension of a 

 likelihood presented by Borchers et al. (2002; p. 118, 

 Eq. 6.11). We extended the likelihood to allow for a 

 temporary effect on spawning behavior due to the cap- 

 ture and tagging process by including separate recap- 

 ture probabilities for each release cohort. The extended 

 likelihood was 



Ls=i^]^"]p:-ii-Ps^''-''--"' 



( M \ 



Mos 



(plf'^a-pl)'^''-'"^- 



where N = the abundance at the start of the recap- 



ture period at the end of May 2003; 

 M,^ = the number of preseason tagged animals 



at large at time s\ 

 M.,^ = the number of prepeak tagged animals 

 at large at time s (M.^=Mj^+M.,J; 

 irij^ and m.,^ = the recaptures of preseason and prepeak 

 tagged animals at time s; 

 u^ = the survey count of untagged at time s; 

 p, = the capture probability for untagged 

 and preseason tagged animals at time 

 s; and 

 Pj* = the capture probability of prepeak tagged 

 animals at time s. 



We also fitted a likelihood that set all recapture prob- 

 abilities to be constant through time, i.e., p^ = p for all 

 recapture surveys, which reduces to Borchers' original 

 likelihood (Borchers et al., 2002: p. 118, Eq. 6.11). 



We used maximum likelihood methods to estimate 

 abundance A^ and recapture probabilities {p^.pj. We 

 used the Petersen estimate for the initial value for 

 N and used mJM^ as the initial value for recapture 

 probabilities. Profile-likelihood intervals were calcu- 

 lated for the abundance estimates (Borchers et al., 

 2002). MathCad (vers. 12, Mathsoft Engineering and 

 Education Inc., Cambridge, MA) and SAS (vers. 9, 

 SAS Institute Inc., Gary, NO were used to find nu- 

 merical solutions to the likelihood and profile-likelihood 

 equations. 



The following assumptions underlie the mark-recap- 

 ture methods that we applied (Borchers et al., 2002): 



1 No emigration or mortality occurred during the 

 period between release and recapture; 



2 the tagged animals represented an adequate 

 sample; 



3 animals were captured independently of one another; 



4 tags were not lost or overlooked; and 



5 recapture probability depended only on recapture 

 occasion, was equal among animals of the same sex, 

 and was equal for tagged and untagged animals. 



The study was designed through the timing and dis- 

 tribution of releases and recaptures to meet the first 

 two assumptions. The prepeak releases and recaptures 

 were designed to be close in time to meet the assump- 

 tions of no emigration and no mortality. Immigration 

 occurred during the time between preseason release 

 and recapture; therefore we estimated the number 

 of adults in Delaware Bay at the time of recapture, 

 which was at the end of May in 2003 (Skalski and 

 Robson, 1992). Some mortality occurred during the 

 time between preseason release and recapture that 

 we were not able to account for; however, we expect 

 that mortality was similar for tagged and untagged 

 animals. We ensured that both initial capture and 

 recaptures were spatially distributed by distribut- 

 ing the releases throughout Delaware Bay during 

 preseason tagging and within strata during prepeak 

 tagging effort (Fig. 1) and by distributing recapture 

 effort systematically by means of the spawning survey 

 (Smith et al., 2002). The third assumption could be 

 violated if horseshoe crabs moved locally in groups. 

 However, recaptures came from widely spaced quad- 

 rats, so that even if the animals moved in groups, 

 the whole group was unlikely to be recaptured within 

 single quadrats. Although tag loss could be a sig- 

 nificant factor over an extended period, we did not 

 believe that significant tag loss occurred, especially 

 over the five days from prepeak release to recapture 

 period (28 May to 2 June 2003). In a tag-loss study 

 conducted at the United States Geological Survey 

 Leetown Science Center with identical tags, no tag 

 loss over ^60 days was reported, indicating that tag 

 loss between preseason and recapture periods would 

 not have been significant (Crawford'^). Tags could have 

 been overlooked during the spawning survey. Females 

 bury themselves in beach sediment during spawning, 

 and their tags could have been readily overlooked. 

 In contrast, males do not bury themselves and the 

 4.4 cm white button tag is highly visible in daylight 

 or when illuminated by flashlight. Nevertheless, tags 

 on males could have been obscured when the horse- 

 shoe crabs piled up during peak spawning. Thus, 

 we restricted our mark-recapture analysis to male 

 horseshoe crabs that were counted and recaptured 

 within 1-m- quadrats when surveyors were focusing 

 on a small area. 



3 Crawford, E. 2003. Unpubl. data. USGS-Leetown Science 

 Center, 11649 Leetown Road, Kearneysville, WV 25430 



