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Fishery Bulletin 108(2) 
~o 
Enamel-base diameter (EBD) (mm) 
Figure 5 
Relationship of band count to enamel-base diameter for spiny 
dogfish ( Squalus acanthias ) collected in the Gulf of Alaska (GOA) 
between 2004 and 2007. The best-fit model (weighted ordinary 
least squares [WOLS]) for (A) the observed data only and (B) 
the observed data with the band-diameter data; both sections A 
and B show the published best-fit relationships for spiny dogfish 
collected from Hecate Strait and the Strait of Georgia, British 
Columbia (McFarlane and King, 2009) for comparison. 
confidence limits) asymptotic lengths (LJ were 
87.2 cm (range 85.3-90.0 cm) and 102.5 cm 
(range 99.9-106.3 cm) and growth coefficients 
( k ) were 0.106 (range 0.097-0.117) and 0.058 
(range 0.052-0.063) for males and females, 
respectively. After including the back-calculated 
data and the mean back-calculated data, the 
two phase models were no longer the best fit 
for males. The best-fit model with inclusion of 
back-calculated data was model 2, and model 
1 fitted best for the data including the mean 
back-calculated data. Similarly, for females the 
two-phase models were not the best-fit based 
on AIC values after the inclusion of back-cal- 
culated and mean back-calculated data: model 
6 was the best fit with inclusion of back-calcu- 
lated data, and model 5c (with L 0 from model 
1) was the best fit for the data including the 
mean back-calculated data (Tables 4 and 5, Fig. 
6, B, C, E, F). 
Predicted length at age was similar for males 
and females for the observed data, up to about 
age 15, when a transition between growth 
phases occurred (Fig. 6). After the transition, 
females continued to grow at a faster rate and 
to larger sizes than males (Fig. 6, A and D). At 
the point of transition in the two-phase models 
growth increased for about five years before 
slowing, for both sexes. 
Discussion 
The model fits for all 10 examined growth 
models were similar and had very small dif- 
ferences in AIC, but the estimated parame- 
ters differed substantially; for example, the 
growth coefficient ( k ) was significantly different 
between some models and thus could impact 
estimates of natural mortality and subsequent 
demographic analyses. The values of k tended 
to fall into two groupings (in both data sets), 
and those models that estimated the higher k 
were also those that estimated lower estimates 
for L x . Interestingly, even with the significantly 
different estimates of k, these estimates were still at the 
lower range of reported growth rates for different types 
of shark species (Cailliet and Goldman, 2004). 
Cailliet et al. (2006) recommended considering more 
than one form of evaluation of model performance and 
considering biological interpretations along with statis- 
tical fit when choosing the best model. Mean squared 
error and the correlation coefficient (r 2 ) were also cal- 
culated for each model, but determinations of best fit 
by the above criteria did not differ from those where 
AIC was used and therefore are not reported. For the 
observed data models 3a and 3b were the statistical 
best fit for males and females, respectively. However, 
the two-phase models tended to be unstable and would 
converge at different localized minima, depending on 
the starting value. A further consideration for the two- 
phase models is that the growth curve indicates a pe- 
riod of rapid growth immediately following the age at 
transition. 
The purpose of a two-phase model is to incorporate 
changes in energy allocation as animals grow: imma- 
ture fish use surplus energy for growth, whereas ma- 
ture fish use surplus energy for reproduction (Soriano 
et al., 1992). Thus, the rate of growth changes after 
maturation. In our case, the transition between the two 
growth phases occurred before the age at 50% maturity 
for both males and females The early age at transition 
and the period of rapid growth after transition indi- 
cate that for female spiny dogfish there is a “growth 
spurt” about 15 years before age at 50% maturity. For 
