737 



Abstract— The green sea urchin iStron- 

 gyloccntrotus droebachiensis) is impor- 

 tant to the economy of Maine. It is the 

 state's fourth largest fishery by value. 

 The fishery has experienced a con- 

 tinuous decline in landings since 1992 

 because of decreasing stock abundance. 

 Because determining the age of sea 

 urchins is often difficult, a formal stock 

 assessment demands the development 

 of a size-structured population dynamic 

 model. One of the most important com- 

 ponents in a size-structured model is a 

 growth-transition matrix. We developed 

 an approach for estimating the growth- 

 transition matrix using von Bertalanffy 

 growth parameters estimated in previ- 

 ous studies of the green sea urchin off 

 Maine. This approach explicitly consid- 

 ers size-specific variations associated 

 with yearly growth increments for 

 these urchins. The proposed growth- 

 transition matrix can be updated read- 

 ily with new information on growth, 

 which is important because changes in 

 stock abundance and the ecosystem will 

 likely result in changes in sea urchin 

 key life history parameters including 

 growth. This growth-transition matrix 

 can be readily incorporated into the 

 size-structured stock assessment model 

 that has been developed for assessing 

 the green sea urchin stock off Maine. 



Developing a growth-transition matrix for 

 the stock assessment of the green sea urchin 

 (Strongylocentrotus droebachiensis) off Maine 



Yong Chen 



School of Marine Sciences 

 218 Libby Hall 

 University of Maine 

 Orono, Maine 04469 

 E-mail address ychen@maine.edu 



Margaret Hunter 



Maine Department of Marine Resources 



P.O. Box 8 



West Boothbay Harbor, Maine 04575 



Robert Vadas 



Department of Biological Sciences 

 University of Maine 

 Orono, Maine 04469 



Brian Beal 



Division of Environmental and Biological Sciences 

 University of Maine 

 Machias, Maine 04654 



Manuscript approved for publication 

 17 April 2003 by Scientific Editor 



Manuscript received 26 June 2003 at 

 NMFS Scientific Publications Office. 



Fish Bull. 101:737-744 (2003). 



The green sea urchin (Strongylocentro- 

 tus droebachiensis) fishery is the state's 

 fourth largest fishery by value, worth 

 $20.3 million to harvesters in 1999. 

 The fishery is managed by limited 

 entry, a limited number of opportunity 

 dates that are established each year 

 by recommendation of the sea urchin 

 zone council (SUZC), and minimum 

 and maximum size limits. The fishery 

 is further regulated seasonally by two 

 zones that correspond to variation in 

 spawning time along the coast (Vadas 

 etal., 1997). 



The Maine sea urchin fishery began 

 in the late 1980s and reached its peak 

 in landings in 1992. It has since experi- 

 enced a continuous decline in landings, 

 mainly resulting from large decreases 

 in sea urchin stock abundance (Fig. 1). 

 Although the large decrease in abun- 

 dance is evident in many studies (Ste- 

 neck and Vadas'; Harris^) and apparent 

 to the sea urchin fishing industry, the 

 catch-per-unit-of-effort (CPUE) data 

 derived from the fishery have shown 

 no significant decreases over the last 



10 years (Fig. 1). We need to perform 

 a formal stock assessment to better 

 understand the population dynamics of 

 the sea urchin stock and to develop an 

 optimal management strategy. 



A population dynamics model for the 

 sea urchin stock should provide reliable 

 estimates of model parameters with 

 suitable statistical methods (Hilborn 

 and Walters, 1992; Chen and Paloheimo, 

 1998; Walters, 1998). A size-structured 

 population dynamics model is needed 

 for the sea urchin fishery because sea 

 urchins are difficult to age and growth 

 varies widely among individuals (Quinn 

 and Deriso, 1999). 



One of the key components of a size- 

 structured population dynamics model 

 is a growth-transition matrix, which 

 describes the probability of an organ- 



1 Steneck, R., and R. L. Vadas. 2002. Per- 

 sonal commun. School of Marine Sciences, 

 University of Maine, Orono, ME 04469. 



2 Harris, L. 2002. Personal commun. 

 Department of Zoology, University of New 

 Hampshire, Durham, NH 03824. 



