268 



Fishery Bulletin 100(2) 



^?\ 



Figure 1 



Photop'aph of a vertebral section from a porbeagle estimated to be 15* years old. Insert shows 

 higher magnification view of narrow bands at edge. Scale bar = 1 mm. White dots are on annuli. 



The VBGF was calculated by using the nonlinear regres- 

 sion function in Statgraphics. Locally weighted least 

 squares regression (LOESS) curves were fitted to the FL 

 vs. age data for each sex by using Statgraphics (Manguis- 

 tics, 1997). 



Length frequency 



Length-frequency data were obtained from the Canadian 

 International Observer Program operating primarily on 

 the Scotian Shelf, and some data from the Grand Banks. 

 Although the entire data set ( 1986-98) was analyzed, only 

 data from the most complete year ( 1991 ) were used for the 

 final analysis. 



Monthly length-frequency histograms were developed 

 for eight months of 1991 for modal analysis. Calculations 

 of mean fork length and annual growth rate for ages and 

 1 were based on the first two modes of these data, which 

 were easily distinguished and tracked across months. 



MULTIFAN (Fournier et al., 1990) was used to esti- 

 mate the VBGF parameters from the 1991 length-frequen- 

 cy data. The model analyzes multiple length-frequency 



distributions by using a maximum likelihood method to 

 estimate the number of age classes present and VBGF pa- 

 rameters L_ and K. An initial systematic search was con- 

 ducted based on user-supplied K values and age classes. 

 Constraints were placed on the estimates of length at age 

 for the first two age classes. MLILTIFAN allows the user to 

 start with a generalized search and then add parameters 

 to further refine the model. The initial search included es- 

 timates of A' ranging from 0.05 to 0.25 and age classes of 

 11 through 20. The hypotheses tested were the following: 



1 ) constant length standard deviation for all age classes; 



2) variable length standard deviation for all age classes; 3) 

 constant length standard deviation for all age classes with 

 seasonal growth; and 4) variable length standard devia- 

 tion for all age classes with seasonal growth. A model in- 

 corporating constant length standard deviation was fitted 

 first with the additional parameters added sequentially. 

 Results from the four models were compared by using log- 

 likelihood tests following Fournier et al. ( 1990) and Fran- 

 cis et al. ( 1999). 



The von Bertalanffy growth parameter /q was estimated 

 from the equation 



