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Columbia (Beamish and McFarlane, 1985; McFarlane 
and Beamish, 1987). Moreover, radioactive carbon iso- 
topes absorbed into spiny dogfish spines provided age 
estimates that agree with previous aging results for the 
British Columbia spiny dogfish (Campana et ah, 2006) 
and verified that periodicity is annual, even at old ages 
(Campana, 2001). We assumed that this annual peri- 
odicity of band formation in spiny dogfish, which was 
confirmed for this species in British Columbia, also ap- 
plies to fish from the GOA. Because spiny dogfish from 
British Columbia have different age characteristics 
(e.g., worn band curves, Fig. 5) from those of the GOA, 
it is possible that the pattern of band deposition may 
also differ. 
Sampling bias was considered by examining potential 
differences in average size at age among gear type and 
location of capture. Because there were no significant 
differences among the average size at age with the 
different gear types used or the areas sampled, we do 
not believe that sampling bias was a significant factor 
affecting our results. However, the lack of significant 
differences in our study should not be misconstrued to 
rule out considerations of sampling bias in future spiny 
dogfish studies, because this species may school by size 
and sex (Nammack et al., 1985; Ketchen, 1986). 
In the western North Atlantic Ocean commercial 
fisheries target the largest and oldest age classes (Rago 
et al., 1998). Thus, the size-frequency distributions 
determined from commercial catches may not be repre- 
sentative of the full size range of fish in the population. 
Moreover, depletion of large old fish from the population 
by heavy exploitation means that subsequent research 
surveys may not catch a representative sample of the 
full size and age ranges of the population. In the GOA, 
spiny dogfish are taken as bycatch in multiple fisheries. 
In some cases, dogfish bycatch is largely unaccounted 
for, owing to the lack of observers on small (<60-ft) ves- 
sels, such as those vessels with salmon gill nets, as well 
as some longline vessels targeting halibut and sablefish, 
resulting in an unknown level of total fishing mortal- 
ity (Courtney et al., 2006). However, in the GOA, it is 
unlikely that the fishing mortality has truncated the 
size distribution of spiny dogfish because spiny dogfish 
are not targeted and recent (2006) estimates of spiny 
dogfish biomass are 80-100% of the estimated theoreti- 
cal population carrying capacity (Rice, 2007). Therefore, 
it is unlikely that the fishery has created size-selective 
impacts that would lead to erroneous selection of the 
two-phase models as the best-fit models (Braccini et 
al., 2007). 
One limitation of our size-frequency distributions 
is the absence of spiny dogfish smaller than 50 cm 
TL ext . The lack of samples from smaller spiny dogfish is 
likely due to fishery-dependent opportunistic sampling 
which apparently occurs in areas devoid of juvenile 
spiny dogfish. Examination of NMFS spring and fall 
trawl surveys along the U.S. east coast revealed that 
in spring most juveniles were caught in water between 
50 and 150 m deep (range: 7-390 m) in offshore waters 
from North Carolina to the eastern edge of Georges 
Bank, whereas in fall most were caught between 25 
and 75 m (range: 12-366 m) in various locations, such 
as on Georges Bank, Nantucket Shoals, and throughout 
the Gulf of Maine (McMillan and Morse, 1999). Spiny 
dogfish smaller than 50cm TL ext have been surveyed in 
both Puget Sound, Washington (Tribuzio et al., 2009), 
and in the northern Strait of Georgia (McFarlane et 
al., 2006) by using bottom trawl gear. In this study, 
we made numerous unsuccessful attempts to capture 
juvenile dogfish smaller than 50 cm TL ext in the GOA 
using sport and longline gear in Yakutat Bay, long- 
line gear with small (10/0 circle) hooks in Southeast 
Alaska (K. Munk, personal commun. 1 ), and commercial 
bottom trawls off Kodiak Island (J. Gauvin, personal 
commun. 2 ). 
A missing size group, such as small dogfish in our 
case, may cause growth models to overestimate t 0 or L 0 , 
thus decreasing the k estimate. Further, this missing 
size group may have caused the age of transition, t h , in 
the two-phase models to be underestimated. Also, the 
lack of small animals may have limited our ability to 
discriminate among competing growth models. We used 
band-diameter data and back-calculated lengths derived 
from unworn spines to attempt to address this data 
gap. The inclusion of the band-diameter data greatly 
improved the worn-band estimation models, but mini- 
mally changed the growth models. Few of the estimated 
growth model parameters based on the back-calculated 
and mean back-calculated data were significantly dif- 
ferent from those estimated from the observed data 
alone. 
Back-calculation methods are designed to be used 
when sample sizes are small or if sampling has not oc- 
curred each month (Cailliet and Goldman, 2004), but 
in this case it was the entire smaller end of the size 
range that was being estimated. With the modified 
Fraser-Lee size-at-birth method, we had to assume that 
average size at birth was known. We use 26.2 cm, which 
is based on data collected from spiny dogfish inside the 
Strait of Georgia, British Columbia (Ketchen 1972). 
Sizes at birth are reportedly similar for the species 
across the northern hemisphere, with ranges of 23-30 
cm (Ketchen 1972, Tribuzio et al. 2009). We also as- 
sumed that 2.45 mm was the spine diameter at birth, 
based on studies of British Columbia spiny dogfish (Mc- 
Farlane and King 2009). Because this is an average as 
well, it is likely that some spines were classified as “un- 
worn” when they were actually “worn.” Spines that are 
classified as “unworn” can lead to underestimating the 
age, and in the case of the back-calculation resulted in 
instances where 20 cm or more of growth was predicted 
in the first year. Back-calculations may not be appropri- 
ate for this species when dorsal fin spines are used as 
aging structures, but may work well if a structure such 
as vertebrae are used. 
1 Munk, Kristen. 2007. Alaska Department of Fish and 
Game, Juneau, AK, 99801. 
2 Gauvin, John. 2007. Gauvin and Associates, LLC. Burien, 
WA 98166. 
