614 



Abstract — The growth of red sea 

 urchins (Strongylocentrotus francisca- 

 nus) was modeled by using tag-recap- 

 ture data from northern Cahfornia. 

 Red sea urchins (n=211) ranging in 

 test diameter from 7 to 131 mm were 

 examined for changes in size over one 

 year. We used the function J,^, = "^i + 

 fit/,) to model growth, in which J, is the 

 jaw size (mm) at tagging, and J,^[ is the 

 jaw size one year later. The function 

 RJ,), represents one of six deterministic 

 models: logistic dose response, Gauss- 

 ian, Tanaka, Ricker, Richards, and von 

 Bertalanffy with 3, 3, 3, 2, 3, and 2 min- 

 imization parameters, respectively. We 

 found that three measures of goodness 

 of fit ranked the models similarly, in the 

 order given. The results from these six 

 models indicate that red sea urchins 

 are slow growing animals (mean of 

 7.2 ±1.3 years to enter the fishery). We 

 show that poor model selection or data 

 from a limited range of urchin sizes 

 (or both) produces erroneous growth- 

 parameter estimates and years-to- 

 fishery estimates. Individual variation 

 in growth dominated spatial variation 

 at shallow and deep sites (F=0.246, 

 n=199, P=0.62). We summarize the six 

 models using a composite growth curve 

 of jaw size, J, as a function of time, t: J 

 =A(B - e-'^') + Dt, in which each model is 

 distinguished by the constants A, B, C, 

 and D. We suggest that this composite 

 model has the flexibility of the other six 

 models and could be broadly applied. 

 Given the robustness of our results 

 regarding the number of years to enter 

 the fishery, this information could be 

 incorporated into future fishery man- 

 agement plans for red sea urchins in 

 northern California. 



Modeling red sea urchin 

 iStrongylocentrotus franciscanus) growth 

 using six growth functions* 



Laura Rogers-Bennett 



California Department of Fistn and Game and 



University of California, Davis 



Bodega Marine Laboratory 



2099 Westside Rd 



Bodega Bay, California 94923-0247 



E-mail address; rogeRbennettis/ucdavis edu 



Donald W. Rogers 



Chemistry Department 

 Long Island University 

 Brooklyn, New York 11201 



William A. Bennett 



John Muir Institute of the Environment 

 University of California, Davis 

 Davis, California 95616 



Thomas A. Ebert 



Biology Department 



San Diego State University 



San Diego, California 92182 



Manuscript approved for publication 

 5 February 2003 by Scientific Editor 



Manuscript received 4 April 2003 at 

 NMFS Scientific Publications Office. 



Fish Bull. 101:614-626 



Marine invertebrates are being fished 

 at an increasing pace worldwide (Kees- 

 ing and Hall, 1998). In California, 

 invertebrates have a greater exvessel 

 (wholesale) value than do fin-fish 

 (Rogers-Bennett, 2001). Invertebrate 

 fisheries are now experiencing seri- 

 ous declines as have fin-fish fisheries 

 (Dugan and Davis, 1993; Safina, 1998; 

 Jackson et al., 2001). The once prosper- 

 ous commercial abalone fishery in Cali- 

 fornia which landed in excess of 2000 

 metric tons per year in the 1950s and 

 1960s was closed in 1997 (CDFG Code 

 5521) following the serial depletion of 

 stocks over time (Karpov et al., 2000). 

 Commercial divers now target red sea 

 urchins and other invertebrates. Red 

 sea urchin landings in California have 

 also declined dramatically from a high 

 of 24 metric tons (t) in 1988 to 6 t in 

 2002, despite management efforts (Kal- 

 vass and Hendrix, 1997). The.se declines 

 have generated interest in exploring the 

 use of alternative fishery management 

 policies, such as spatially explicit strat- 

 egies that would protect large old sea 

 urchins (Rogers-Bennett et al., 1995). 



Sea urchin growth models are criti- 

 cal in the development of innovative 

 management strategies to sustain the 

 fishery because, among other things, 

 models can be used to predict the time 

 required for sea urchins to enter the 

 fishery (referred to as "years to fish- 

 ery") and the age of the broodstock. 

 Despite the interest in examining sea 

 urchin growth, modeling efforts have 

 been hampered by several factors in- 

 cluding model selection and a lack of 

 data from a sufficiently wide range of 

 urchin sizes. Perhaps as a consequence, 

 estimates of red sea urchin growth 

 have varied widely, ranging from 3 

 to 12 years for urchins to grow into 

 the fishery (Kato and Schroeter, 1985; 

 Tegner, 1989; Ebert and Russell, 1992; 

 Smith et al., 1998). Because of the wide 

 variation in growth estimates, the num- 

 ber of models and methods being used, 

 and the difficulties that these present 



* Contribution 2176 from the Bodega Marine 

 Laboratory, University of Davis, Davis, CA 

 94923-0247. 



