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Fishery Bulletin 109(1 ) 
final age because marginal increment growth beyond 
a complete annulus, and thus a whole year, was 
considered to be negligible. Final margin categories 
of II were considered to be closer to half a complete 
annulus, and thus the equivalent of growth for half 
a year, and therefore the age was adjusted by adding 
0.5 to the count of annuli to give the final age. For 
otoliths with a final margin category of III, the 
marginal increment was considered to be close to a 
whole annulus and therefore the age was adjusted 
by adding one to the agreed upon count of annuli. 
For otoliths with margin categories that were not 
the same, the higher of the category estimates was 
accepted as the final margin category and age was 
adjusted accordingly. 
For otoliths with no agreed upon age, it was still 
possible to assign an adjusted age in some cases on 
the basis of the margin increment category and the 
age estimates. If multiple age estimates were no 
more than one year apart, the margin category of 
the higher age was 0 or I, and the margin category 
for the lower age estimate was III, the adjusted age 
was accepted as the higher of the two age estimates. 
If there was still no agreement between readings on 
ages and margin categories, the otolith was rejected 
for age adjustment. Less than 0.5% of all otoliths 
were rejected for age adjustment. 
Formula adjustment was based on a modification of 
the age adjustment algorithms used in Williams et al. 
(2008). The age adjustment formula corrected for the 
collection of samples across different months of the 
year by adjusting observed-age estimates to account for 
the period of annuli formation, spawning period (birth 
date), and the date of capture. The following algorithms 
were used to adjust age estimates: 
If IV = 0, age m = m c , (1) 
If N > 0, age m =((N -l)xl2) + m h + m c , (2) 
where N = number of complete annuli; 
age m = age in months; 
m b = number of months from the assigned birth 
date to the assigned date of annuli forma- 
tion; and 
m c = number of months from the assigned date of 
annuli formation to the date of capture. 
It was inferred from previous studies that the pe- 
riod of annuli formation coincides with the spawning 
period for both species (McPherson, 1992, 1993; Tobin 
and Mapleston 1 ; Welch et al. 2 ; Cameron and Begg 3 ). 
The birth date and date of annulus completion was 
3 Cameron, D., and G. Begg. 2002. Fisheries biology and 
interaction in the northern Australian small mackerel 
fishery. Final report to the Fisheries Research and 
Development Corporation, projects 92/144 and 92/144.02, 
236 p. Department of Primary Industries, Brisbane, 
Queensland, Australia. 
Figure 1 
Otolith of narrow-barred Spanish mackerel ( Scomberomorus 
commerson ), showing the margin categories used in age 
adjustment (see Table 1). In this example a complete opaque 
band (annulus) is visible at the otolith margin (margin 
category=0, adjusted age = 2). 
assigned as 1 November, which represents the mid 
spawning period for both species (McPherson, 1993; 
Welch et al. 2 ; Cameron and Begg 3 ). As a result, the time 
between spawning (birth date) and the timing of annuli 
formation ( m b ) was assigned as 12 months. 
All analyses were done separately for females and 
males as previous studies have shown both species have 
sexually dimorphic growth (McPherson, 1992; Ballagh 
et al., 2006; Welch et al. 2 ; Cameron and Begg 3 ). The 
von Bertalanffy growth function (VBGF, Beverton and 
Holt, 1957) was used to describe the growth of both 
species for all length-at-age data and is described by 
the following equation: 
L t = LJl-e^ K(t ~ to)) ), (3) 
where L t = length at age t; 
L, = theoretical maximum length; 
K = growth coefficient or the rate at which L ¥ is 
asymptotically reached; and 
t 0 = theoretical age where length is equal to zero. 
VBGF curves were fitted to length-at-age data by non- 
linear regression. Likelihood ratio tests (Kimura, 1980) 
were used to test for differences in growth among the 
different methods for estimating length-at-age for both 
species. Likelihood ratio tests were used to test for 
overall differences in growth (all parameters assumed 
equal), as well as differences in individual parameters 
of the VBGF. Data were truncated for all likelihood 
ratio tests so that equivalent age ranges were compared 
(Haddon, 2001). Where differences were found, mul- 
tiple comparisons were performed by using likelihood 
