UC Davis UC Davis Previously Published Works Title Modeling Red Sea Urchin Growth Using Six Growth Functions Permalink https://escholarship.org/uc/item/8gn2v2xn Journal Fishery Bulletin, 101 Author Rogers-Bennett, Laura, Dr. Publication Date 2003 Peer reviewed eScholarship.org Powered by the California Digital Library University of California 614 Abstract—The growth of red sea Modeling red sea urchin urchins (Strongylocentrotus francisca- nus) was modeled by using tag-recap- (Strongylocentrotus franciscanus) growth ture data from northern California. Red sea urchins (n=211) ranging in using six growth functions* test diameter from 7 to 131 mm were examined for changes in size over one Laura Rogers-Bennett year. We used the function J = J + t+1 t California Department of Fish and Game and f(J ) to model growth, in which J is the t t University of California, Davis jaw size (mm) at tagging, and J is the t+1 Bodega Marine Laboratory jaw size one year later. The function 2099 Westside Rd. f(J ), represents one of six deterministic t Bodega Bay, California 94923-0247 models: logistic dose response, Gauss- E-mail address: [email protected] ian, Tanaka, Ricker, Richards, and von Bertalanffy with 3, 3, 3, 2, 3, and 2 min- imization parameters, respectively. We Donald W. Rogers found that three measures of goodness Chemistry Department of fi t ranked the models similarly, in the Long Island University order given. The results from these six Brooklyn, New York 11201 models indicate that red sea urchins are slow growing animals (mean of 7.2 ±1.3 years to enter the fi shery). We William A. Bennett show that poor model selection or data John Muir Institute of the Environment from a limited range of urchin sizes University of California, Davis (or both) produces erroneous growth- Davis, California 95616 parameter estimates and years-to- fi shery estimates. Individual variation in growth dominated spatial variation Thomas A. Ebert at shallow and deep sites (F=0.246, Biology Department n=199, P=0.62). We summarize the six San Diego State University models using a composite growth curve San Diego, California 92182 of jaw size, J, as a function of time, t: J = A(B – e–Ct) + Dt, in which each model is distinguished by the constants A, B, C, and D. We suggest that this composite model has the fl exibility of the other six Marine invertebrates are being fi shed Sea urchin growth models are criti- models and could be broadly applied. at an increasing pace worldwide (Kees- cal in the development of innovative Given the robustness of our results ing and Hall, 1998). In California, management strategies to sustain the regarding the number of years to enter invertebrates have a greater exvessel fi shery because, among other things, the fi shery, this information could be (wholesale) value than do fin-fish models can be used to predict the time incorporated into future fi shery man- agement plans for red sea urchins in (Rogers-Bennett, 2001). Invertebrate required for sea urchins to enter the northern California. fisheries are now experiencing seri- fi shery (referred to as “years to fi sh- ous declines as have fi n-fi sh fi sheries ery”) and the age of the broodstock. (Dugan and Davis, 1993; Safi na, 1998; Despite the interest in examining sea Jackson et al., 2001). The once prosper- urchin growth, modeling efforts have ous commercial abalone fi shery in Cali- been hampered by several factors in- fornia which landed in excess of 2000 cluding model selection and a lack of metric tons per year in the 1950s and data from a suffi ciently wide range of 1960s was closed in 1997 (CDFG Code urchin sizes. Perhaps as a consequence, 5521) following the serial depletion of estimates of red sea urchin growth stocks over time (Karpov et al., 2000). have varied widely, ranging from 3 Commercial divers now target red sea to 12 years for urchins to grow into urchins and other invertebrates. Red the fi shery (Kato and Schroeter, 1985; sea urchin landings in California have Tegner, 1989; Ebert and Russell, 1992; also declined dramatically from a high Smith et al., 1998). Because of the wide of 24 metric tons (t) in 1988 to 6 t in variation in growth estimates, the num- 2002, despite management efforts (Kal- ber of models and methods being used, vass and Hendrix, 1997). These declines and the diffi culties that these present Manuscript approved for publication have generated interest in exploring the 5 February 2003 by Scientifi c Editor. use of alternative fi shery management Manuscript received 4 April 2003 at policies, such as spatially explicit strat- * Contribution 2176 from the Bodega Marine NMFS Scientifi c Publications Offi ce. egies that would protect large old sea Laboratory, University of Davis, Davis, CA Fish Bull. 101:614–626 urchins (Rogers-Bennett et al., 1995). 