270 



Fishery Bulletin 100(2) 



the L . Using a wide range of species, 

 Hoenig (1983) calculated the relation- 

 ship between longevity, ^„,„j-, and the 

 natural mortality rate, M, needed to 

 attain one percent of initial abundance 

 in an unfished population as 



ln(M)= 1.44 



0.982 ln(^„„_,). 



However, a relationship based on other 

 species need not be used (Campana 

 et al.^). Assuming a constant instan- 

 taneous natural mortality, M, in an 

 unfished population, the following equa- 

 tion applies: 



Ln (proportion offish that survive to 



As with Hoenig 1 19831, this equation 

 was evaluated at a value of 0.01 for the 

 proportion offish that survive. 



Results 



Vertebral aging 



250 



200 



Mean radius of birth mark (n=575) 



150 



s , Smallest 



g I free-living 



100 



50 



Size at birtfi 



10 15 



Vertebral radius (mm) 



20 



25 



Figure 2 



Relationship between vertebral radius and fork length for male and female por- 

 beagles. The solid diamond is the mean vertebral radius of the smallest free-living 

 specimens (n=2), the solid circle is the mean vertebral radius of the largest 

 embryos (n=3). The horizontal line represents the size at birth and the vertical 

 line represents the mean radius of the birth mai'k in sharks less than 1.50 cm FL. 



Vertebral samples from 578 porbeagles 

 were used in our analysis; 283 were 

 males, 292 were females, and 3 were of unknown sex. All 

 vertebrae had distinct band-pair patterns (Fig. 1). The 

 birth mark was indicated by a slight change in angle of 

 the centra and was often the most pronounced first band 

 pair. Subsequent annuli consisted of a pair of alternating 

 opaque and translucent bands that crossed the entire 

 centrum, except in the oldest sharks. Band-pair width 

 decreased with age, narrowing substantially in the oldest 

 individuals (Fig. 1). 



The FL-VR relationship was curvilinear 'Fig. 2i, and al- 

 though the In-transformed relationship was not complete- 

 ly linear, it was preferable. Therefore, regressions were 

 calculated based on the ln(FL)-ln(VTl) relationship where 



ln(FL) = 0.88 ^ In(VR) -^ 2.96 



|r-=0.94./;=5751. 



There was no significant difference between the regres- 

 sions of males and females (ANCOVA, P>0.01). 



The identity and location of the birth band was confirmed 

 through comparison of the BR of all individuals to the VR 

 of YOY and embryos. The mean VR of three late-term em- 

 bryos ranging in size from 56.1 to 58 cm FL (mean VR=4.3 

 mm, 01=0.57) was slightly less than the mean BR value of 

 the total sample (mean BR=5.4 mm, CI=0.03 mm, /)=578l. 

 The mean BR those of two early YOY (67.7 and 69.2 cm FL) 

 were also similar to those of the total sample (mean VR=5.3 

 mm, CI=1.27 mm). The VR of the age-0 individuals ranging 

 in size from 76.5 to 100 cm FL (mean VR=6.2 mm, Cl=0.31 

 mm,/i = 16) was slightly higher (Fig. 2). The placement of the 

 mean BR between the VR of both the YOY and embrvos in- 



dicates that the birth ring was identified correctly. The birth 

 ring radius increased slightly with increasing FL likely be- 

 cause of an increase in the length of the isthmus of the how- 

 tie section in larger sharks. 



Validation 



Known-age recaptured porbeagles and OTC-injected recap- 

 tured porbeagles returned with vertebrae confirmed the 

 accuracy of the band-pair counts as indicators of age. Six 

 porbeagles tagged as YOY were recaptured after three to 

 five years at liberty (Table 1 ). Of the four sharks that were 

 recaptured in the spring, all had translucent material at 

 their gi'owing edge. In contrast, the two sharks recaptured 

 in November had a broad opaque zone at the gi'owing edge. 

 In each case, the vertebral band-pair counts matched the 

 expected counts based on time at liberty (Fig. 3). Vertebrae 

 from six OTC-injected sharks were returned after 0.02 to 

 2.5 years at liberty. All vertebrae showed a distinct fluo- 

 rescent mark indicating that the OTC was incorporated 

 within six days (0.02 years) of injection (Fig. 3). Two of 

 the OTC-injected sharks were at liberty for over one year 

 and were used for validation. In both cases, the expected 

 number of growth bands was deposited on the vertebrae 

 between the date of injection and the date of recapture 

 (Table 1). The shark at liberty for 2.5 years had 3 full 

 bands after the OTC mark, the last band having formed 

 just prior to capture. The OTC-injected shark at liberty 

 for 1.5 years was an adult (189.8 cm FL) at tagging and 

 was aged, by vertebrae, to be 11 years at recapture. This 



