156 



Fishery Bulletin 97(1), 1999 



M = mass at capture; and 

 b - the constant derived from the multi- 

 pUcative regression of M on CD. 



The constant b was derived by using the "body-pro- 

 portional-hypothesis," where "if a fish at time of cap- 

 ture was 10 per cent smaller than the average fish 

 with the same size of scale, the fish would be 10 per 

 cent smaller than the expected length for the size of 

 that scale throughout life" (Whitney and Carlander, 

 1956, cited by Francis, 1990). 



Confirmation of the annual periodicity of GRs 

 (Cailliet et al., 1983a, 1983b) was attempted with 

 two methods of centrum analyses. First, the last de- 

 posited band was classified as translucent or opaque 

 and related to the month of capture (Kusher et al., 

 1992). The observed and expected ratios of translu- 

 cent to opaque last bands were then compared. Sec- 

 ond, the marginal increment ratio (MIR) (Hayashi, 

 1976; Skomal, 1990) was calculated with the follow- 

 ing equation: 



MIR = (VR-R)/{R-R 



n-l 



where VR = 



vertebral radius; 



radius to the last complete GR; and 



radius to the previously completed 



GR. 



Mean MIR, with range and standard error, was then 

 plotted against month. 



In addition, 16 white sharks (between 1993 and 

 1995) were injected with oxytetracycline (OTC) so- 

 lution (Engemycin, Intervet International B.V.), at a 

 dose of 25 mg per kg body mass as recommended by 

 Holden and Vince (1973) and McFarlane and 

 Beamish ( 1987). Mass was estimated from the mass- 

 length equation of Cliff et al. (1989). The OTC was 

 administered in several places in the muscle around 

 the first dorsal fin with a 15G x 1.5" disposable needle 

 and 20-mL plastic syringe. Each shark was tagged 

 with an orange identification tag (Hallprint PDA 

 large plastic dart tag), labelled "tetracycline" and 

 given a unique "BT" number. 



Age and growth 



The program PC-YIELD II (Punt and Hughes, 1989) 

 was used to determine which of 10 different growth 

 models provided the best fit to the data sets obtained 

 by the three methods. Whe.re appropriate, von 

 Bertalanffy growth parameters (VBGP) were com- 

 puted. The equation (von Bertalanffy, 1938) is 



L, ^L^d-e-*"-'"'), 



where L^ = length at GR t; 



maximum theoretical length; 



the rate at which L^ is reached; and 



the theoretical number of GR at length 



zero. 



k" = 



t„ = 



To determine whether GR deposition was related to 

 an increase in mass rather than to time of year, Gom- 

 pertz growth parameters were also calculated. The 

 Gompertz equation (Silliman, 1967; Ricker, 1975) is 



W,= u'oe«'i- 



where w^ = mass at GR t; 



G - initial exponential growth; and 

 g = exponential rate of decline. 



Both growth equations were fitted by using the nonlin- 

 ear regression procedure of STATGRAPHICS, which 

 uses Marquardt's algorithm (Draper and Smith, 1981). 

 Because this procedure is highly dependent upon ini- 

 tial estimates for the parameters, a wide range of ini- 

 tial parameters was used to prevent the models con- 

 verging to a local minimum, i.e. converging to an un- 

 wanted stationary point of the sum of squares, rather 

 than to a global minimum (Draper and Smith, 1981). 



Results 



Of the 1 14 processed vertebrae, between two and six, 

 depending on the method, had an APE of over 209^ 

 after a recount and were discarded (Table 1). The 

 final APE indices and D values showed little differ- 

 ences amongst methods, indicating similar reproduc- 

 ibility (Table 1). The percentage agreement among 

 the three counts was high, e.g. with method SC-A, 

 for 58. 0'^ of the sample the three counts were the 

 same (Table 2). In all three methods the majority of 

 the readings was the same or differed only by one 

 GR. For this reason, a mean of the three counts was 



