Tribuzio et al.: Age and growth of Squalus acanthias in the Gulf of Alaska 
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Table 3 
Summary of the parameters used in the worn-band estimation models and model fits for spiny dogfish (Squalus acanthias). The 
observed data are sample data, the band-diameter data were determined from a subsample of unworn spines where the diam- 
eter of each band was measured to simulate bound count at spine size for younger animals that were not sampled in this study. 
Regression models are ordinary least squares (OLS), weighted ordinary least squares (WOLS), nonlinear least squares (NLS) 
and weighted nonlinear least squares (WNLS). Estimated model parameters (95% confidence intervals in parentheses) and 
goodness-of-fit indicator AIC, the Akaike information criteria. 
Model 
Parameter 
Observed sample data 
ti = 685 
Observed band-diameter data 
71 = 3877 
Estimate 
AIC 
Estimate 
AIC 
OLS 
b o 
2.690(1.952-3.708) 
6.205 
0.211 (0.199-0.223) 
3.738 
K 
1.135 (0.949-1.322) 
2.867(2.825-2.910) 
WOLS 
\ 
2.471 (1.788-3.415) 
6.219 
0.212 (-0.201-0.224) 
3.721 
K 
1.179(0.991-1.367) 
2.856(2.814-2.898) 
NLS 
b o 
4.325 (3.400-5.444) 
4.016 
0.539(0.487-0.594) 
3.781 
b. 
0.955 (0.807-1.111) 
2.241 (2.178-2.309) 
WNLS 
b o 
4.009 (3.106-5.231) 
4.018 
0.528 (0.475-0.586) 
3.763 
K 
0.998(0.826-1.164) 
2.247 (2.180-2.318) 
more variable for band counts less than 20 (Fig. 3F). 
The CV between all three readers was generally low 
(<30%) for band counts less than 30, and there was 
a notable increase in the variability and CV for band 
counts greater than 30. 
Spiny dogfish spines grow in a predictable pattern 
with age (Fig. 4). The brownish-black banded, enameled 
portion of the spine grows in length at a faster rate 
than the white base portion. 
Inclusion of the back-calculated band diameter 
data dramatically changed the worn band estima- 
tion models (Fig. 5), and therefore further worn band 
estimations were made with both the observed and 
back-calculated band diameter data. There were no 
significant differences between the estimated worn- 
band model parameters, but the WOLS model had 
the lowest AIC value and therefore was chosen as the 
best-fit model (Table 3). Alternative fits to the WOLS 
and WLNS models, based on weightings by using the 
inverse variance in assigned ages for each readability 
category, yielded very similar parameter values and 
nominally poorer fits indicated by slightly larger AIC 
values (not shown). A high degree of natural varia- 
tion resulted in wide 95% confidence intervals for all 
parameters. Moreover, parameter confidence inter- 
vals for the WOLS GOA model widely overlapped the 
parameter confidence intervals for the Hecate Strait 
and Strait of Georgia models (McFarlane and King, 
2009). Although the parameters were not statistically 
significantly different, the GOA, Hecate Strait, and 
Strait of Georgia models appear to represent biologi- 
cally meaningful differences in growth (Fig. 5). The 
Hecate Strait and Strait of Georgia models tend to 
overestimate the band count for larger spines and 
underestimate for smaller spines of spiny dogfish col- 
lected from the GOA. 
0 10 20 30 40 50 60 70 80 90 100 
Size class (cm) 
Figure 4 
Relationship between mean second dorsal spine 
length and fish size determined from unworn spines 
from spiny dogfish ( Squalus acanthias) collected 
in the Gulf of Alaska. The top line is spine total 
length ( TL ) and bottom line is base length ( BL ) in 
millimeters. Numbers above upper line represent the 
sample size for each 10-cm size class. Solid vertical 
lines represent 95% confidence intervals. The dashed 
vertical line represents the approximate size at birth 
(Ketchen, 1972). 
Fitting of growth models 
The two-phase vB models fitted the observed data best 
for males and females based on AIC values (Fig. 6, A 
and D, Tables 4 and 5). For males, the two-phase model, 
where L 0 was used from model 1 (model 3b), was the 
best fit and for females, it was the model where L 0 was 
estimated from model 1 (model 3b). Estimated (and 95% 
