Carlson et a\ Life history and population dynamics of Carcharhinus isodon 



283 



Figure T 



Sagittal section from a finetooth sharktCarcharhmus isodon ) vertebra used for age determination. Winter 

 marks correspond to thin dark areas under transmitted light, whereas summer marks correspond to wide 

 light zones. Each growth band includes a dark zone and a light zone. 



and fish at the time of hatching (Campana, 1990). For the 

 finetooth shark, we used the estimated size at birth in the 

 northeastern Gulf of Mexico (520 mm TL; Carlson, unpubl. 

 data). 



In developing theoretical growth models, we assumed 

 that 1 ) the birth mark is the band associated with a pro- 

 nounced change in angle in the intermedialia and is formed 

 on an arbitrary birth date of 1 June, 2) growth bands are 

 formed once a year, and 3 ) the narrow dark marks are de- 

 posited in winter on an arbitrary date of 1 January. Ages 

 were calculated by using the algorithm: age = the birth 

 mark + number of winter marks -1.5, -i- the proportion of 

 the year fr-om winter mark deposition to the date of capture. 

 If only the birth mark was present, age was calculated as 

 the time between birth and date of capture. 



The von Bertalanffy growth model (Eq. 1; von Berta- 

 lanffy, 1938) was fitted separately to obsei-ved and back- 

 calculated size-at-age data using the equation 



LJl-e 



-K(l-ln) 



'"'), 



Growth model parameters were estimated by using least- 

 squares nonlinear regression (SAS PROC NLIN; SAS, 

 1988). 



For comparison, an alternate equation of the von Berta- 

 lanffy growth model (Eq. 2; Fabens, 1965) was also fitted 

 separately to observed size at age data. This equation is 

 described as 



L, = L, ( l-be-i^') = L,- (L .-LoJe-'^', 

 b = iL^-Lg)/ L^=e'<'o, 



where L, - predicted length at time t; 



L^ - theoretical asymptotic length; 

 K = growth coefficient; and 

 Lg = the length at birth. 



Verification of the annual period of band formation was 

 attempted by using the relative marginal increment analy- 

 sis (Natanson et al., 1995): 



where L, = predicted length at time t; 



L^ = theoretical asymptotic length; 



K = growth coefficient; and 



Iq = theoretical age at zero length. 



MIR = iVR-R„)HR,-R„_^l 



where MIR = the marginal increment ratio; 

 VR = the vertebral radius; 



