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Fishery Bulletin 103(2) 



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Figure 7 



Spatial distribution of residuals and frequency distribution, insert (median=0, 

 standard deviation = 1.86, skewness=2.80, n=60), from the cross-validation study 

 that addressed uncertainty in the TIN estimation process for estimating bio- 

 mass for the green sea urchin (Strongyloeentrotus droebachiensis) fishery. 



concentrated in the eastern corner of management area 

 2, which is the most northeastern location on the coast 

 of Maine. This area has high total sea urchin densities, 

 but relatively low densities of legal-size adults, and is 

 an important location for the trawling industry. When 

 the threshold was based on the density of legal-size sea 

 urchins (method 2), however, exploitable biomass was 

 concentrated in the eastern portion of management area 

 1 and the central portion of area 2. These regions have 

 lower average sea urchin densities, but higher percent- 

 ages of legal-size adults, and are key fishing grounds for 

 the state's dive-based fishery. 



Because the two methods reflected different aspects 

 of the fishery, it is not surprising that they produced 

 different estimates of exploitable biomass (Table 3). 

 Nevertheless, these estimates did not differ consider- 

 ably from those of the population dynamics model. The 

 spatial analysis estimates bordered the ones derived 

 from the population dynamics model; method-1 esti- 

 mates were smaller than those derived from the popula- 

 tion dynamics model whereas method-2 estimates were 

 larger. The biomass estimates were similar despite 

 the fact that they were derived from different models 

 (spatial analysis and population dynamics model) using 

 entirely different data sources (fishery-independent and 

 fishery-dependent). 



The status of a fishery is often determined by com- 

 paring the current fishing mortality or stock biomass 

 with biological reference points (BRPs) (Hilborn and 

 Walters, 1992). The previous stock assessment study 

 estimated that the sea urchin stock biomass in Maine is 

 only about 10% of the virgin biomass, implying that the 



fishery has been severely overfished. A preliminary in- 

 vestigation into BRPs recently estimated a BRP F l for 

 the urchin fishery, based on a yield per recruit analysis, 

 and concluded that estimates of the current exploitation 

 rate are much higher than the BRP, which means that 

 the fishery is being overfished (Grabowski and Chen, 

 2004). However, when we compare the TIN exploita- 

 tion rates with the preliminary mean BRP F ,, which 

 ranged from 0.37 to 0.43 depending upon uncertainty 

 levels, we get an unclear assessment of the stock status. 

 The fishery is being drastically overfished according 

 to method 1, but is healthy according to method 2. We 

 believe that the assessment generated by method 2 was 

 unrealistically optimistic, considering the results from 

 the stock assessment and the decade-long declining 

 trend in landings. 



Uncertainty and further studies 



The TIN method was an appropriate spatial statistical 

 approach for estimating biomass for the sea urchin fish- 

 ery; however, a disadvantage of this technique is that 

 there is no straightforward method to estimate the uncer- 

 tainty in the biomass estimates. Because the technique 

 does not incorporate a variance structure into the estima- 

 tion process, we could not directly estimate uncertainty. 

 Therefore, we used cross-validation to approximate the 

 uncertainty associated with the TIN method (Fig. 7). 

 We found that the mean residual did not equal zero, 

 indicating that there is a global bias in the TIN surfaces 

 and that biomass estimates were likely overestimated 

 (Simard et al., 1992). This bias was most likely caused 



