Natanson e! a\ Age and growth of Lamnus nasus in the western North Atlantic 



267 



Materials and methods 



Vertebral aging 



Vertebral samples from porbeagle sharks were obtained 

 between 1966 and 1999 on board commercial and research 

 vessels. The majority of samples idT'i) were collected 

 after 1990 on Canadian commercial longline vessels. Sam- 

 pling took place in U.S. and Canadian waters between 

 Massachusetts (NE U.S.) and the Grand Banks (off south- 

 ern Newfoundland) and all individuals were treated as 

 belonging to the same stock on the basis of tagging data 

 (Campana et al.-). Multiple vertebrae were removed from 

 the area just above the branchial chamber wherever pos- 

 sible; except on commercial vessels where samples were 

 obtained closer to the head. Vertebrae were then stored 

 frozen or in VO'^f ETOH until processing. 



Only samples that had measured fork length (FL — tip 

 of the snout to the fork in the tail, over the body) or total 

 length (TL — tip of the snout to a point on the horizontal 

 axis intersecting a perpendicular line extending down- 

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

 angle, over the body; Kohler et al., 1995) were used. All 

 lengths reported in this document are over-the-body FL 

 unless othei-wise noted. Total length in centimeters (cm) 

 can be converted to FL cm by using the regression equa- 

 tion (Campana et al.M: 



FL = 0.885(rLi + 0.99 



[n = 361 ;--=0.99]. 



One vertebra from each sample was removed for processing. 

 The centrum was sectioned by using a Ray Tech Gem saw 

 with two diamond blades separated by a 0.6-mm spacer. 

 Each centrum was cut through the middle along the sagit- 

 tal plane and the resulting "bow-tie" sections were stored 

 individually in capsules in TOVf ETOH. Each section was 

 digitally photographed with a MTI CCD 72 video camera 

 attached to a SZX9 Olympus stereo microscope by using 

 reflected light. Magnification depended on the size of the 

 section and varied from 4x to 12. 5x. Band pairs (consisting 

 of one opaque and one translucent band) were counted and 

 measured from the images by using Image Pro 4 software 

 (Media Cybernetics, 1998). Measurements were made from 

 the midpoint of the isthmus of the full bow-tie to the middle 

 of the opaque growth bands at points along the internal 

 edge of the corpus calcareum (Fig. 1). The vertebral radius 

 (VR) of each centrum was measured from the midpoint of 

 the isthmus to the distal margin of the intermedialia along 

 the same diagonal as the band measurements. 



The identity of the birth band in the vertebra was con- 

 firmed through comparison of the birth band radius (BR) 

 measurements to vertebral radius measurements of late- 

 term embryos, early young-of-the-year, and late age-0 fish. 



- Campana, S., L. Marks. W. Joyce, P. Hurley, M. Showell, D. 

 Kuika. 1999. An analytical assessment of the porbeagle shark 

 iLamna nasus) population in the northwest Atlantic. Cana- 

 dian Stock Assessment Secretariat Research Document 99/158. 

 57 p. Marine Fish Division, Bedford Institute of Oceanogra- 

 phy, P.O. Box 1006, Dartmouth, Nova Scotia, Canada B2Y 4A2. 



The late-term embryo vertebral samples were obtained 

 from the South Pacific porbeagle population, courtesy of 

 Malcolm Francis.'' The assumptions were made that verte- 

 bral growth ;/( utero was comparable between the two pop- 

 ulations and that measurements of the rehydrated dried 

 South Pacific vertebrae were similar to those from wet 

 NW Atlantic preparations. 



The relationship between VR and FL was calculated in 

 order to confirm the interpretation of the birth band and 

 to determine the best method for back-calculation of size- 

 at-age data. The FL to VR relationship was curvilinear; 

 therefore, the data were In-transformed before linear re- 

 gression. The Fraser-Lee equation of the In-transformed 

 data was derived for back calculation: 



ln(FL„ ) = h + (InlFL,, \-h)(\n radius,, } 



{\n radius,) 



where a = age; 



b = intercept from the FL-VR regression; and 

 c = capture. 



Validation 



The accuracy of the vertebral band pair counts as annual 

 indicators was determined by using both known-age recap- 

 tures and recaptures of oxytetracycline (OTC)-injected 

 and tagged individuals. Vertebrae from young of the year 

 ( YOY) sharks whose FL was measured at both tagging and 

 recapture were used for known-age analyses. Band pair 

 counts were compared with time at liberty to determine 

 band pair periodicity. One hundred and fifty-five porbea- 

 gles of various lengths were also tagged and injected with 

 25 nig/kg of OTC (senior author, unpubl. data) Returned 

 vertebrae from these sharks were examined with reflected 

 UV light for the OTC mark. The number of band pairs 

 distal to the OTC mark were then compared with the 

 number of years at liberty. 



Data analysis 



Aging bias and precision of annulus counts were exam- 

 ined by using age-bias plots and the coefficient of varia- 

 tion (Campana et al., 1995). Two readers independently 

 counted 100 vertebral sections from which the pair-wise 

 age-reader comparisons were generated. 



Von Bertalanffy growth functions (VBGF) were fitted 

 to the length-at-age data by using the following equation 

 (von Bertalanffy, 1938): 



LJl 



.g-K"-WI) 



where L, = predicted length (cm) at age /; 



L = mean theoretical maximum fork length; 

 K = a growth rate parameter (per yr); and 

 tg = the theoretical age (yr) at zero length. 



■' Francis, M. 2000. Personal commun. National Institute of 

 Water and Atmospheric Research P.O. Box 14-901, Wellington, 

 New Zealand. 



