Grabowski et al.: Estimating stock biomass of Strongylocentrotus droebachiensis 



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Figure 1 



Map of the Maine coastline, showing the two management areas and the nine study strata from the fishery-inde- 

 pendent survey program for green sea urchins (Stro/igylocentrotus droebachiensis). 



2001 the DMR began an extensive fishery-independent 

 survey program. This program generates large, spa- 

 tially referenced, scientific data sets each year, which 

 can be incorporated into stock assessments by using 

 either fisheries population dynamics models or spatial 

 analysis techniques. 



Spatial statistics, also known as spatial statistics or 

 geostatistics, encompasses a diverse group of techniques 

 that can be used to model the spatial variability of a 

 process, such as sea urchin density, to estimate the 

 value at unobserved locations (Bailey and Gatrell, 1995; 

 Petitgas, 2001). Spatial variability is routinely divided 

 into two categories: first- and second-order effects, or 

 similarly, large- and small-scale variability. Large-scale 

 variability is the variation in the mean value of the 

 process over the study area, whereas small-scale vari- 

 ability is the spatial dependence of the process, in other 

 words the similarity between neighboring sites (Bailey 

 and Gatrell, 1995). 



Intrinsic second-order methods, along with kriging, 

 have become the most popular geostatistical tools and 

 are now commonly used to estimate exploited fish stock 

 biomass (e.g., Simard et al., 1992; Petitgas, 1993; Pelle- 



tier and Parma, 1994; Maravelias et al., 1996; Lembo 

 et al., 1998; Maynou et al., 1998; Rivoirard et al., 2000; 

 Petitgas, 2001). Two assumptions must be met to use 

 intrinsic geostatistical methods: 1) independence be- 

 tween the variable and the region's geometry and 2) 

 stationarity (Petitgas, 1993; Warren, 1998; Rivoirard 

 et al., 2000). If these assumptions are violated, we can 

 attempt to modify the data to make them more appli- 

 cable or we must use other spatial analysis techniques 

 to estimate the spatial patterns. 



Tessellation is a spatial analysis technique that in- 

 vestigates first-order, or large-scale, spatial variability 

 of a process (Ripley, 1981; Bailey and Gatrell, 1995). 

 Triangulated irregular networks (TINs), or Delaunay 

 triangulation, are the simplest and most common tes- 

 sellation technique, in which a three-dimensional sur- 

 face of contiguous, non-overlapping triangles is created 

 by linear interpolation of the variable. TINs are most 

 commonly used for visualization purposes but can be 

 used to estimate the biomass of a process (Simard et 

 al., 1992; Guan et al., 1999). They have received limited 

 use in fisheries stock assessment, however, because if a 

 stock exhibits stationarity, second-order methods tend 



