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Fishery Bulletin 103(2) 



to provide more precise biomass estimates, as well as 

 a quantification of their variances (Simard et al., 1992; 

 Bailey and Gatrell, 1995; Guan et al., 1999). 



The objective of our study is to investigate the spatial 

 trends in green sea urchin density using spatial analy- 

 sis techniques to estimate stock biomass. In doing so, 

 we address the suitability of second-order methods to 

 analyze a fishery with a target species that is highly 

 spatially variable over a large, complex study area. We 

 compare biomass estimates from several techniques to 

 address the suitability of TINs for biomass estimation 

 in the green sea urchin fishery. 



Materials and methods 



Data collection and processing 



Sea urchin density and size-frequency information were 

 obtained from the 2001 pilot study for the State's annual 

 fishery-independent survey. The Department of Marine 

 Resources conducted the survey in June and early July, 

 after the fishing season had ended. The survey was 

 restricted to rock and gravel habitats along the Maine 

 coast and we used two modes of data collection, divers 

 and video. In the first part of the study, divers sampled 

 144 sites according to a stratified random sampling 

 design. The design consisted of 16 sites in each of 9 

 survey strata, where the width of a survey stratum was 

 inversely proportional to the commercial landings in the 

 region. At each site, SCUBA divers randomly sampled 

 .30 quadrats (1 m 2 each) along three parallel linear 

 transects set perpendicular to shore, for a total of 90 

 quadrats per site. The sampling intensity was divided 

 equally among three depth zones: 0-5 m, 5-10 m, and 

 10-15 m. At each site, size-frequency data were obtained 

 by randomly subsampling one quadrat in each depth 

 zone, in which test diameters were measured for all 

 individuals in the quadrat. An additional 148 sites were 

 sampled, in a 15-40 m depth zone, with a video camera 

 that recorded 10 quadrats (0.5 m 2 each) at each site. 

 Because of the low sea urchin densities at these sites, 

 test diameters were measured for all recorded speci- 

 mens. Mean sea urchin density values were calculated 

 for each site (rc=292) and for each depth zone within a 

 site (« = 580). An analysis of variance (ANOVA) was used 

 to test if there were significant differences in mean sea 

 urchin density and test diameter among survey strata. 

 Five test diameter categories were created to more 

 accurately represent the wide range of individual sea 

 urchin weights. The categories were based on the state's 

 minimum and maximum size restrictions, allowing 

 us to separately estimate the biomass of sea urchins 

 that have not yet recruited to the fishery, sea urchins 

 within the fishery, and sea urchins that have escaped 

 the fishery. The minimum (50 mm) and maximum (80 

 mm) size limits for our study were set slightly wider 

 than the those of the state, because, according to the 

 fishery regulations, up to 10% of the catch can be il- 

 legal-size sea urchins. Size-frequency data from sub- 



sampled quadrats were applied to the mean sea urchin 

 density for the specific depth zone and site, to generate 

 density values for each size category. Weight per sea 

 urchin was calculated from the mean length of the cat- 

 egory by using a length-weight relationship (Scheibling 

 et al., 1999). 



Spatial interpolation 



A sample semivariogram, often abridged to variogram, 

 was generated from mean sea urchin densities by site, to 

 examine the second-order spatial variation in the data 

 set. The sample variogram was calculated with the fol- 

 lowing equation (Bailey and Gatrell, 1995): 



yUi)- 



2n(h) 



!(*,-*/, 



(i) 



SiS:, 



where S, and S = sampling point pairs with (x,y) coor- 

 dinates; 

 n = the number of sample point pairs; 

 h - the distance between pairs; and 

 2 = mean urchin density for the sample. 



Trends in the variogram provide insights into the viabil- 

 ity of second-order methods for the sea urchin data. 



Representations of the large-scale trends in sea ur- 

 chin density were created by using Delaunay triangu- 

 lated irregular networks (TINs) (ArcView 3.2a, 3D and 

 Spatial Analyst Extensions, Redlands, CA). First, the 

 sample points were plotted by using sea urchin density 

 (/m 2 ) as the z value. Second, each point was connected 

 to the three nearest sites by linear interpolation, form- 

 ing a continuous surface of nonoverlapping triangles 

 (Fig. 2) (Bailey and Gatrell, 1995; Guan et. al., 1999). 

 Thus, the z value of any location within a triangular 

 surface is based solely on the three nearest sites. TIN 

 surfaces were generated for 40 different scenarios, ac- 

 cording to the size category, depth zone, and manage- 

 ment area, which minimizes variability and allows us 

 to produce more realistic biomass estimates. Finally, 

 using a customized C++ program, 1 we modified each 

 surface to include only areas of appropriate sea urchin 

 habitat. The green sea urchin is most commonly found 

 on rocky substrate in the shallow subtidal (Scheibling 

 and Hatcher, 2001), and, accordingly, the original sur- 

 vey program was limited to areas with predominately 

 rock or gravel substrata in areas less than 40 meters 

 deep. Therefore, we used a map of surficial geology to 

 identify areas of the correct substrate type (1:100,000 

 scale) (Kelley et al., 1997) and digital gridded bathym- 

 etry data to create a plot of 5-m isoline contours. The 

 bathymetry data source consisted of digital bathymetry 

 data sets from sources such as NOAA and the Naval 

 Oceanographic Office (15 arc second resolution) (Row- 

 orth and Signell, 2002). 



1 The C++ code used in this study is available upon request 

 from the principal author (RCG). 



