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Fishery Bulletin 103(2) 



urchin density that could attract fishermen, ranged 

 from 20-50 sea urchin/m 2 . For the first scenario, the 

 mean density from the range of recommended values, 

 35 sea urchin/m 2 , was selected. Therefore, the biomass 

 of legal-size sea urchins was calculated only in areas 

 where total sea urchin density was equal to or greater 

 than 35/m 2 . For the second scenario, we estimated that 

 commercial divers target areas that have greater than 

 10 legal-size sea urchins/m 2 . 



Estimation of uncertainty and stock assessment 



Because information on uncertainty cannot be directly 

 obtained from the TIN method, cross validation was 

 employed to approximate uncertainty in the estimation 

 process. Cross validation involves randomly removing 

 a site from a data set and predicting its value based 

 on the other data points using the TIN process (Bailey 

 and Gatrell, 1995). Residuals, or prediction errors, are 

 calculated between the predicted and true values at 

 the site. The process is repeated n times, resulting in 

 an observed set of n prediction errors, or residuals. The 

 frequency distribution and spatial distribution of residu- 

 als provide insights into the accuracy of the model; an 

 ideal model would have a mean residual value of and 

 positive and negative residuals would be distributed 

 randomly over the study area. 



Sea urchin biomass values were also calculated with 

 the arithmetic mean to provide comparisons with the 

 spatially derived estimates. For total biomass, mean sea 

 urchin densities by survey strata were multiplied by a 

 spatially derived area estimate of suitable sea urchin 

 habitat (<40 meters in depth) in the strata and the mean 

 sea urchin mass per strata. Fishable biomass was calcu- 

 lated the same way but sea urchin density values were 

 scaled by the proportion of legal-size sea urchins in the 

 stratum. Finally, exploitation rates, or the ratio of com- 

 mercial landings to the exploitable biomass estimates, 

 were calculated to facilitate comparison with the results 

 generated from the population dynamics stock assess- 

 ment and a recent study on biological reference points 

 (Chen and Hunter, 2003; Grabowski and Chen, 2004). 



Results 



Sea urchin density and size frequency, which were used 

 to calculate biomass, varied considerably along the coast 

 of Maine. Density (number of sea urchins/m 2 ) differed 

 significantly among survey strata (P<0.05; ANOVA), 

 showing a general large-scale trend of increasing den- 

 sity from stratum 1 to 9 (Table 1). Density also varied 

 by depth; the sea urchin density in the 15-40 m depth 

 zone was 0.32 sea urchins/m 2 , significantly lower than 

 those of the three shallow (<15 m) depth zones (P<0.05, t- 

 test), which each had approximately 9.50 sea urchins/m 2 . 

 Sea urchin test diameter varied from 3 mm to 114 mm 

 (mean at 35.90 mm). Test diameter differed significantly 

 among survey strata (P<0.05; ANOVA), in which strata 

 4, 5, and 9 had the smallest size sea urchins, and strata 



3 and 5 had the largest (Table 2). No meaningful trend 

 was evident in the sample variogram, which showed a 

 pure nugget effect (Fig. 3). This result indicates that the 

 sea urchin density data were too spatially variable to be 

 analyzed by intrinsic small-scale methods. 



Total sea urchin biomass was estimated at approxi- 

 mately 250,000 metric tons (t), and legal-size sea 

 urchins accounted for 165,000 t (Fig. 4). Most of the 

 biomass was found in management area 2, which ac- 

 counted for over 75% and 80% of the total and fishable 

 biomass, respectively (Table 3). For both estimates, bio- 

 mass varied by depth, being highest in the 0-5 m depth 

 zone and lowest in the 15-40 m depth zone (Fig. 5). 



The two methods used to estimate exploitable bio- 

 mass produced different biomass estimates with unique 



