Tribuzio et al.: Age and growth of Squalus acanthias in the Gulf of Alaska 
127 
Female 
Age (years) 
Figure 6 
Model fits for male (A-C) and female (D-F) spiny dogfish ( Squalus acanthias) length-at-age data. 
(A and D) Best-fit growth models based on the observed sample data; (B and E) best-fit growth 
models based on the observed sample data and the back-calculated data; and (D and F) best-fit 
growth models based on the observed sample data and the mean back-calculated data. n obs is the 
number of samples, n back is the number of data points created through back calculation of the ages 
from band-diameter data, and is the number of mean back-calculated data points. 
’ mean 1 
males, the pattern was similar, but occurred just before 
age at 50% maturity. This finding does not follow the 
theory behind the two-phase model and indicates that 
a two-phase model may not be most appropriate in this 
situation. 
The two-phase vB model by Soriano et al. (1992) has 
been examined with data sets from many species of 
sharks to determine whether it is an adequate descrip- 
tor of shark growth (Araya and Cubillos, 2006). Where- 
as the two-phase model was better than the standard 
vB model in 8 of 11 species for females and 7 of 11 for 
males, the two-phase model did not perform better than 
the vB (model 1 here) for spiny dogfish. Because Araya 
and Cubillos (2006) included only one spiny dogfish 
population (Black Sea), which appears to have different 
age and growth characteristics from those in the GOA, 
and only examined average length at age data (Avsar, 
2001), we felt that it was worth while to investigate the 
two-phase family of models in this study. Braccini et 
al. (2007) found that the two-phase model was the best 
statistical fit for the piked spurdog, which is a species 
similar to spiny dogfish; however, the resultant mod- 
els showed some of the same characteristic difficulties 
that we encountered. Those results also indicated a de- 
crease in length after transition (Fig. 7, Braccini et al. 
2007) and that the A t parameter appears to change only 
briefly before returning to its original value. Braccini et 
al. did not address these issues as we have attempted 
here. A more comprehensive examination, which would 
include multiple data sets from different regions for 
