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Fishery Bulletin 108(2) 
EBD 
— 
Figure 2 
Measurements taken on spiny dogfish ( Squalus acanthias) spines. 
Last readable point (LRP) is the point where the bands are no longer 
visible on the leading edge of the spine (upper edge in this picture). 
EBD = enamel base diameter, SBD = spine base diameter, BL = base 
length, and TL = spine total length, which only applies to spines that 
are unworn. All measurements were taken in millimeters. 
Image Measurement vers 5.0 software 
(Bersoft, Inc., http://bersoft.com). Mea- 
surements included spine base diameter 
(SBD), enamel base diameter (EBD), last 
readable point (LRP, also called the no- 
wear point); and, for nonworn spines, base 
length (BL), and spine total length (TL, 
Fig. 2) were also measured to the near- 
est 0.01 mm. Nonworn spines were those 
spines with a LRP<2Ab mm (McFarlane 
and King, 2009), which is the EBD at 
birth. 
Aging bias and precision were evalu- 
ated for all three readers. Pair-wise age- 
bias plots were used to compare each 
reader against the other two (Campana 
et al., 1995) and a % 2 test for symmetry 
was used to test for statistically significant systematic 
bias among the three readers (Hoenig et al., 1995). 
Readers were considered to be in agreement when ages 
were within 10% of each other rather than within some 
fixed 1- or 2-year age interval. For instance, if reader 
X counted 10 bands, then reader Y’s count would have 
to have been between 9-11 bands to be in agreement, 
but if reader X counted 40 bands, then reader Y’s count 
would have to be between 36-44 to be in agreement. 
We contend that the use of a percentage to define the 
interval size is more appropriate for this long-lived spe- 
cies. Finally, the coefficient of variation (CV) between 
readers was calculated according to Campana’s methods 
(2001). 
Spiny dogfish ages are not always equal to the num- 
ber of counted bands for two reasons: 1) bands are de- 
posited during embryonic development, and 2) because 
the external spines can become worn or can break off. 
This problem was addressed by a correction method 
for estimating the number of missing bands that was 
based on a regression of band counts on the SBD of 
unworn spines (Ketchen, 1975). This method was sub- 
sequently re-examined and accepted as the best avail- 
able method for the original samples plus additional 
samples from the same geographic region (McFarlane 
and King, 2009). 
Various regression approaches were compared to de- 
termine which method resulted in the best model for 
estimating the number of worn bands in spiny dog- 
fish collected from the GOA, including: nonlinear least 
squares regression (NLS, Eq. 1), and ordinary least 
squares (OLS, Eq. 2): 
Band count = b 0 EBD t>1 (1) 
In (Band count) = ln(6 0 ) + ln(EBD)6 1 , (2) 
where b 0 and b x are estimated parameters (based on 
Ketchen 1975, McFarlane and King 2009). Also, we 
fitted parameters for Equations. 1 and 2 with weighted 
nonlinear least squares (WNLS) and weighted ordi- 
nary least squares (WOLS), where weights were applied 
to the residuals as follows: spines in readability cat- 
egory 1 were given a weight of 1, those in category 2 
were weighted by 0.5, and those in category 3 by 0.3. 
These values were chosen to discount the contribution 
of individual length at-age data points to the estimation 
process based on the degree of uncertainty in the age 
estimates for difficult-to-read spines. As an alternative 
to this weighting scheme, we explored the weighting 
process by using the inverse of the variance in assigned 
ages for each readability category. Ages of worn spines 
were then estimated by equating the LRP to the EBD 
in the best-fit model from Equations 1-4 and by adding 
the resultant number of bands to the median band count 
from the three readings and by subtracting two years 
(for bands deposited during gestation) to obtain the final 
estimated age of the animal (Ketchen, 1975). In the case 
of nonworn spines, age was estimated by the median 
band count minus two years. Data for males and females 
were combined for these worn band models. 
Fitting of growth models 
A total of 10 growth model variations were fitted sepa- 
rately to the length-at-age data for males and females 
(Table 2). The growth models included 1) the vB growth 
model for estimating / 0 ; 2) the two-parameter vB with 
fixed L 0 ; 3) the two-phase vB with L 0 (used in the present 
study); 4) the Gompertz; 5) the two-parameter Gompertz; 
and 6) the logistic. For comparison with previous studies 
L 0 is estimated for model 1 by setting /=0. An estimate 
of L 0 (i.e., the size at birth) for GOA spiny dogfish was 
not available; therefore model 2 was run with L 0 fixed 
at 26.2 cm (size at birth for spiny dogfish from British 
Columbia; Ketchen, 1972). Models 3 and 5 were run in 
three different ways: 1) L 0 was estimated by the model; 
2) with L 0 set at the value estimated from model 1; and 
3) with L 0 set at 26.2 cm. Model 3 is an adaptation of 
the two-phase vB model (Soriano et al., 1992). Standard 
fitting procedures with the two-phase model resulted in 
the A t parameter from Soriano et al. (1992) changing for 
a brief time period and then returning to its original 
value. To correct this we reformulated the A t parameter 
from Soriano et al. (1992); this treatment changes k, 
depending on the age of the dogfish, so that A t would 
