916 



Fishery Bulletin 101(4) 



therefore the Tanaka model was modified from previous 

 uses to make AJ a function ofJf^^f the size on the date of 

 recapture rather the date of marking, which is the usual 

 way of estimating growth parameters. Also, At was explic- 

 itly included as a variable (Eq. 2), 



A/ = y„ 



V7 



In 



lG + 2^G-+fa 



where 



and 



G = EIA-falE-fAt 



E = exp{4fU„^-d}) 



(1) 



(2) 



(3) 



The three parameters of the Tanaka function, a, d, and f, 

 have biological meaning: "a" is related to maximum growth 

 rate, which is approximately l^/a; "d" shifts the size at 

 which growth is maximum; and "/" is a measure of the rate 

 of change of the growth rate. A graphical presentation of 

 how changes in these parameters change the growth curve 

 is given in Ebert et al. (1999). 



Explicit use of At and making AJ a function of Jf+^t 

 required a modification of the usual presentation of the 

 Tanaka function. In Ebert et al. (1999) Equation 2 was 

 written as 



G = E/4-fa/E+f (4) 



with no At and with "+ /". Equation 3 was written as 



E = exp[4f{J,-d)). (5) 



with Jf, rather than J^^^^. Tetracycline tagging for a period 

 of one year, At = 1, provides the Tanaka parameter esti- 

 mates and these parameters were used to estimate a Ajaw 

 size that would cover the time from the date of collection to 

 a time. At, before A-bomb testing; At is time run backwards 

 from the date of collection, which is the reason for the sign 

 change from Equation 4 to Equation 2. 



The samples of red sea urchins that were selected for 

 radiocarbon analysis were part of the tagging study at 

 Halftide Rocks off San Juan Island, Washington (Ebert et 

 al., 1999). Individuals were tagged with tetracycline on 26 

 October 1991 and collected again on 21 October 1992. The 

 recaptured tagged individuals {n=365) are part of the 1582 

 tagged sea urchins from northern California, Oregon, and 

 Washington that were used to estimate Tanaka param- 

 eters. For ''*C analysis, specimens were selected from the 

 Halftide Rocks collection that did not show fluorescence in 

 the skeleton and therefore probably had not been handled 

 in 1991. The use of untagged individuals for radiocarbon 

 analyses avoids any possible contamination from handling 

 and tagging in 1991. 



Cleaned jaws for ''*C analysis were cemented to alumi- 

 num blocks with a two-part epoxy cement and aligned so 

 that the esophageal margin was approximately parallel 

 with the block base. The block was held on the stage of a 

 small milling machine and the stage tilted so that the jaw 



was as parallel as possible with the milling bit. Approxi- 

 mately 0.5 mm of the jaw surface was removed and sides 

 were milled to remove recently deposited calcite and to ex- 

 pose the underlying older skeleton. The jaw was measured 

 and successive samples were milled from the esophageal 

 edge to a depth of 0.5 mm, which produced samples larger 

 than 1 mg of carbonate in most cases. Samples were placed 

 in individual reaction chambers, evacuated, acidified with 

 orthophosphoric acid, and heated. The evolved CO2 was 

 converted to graphite by reduction with an excess of hydro- 

 gen in individual reactors with iron powder as a catalyst 

 (Vogel et al., 1987). Analysis of "C in the graphite targets 

 was done at the Center for Accelerator Mass Spectrometry, 

 Lawrence Livermore National Laboratory, and reported as 

 A^'^C7cc (Stuiver and Polach, 1977), which includes a correc- 

 tion for a S^^C of -3 based on stable isotope analyses. Mean 

 precision (1 standard deviation) of radiocarbon measure- 

 ments was 4.2%o (range: 3.0-7.9). 



Results 



Of the 1582 tag recoveries from all sites, 739 jaws showed a 

 growth increment, AJ, of <0.02 cm and of these only 13 had 

 a labial measurement >0, which is at the end of the jaw at 

 the mouth opening. The smallest nonzero measurements 

 were 0.001 cm and therefore growth less that this was 

 recorded as 0; 54 sea urchins in the sample had clear tetra- 

 cycline marks but measurable growth. For large jaws, the 

 measured labial component was too small to be measured 

 and therefore all of the calculated AJ since the late 1950s 

 was milled from the esophageal end of the jaw only. 



Tetracycline tagging indicated that annual jaw growth 

 (Fig. 1) was very slow for large sea urchins and many in- 

 dividuals showed annual increments of less than 0.01 cm. 

 The resulting growth curve of jaw length as a function of 

 age (Fig. 2A) showed that at least some large individuals 

 would be expected to have ages in excess of 100 years. If 

 this age estimate is correct, a drop in ^^C should be found 

 in successive small slices removed from large jaws, which 

 would first show current ^^C levels and then drop to pre- 

 bomb levels. Because the Halftide Rocks samples were col- 

 lected in 1992 we used At = 35 years, which would go back 

 to 1957. Using Equations 1-3, growth parameters given in 

 Fig. 1, and At = 35 years, we estimated the increment to 

 be between 1 and 2 mm for jaws between 2.5 and 2.6 cm 

 (Fig. 2B). 



Successive milled samples from the esophageal ends 

 of large jaws (Fig. 3, A-D) showed a precipitous drop in 

 radiocarbon to prebomb levels over 1-2 millimeters, in 

 agreement with predictions. Variations across replicates 

 and samples probably are the result of differences in the 

 width of milled samples and an inability to remove all re- 

 cently deposited calcite or to follow the exact growing edge 

 of the jaw with the milling machine. Smaller jaws (Fig. 

 3, E-G) were not expected to show a prebomb signature, 

 and indeed they did not. They do, however, indicate the 

 ^*C level to be expected in recent skeletal material and 

 emphasize the rapid change in radiocarbon shown in large 

 jaws. Changes in ^•*C in successive milled samples in jaws 



