Grabowski et al.: Estimating stock biomass of Strongy/ocentrotus droebachiensis 



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Figure 6 



Final spatial representations of the density of exploitable green sea urchins (Strongylocentrotus droebachiensis). Top row, method 

 1: threshold was based on total sea urchin density. Bottom row, method 2: threshold was based on legal-size sea urchin den- 

 sity. Left column, eastern portion of management area 1; middle column, central portion of management area 2; right column, 

 northeastern corner of management area 2. 



benthic algal presence, and the presence and level of 

 fishing or predatory activity all greatly affect urchin 

 density, growth rates, and size frequency (Vadas et 

 al., 1986; Scheibling and Hatcher, 2001). Mean sea 

 urchin density and size frequency were not constant 

 over the study area (Tables 1 and 2). Density exhib- 

 ited large-scale spatial trends along the coast, which 

 are related, at least, to depth and fishing activity. The 

 eastward increase in total sea urchin density along the 

 coast corresponded well with the historical patterns of 

 commercial sea urchin fishing in the State of Maine 

 (Table 1). The fishery began in the southwest, but as 

 sea urchin densities dropped in those regions, the fish- 

 ery steadily progressed northeastward along the coast. 

 Spatial patterns in density by depth (0-15 m vs. 15-40 

 m) may have been caused, in part, by the difference in 

 sampling techniques, yet the magnitude of the differ- 

 ences and support from ecological studies indicate that 

 there is a pattern. Finally, sea urchin densities varied 

 dramatically on small spatial scales — variations on 

 the order of one magnitude within the same habitat, 

 and sometimes only meters apart, are not uncommon 

 (Scheibling and Hatcher, 2001). This variability was 

 evident in the variogram analysis, which showed no 

 meaningful small-scale spatial structure and thus no 

 stationarity (Fig. 3). 



We were interested in identifying a spatial statisti- 

 cal approach that would generate reasonable estimates 



of stock biomass. The numerous discontinuities in the 

 study area, the dependence of variables on ecological 

 factors, and the high spatial variability indicated that 

 an intrinsic spatial statistical approach was not ap- 

 propriate for the investigation. Therefore, we needed 

 an approach that was geared towards the detection 

 and modeling of large-scale variability and that also 

 exhibited some robustness to discontinuities caused by 

 the indented coastline, islands, and habitat constraints. 

 We believe the TIN approach used in this study satisfies 

 these requirements, and, additionally, allows for vary- 

 ing levels of resolutions, with finer resolution in high 

 density sampling areas. 



Biomass estimates 



We calculated exploitable biomass in two different ways 

 because of the different assumptions they make about 

 the fishery. Method 1 assumes that fishermen target 

 areas based on total sea urchin density, whereas method 

 2 assumes that fishermen target areas based on the 

 density of legal-size sea urchins. The spatial distribu- 

 tions of legal-size sea urchin density, which were used 

 to calculate exploitable biomass, were distinctive and 

 showed little overlap between methods (Fig. 6). The 

 spatial distributions appear to reflect different aspects 

 of the sea urchin fishery. When the threshold was based 

 on total density (method 1), exploitable biomass was 



