Natanson et al.: Age and growth estimates for Carcharhmus obscurus 



I 17 



studies (Casey and Natanson, 1992). These data are 

 not available for the dusky shark nor is validation of 

 vertebral band periodicity. Previous attempts to age 

 the dusky shark were based on limited data and were 

 inconclusive (Lawler, 1976; Hoenig, 1979; Schwartz, 

 1983). We have attempted to strengthen age esti- 

 mates of C. obscurus by using vertebral band counts 

 together with marginal increment analysis and by us- 

 ing comparisons with length-frequency data. With the 

 von Bertalanffy growth function thus derived, we esti- 

 mate age at maturity and longevity for this species. 



Materials and methods 



Data and vertebral samples from dusky sharks were 

 obtained between 1963 and 1993 from research 

 cruises, sport fishing tournaments, and commercial 

 shark fishermen from Cape Cod, Massachusetts, to off 

 the east coast of Florida. Vertebral samples were taken 

 in all months except January, March, and November. 



Length measurements 



Total and fork lengths were measured to the nearest 

 centimeter (cm) for each specimen. Fork length (FL) 

 was measured from the tip of the snout to the fork of 

 the tail. Total length (TL) is defined as the distance 

 from the snout to a point on the horizontal axis in- 

 tersecting a perpendicular line extending downward 

 from the tip of the upper caudal lobe to form a right 

 angle (Kohler et al. 2 ). All lengths used are fork 

 lengths unless otherwise noted. FL can be converted 

 to TL by using the regression equation: 



FL = 0.8352 (TL) -2.2973. [r 2 = 0.99, n = 167] 



Vertebral samples 



Vertebral samples were taken from above the bran- 

 chial chamber. Sections of vertebral columns were 

 trimmed of excess tissue and then frozen or preserved 

 in 70% ethanol (Casey et al., 1985). 



Two vertebrae from each specimen were processed 

 histologically following Casey et al. (1985), with the 

 exception of the use of RDO (DuPage Kinetics) for 

 decalcification. All vertebral sections were cut sagit- 

 tally through the focus to a thickness of 80-100 mi- 

 crons, stained with Harris hematoxylin, and mounted 

 in glycerin jelly (Humason, 1972). 



Bands in the vertebra were counted from an im- 

 age projected on a Summagraphics MM-1812 digi- 



tizing tablet (Skomal, 1990). Measurements from the 

 focus to growth bands at points along the internal 

 corpus calcareum were digitized directly into an IBM 

 PC-XT computer. The radius of each centrum was 

 measured from the focus to the distal margin of the 

 intermedialia along the same diagonal as the band 

 measurements. Annual growth marks were defined 

 following Casey et al. (1985) for the sandbar shark, 

 Carcharhinus plumbeus, where the annual mark is 

 defined by a wide translucent zone that traverses 

 the intermedialia and continues into the corpus 

 calcareum as an opaque band. 



Vertebral sections from 171 dusky sharks were 

 prepared. Bands in the same centrum section were 

 counted at least once by each of four investigators to 

 verify that the band counts were repeatable. Sections 

 were considered unreadable if bands could not be 

 discerned in accordance with the above definition. If 

 two readers considered the section unreadable, the 

 sample was eliminated from the final analysis. 



Counts were accepted if two or more readers 

 agreed. The individual ring measurements for all 

 readers in agreement were then averaged. If two 

 readers agreed on one count and two on another for 

 the same specimen, the higher count was accepted. 

 Specimens where there was no initial agreement 

 were recounted until two of the investigators reached 

 a consensus or the sections were discarded. 



The relationship between vertebral radius (VR) 

 and FL was calculated to determine the most appro- 

 priate method for back calculation of the size-at-age 

 data (Ricker, 1969). The FL to VR relationship was 

 linear but did not pass through the origin. There- 

 fore, the Lee method was considered more appropri- 

 ate (Ricker, 1969): 



I - a + (b x s), 



where / = the length of fish when the vertebra was 

 obtained; 

 a = the intercept on the length axis; 

 b = the slope of the line; and 

 s = the total vertebral radius. 



A von Bertalanffy growth function (VBGF) was fit- 

 ted to the data by using the following equation (von 

 Bertalanffy, 1938): 



L t =L„(l-e- k «-<°>), 



2 Kohler, N. E., J. G. Casey, and P. A. Turner. Length-weight re- 

 lationships for 13 Atlantic sharks. Unpubl. manuscr. 



where L t = predicted length at time t\ 



L x = mean asymptotic fork length (of the fish); 

 K = a growth rate constant (yr _1 ); and 

 t = the theoretical age at which the fish 

 would have been zero length. 