94923-0247. Rogers-Bennett et al.: Modeling growth of Strongylocentrotus franciscanus 615 for management, there is a need to evaluate a number of sites and released. Juveniles were stocked (120 at each growth models with a single data set that encompasses a of the two depths) on 31 August 1992 and harvested on large range of urchin sizes. 18 September 1993 with the adults (see Rogers-Bennett, In our study we report the results from six individual 2001). growth models applied to data from a one-year tag and Urchins at the Caspar Reserve were tagged internally recapture study of red sea urchins (Strongylocentrotus with personal individual transponder (PIT) tags on 28 franciscanus) in northern California. We supplemented August 1996 and recovered 20 August 1997 (Kalvass1). the number of juveniles in the fi eld by stocking tagged ju- PIT tags are glass coated mini-transponders with unique veniles. Estimates of the number of years required for ur- individual codes that can be read noninvasively by using chins to grow to minimum legal size in northern California a Destron® tag reader. Tags were implanted into the body are generated by the models. We examine the robustness of cavity of the sea urchins through the peristomial mem- these results to changes in the parameters and the impact brane. PIT tags are too large for tagging small urchins of a limited data set from a small range of urchin sizes on (<40 mm). our results. We determine if there are spatial differences Estimates of urchin density were made within a circle in growth between shallow and deep sites. Finally, we rank (12 m in radius) at each of the two Salt Point sites at the the models according to quality of fi t, present a generic time of harvest. Drift algae collections were made along a growth curve that combines the six models, and discuss the 2 × 10 m transect (20 m2) at each site. Gut contents were implications of our results for fi shery management. collected from a subsample of 20 urchins from each site. Gut contents were fi xed in alcohol, sorted on a petri dish, and the most abundant items were recorded from 5 out Materials and methods of 25 10-mm2 grids (Harrold and Reed, 1985). We used a conservative defi nition of optimal foods, defi ning them as Study sites fl eshy red or brown algae (Harrold and Reed, 1985). Sub- optimal foods included green algae, upright and encrust- Growth rates were determined for red sea urchins in ing coralline algae, detritus (animal, plant, and inorganic), the Salt Point (38°33′06′′N, 123°19′45′′W) and Caspar plants (Phyllospadix), mud, and sand. (39°21′49′′N, 123°49′47′′ W) urchin harvest reserves in northern California. Commercial urchin harvesting is pro- Growth measurements hibited in these reserves. We examined spatial variation within Salt Point by tagging red sea urchins at one shal- Sea urchins can not be reliably aged by using rings on low site (5 m) south of the southern border of the Gerstle test ossicles (Pearse and Pearse, 1975; Ebert 1988; Gage, Cove Reserve and at one deep site (17 m) on the leward 1992), therefore growth increments after one year must be side of a large wash-rock. In addition, laboratory-reared measured directly. For the urchins tagged with fl uorescent juvenile red sea urchins were stocked at the two sites in dyes (tetracycline and calcein), growth was measured as Salt Point. Both of these sites are relatively isolated, sur- the change in urchin jaw length (ΔJ =Jt+1−Jt) after one rounded by sand and seasonally dense kelp (Nereocystis). year (Ebert and Russell, 1993). Urchin jaws were dissected At the Caspar Reserve, sea urchins were tagged outside a from Aristotle’s lantern, excess tissue was removed with small cove with seasonally dense kelp (Nereocystis) at a 10% sodium hypochlorite, and the jaws were measured to single depth (7 m). the nearest 0.1 mm. Growth was measured by determining the width of the calcium deposit one year after tagging. Tagging Tags on jaws are more accurate than tags on test ossicles because ossicles move toward the oral surface during Sea urchins at the study sites were tagged internally and growth (Duetler, 1926), requiring matching ossicles at the recaptured after one year. At Salt Point, wild sea urchins time of tagging with ambitus ossicles at the time of collec- were tagged with tetracycline injections in situ by using tion (Ebert, 1988). 0.5–1.2 mL of 1 g tetracycline/100 mL of seawater (cf. Fluorescence tagged urchins were identifi ed when ex- Ebert, 1982; Ebert and Russell, 1992). Six hundred and posed to an ultraviolet epi-illuminator (Lite-Mite) on a nine red urchins were measured with vernier calipers dissecting scope.