Davis et al Population assessment of Limulus polyphemus 



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3.00 



200 



1.00 



00 



rn -100 



-2 00 



MD coastal bays 



DE 16-tt trawl, 

 <160-mm crabs 



DE 16-ft YOY 



DE 30-ft trawl 



NJ ocean 



NMFS spring 



NMFSfall 



DB spawning 



1 1 1 1 r 



1991 1993 1995 



1997 

 Year 



1999 



2001 



2003 



Figure 1 



Fishery-independent survey indices for the Delaware Bay (DBi region from 1991 through 

 2003, standardized by survey for comparison. MD = Maryland; DE = Delaware: NJ = 

 New Jersey; DB = Delaware Bay. 



where /• = the stock's intrinsic growth rate; 



K = the carrying capacity, both of which are 

 assumed to be constant (Prager, 19941; 

 and 



F, and B, = Fishing mortality and biomass, respec- 

 tively, at time t. 



In addition, the harvest was not assumed to equal sur- 

 plus production (i.e., the model was a dynamic or non- 

 equilibrium model; Quinn and Deriso, 1999). This model 

 assumes B^jy = 0.5K, where By^jy is the spawning 

 biomass that would produce MSY. This form is often 

 used because of its theoretical simplicity and because 

 it is central among possible production model shapes. 

 This production model was conditioned on catch, mean- 

 ing that landings data were assumed to be more precise 

 than abundance indices. By assuming that abundance 

 indices are correlated measures of population abun- 

 dance, the model is able to incorporate multiple indices 

 by interpreting differences among indices as sampling 

 error. To fit the production model, we used the ASPIC 

 software (vers. 5.02) of Prager (1994), a program that 

 has been used extensively in stock assessments (Cadrin 

 and Hatfield, 2002; MacCall, 2002). We included data 

 from fishery-independent and fishery-dependent sources 

 in model runs. 



Abundance indices 



In the Delaware Bay region, there are a number of fish- 

 ery-independent surveys that collect data on horseshoe 



crabs (Fig. 1). These include National Marine Fisheries 

 Service (NMFS) trawl (spring, 1968-2003, and fall, 

 1963-2002), New Jersey (NJ) ocean trawl (1989-2002), 

 Maryland (MD) coastal bays trawl (1988-2002), Dela- 

 ware (DE) 16-ft trawl (juvenile and young-of-the-year; 

 1992-2002), DE 30-ft trawl (1990-2002), and Delaware 

 Bay spawning survey (1999-2003). Detailed descriptions 

 of these surveys can be found in ASMFC.^ We selected 

 1991-2003 as the modeling timeframe because both 

 harvest data and abundance index data were available 

 for this period. 



In spite of the large number of surveys and long time 

 series for some of these surveys, many had high vari- 

 ability and low power to detect a decline. Additionally, 

 many of these surveys were negatively correlated with 

 each other for the years investigated (Table 1). Be- 

 cause an underlying assumption for the model is that 

 each survey is representative of the population being 

 evaluated, total disagreement (i.e., negative correla- 

 tion) among any pair of surveys cannot be reconciled 

 by the model, resulting in model errors. We therefore 

 used three subsets of fishery-independent surveys in 

 which all pairs were positively correlated for popula- 

 tion modeling (Table 2), incorporating six of the eight 

 fishery-independent surveys into production model runs. 

 Fishery-dependent data were also available from 1991 

 to 2002 from the Delaware hand and dredge fisheries. 

 Abundance indices based on catch-per-unit-of-effort 

 (CPUE) for these fisheries were calculated from the 

 annual number of trips and landings for each fishery 

 (Fig. 2). 



Within the models, abundance indices were weighted 

 by the inverse of the coefficient of variation (CV) from 

 regressions, which gave more weight to surveys with less 

 variability. For comparison, we also conducted model 



