Grabowski et al .: Estimating stock biomass of Strongylocentrotus droebachiensis 



329 



by a combination of the underlying patterns in spatial 

 variability, the linear interpolation method employed in 

 TIN formation, and the effects of sample selection in the 

 cross-validation study. There are several possible ways 

 to reduce the bias in the estimation process, such as 

 incorporating a smoothing function or weighting based 

 on neighbors into the TIN model. This procedure would 

 not completely address uncertainty, however, because it 

 would only acknowledge uncertainty in the TIN estima- 

 tion process. To obtain confidence intervals for biomass 

 estimates, we needed to incorporate uncertainty in mean 

 density and in TIN estimation. We are currently inves- 

 tigating methods to estimate confidence intervals, such 

 as using a Monte Carlo simulation approach. A thorough 

 examination and quantification of uncertainty is beyond 

 the scope of this article. 



In this study, we identified a basic approach for inves- 

 tigating spatial patterns, and estimating stock biomass 

 in situations where second-order methods are inappro- 

 priate. The TIN technique generated realistic biomass 

 estimates that are similar to those derived with other 

 approaches, but before we can recommend this tech- 

 nique for the green sea urchin fishery, several points 

 must be addressed. First, the two methods used to es- 

 timate exploitable biomass must be integrated because 

 they reflect different aspects of the fishery and result 

 in different stock assessments. Second, a process must 

 be established to estimate threshold levels because they 

 have a large control over exploitable biomass estimates. 

 Finally, a technique must be developed to estimate 

 uncertainty in biomass. We would also recommend fur- 

 ther investigations into tracking fishing pressure and 

 identifying its effects on the benthic ecosystem and the 

 spatial distribution of sea urchins. 



Acknowledgments 



We would like to thank the staff at the Maine Depart- 

 ment of Marine Resources for collecting and compiling 

 the sea urchin fishery data. We would especially like to 

 thank Margaret Hunter and Robert Russell from the 

 DMR, Kathryn Wisz, our laboratory assistant, Ryan 

 Weatherbee, for his help with the manuscript, and Oliv- 

 ier Mette, for his technical assistance. This project was 

 partially supported by grants from the Northeast Con- 

 sortium (UNH SUB 302-628), the Maine Department of 

 Marine Resources (G1102012), and the Sea Urchin Zone 

 Council to Y. Chen and a Maine Marine Science Fellow- 

 ship from the Marine Department of Marine Resources 

 and the University of Maine School of Marine Sciences 

 to R. Grabowski. 



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