96 
Fishery Bulletin 109(1) 
Table 4 
Von Bertalanffy growth function parameter estimates (growth coefficient [K \ , theoretical maximum length [L J , and theoretical 
age where length is equal to zero [t 0 ], ± standard error), sample numbers in), age ranges, and adjusted R 2 values from different 
combinations of substituted methods (observed [Obsv], category adjusted [Adj-cat], formula adjusted [Adj-frm], back-calculation 
to all annuli [BC-al 1 1 , and back-calculation to the last annulus only [BC-last]) for estimating length-at-age for Scomberomorus 
commerson and S. semifasciatus. 
Species Sex 
BC data 
Method 
K 
(mm) 
t 0 (years) 
n 
Min age 
Max age 
* 2 a dj 
S. commerson Female 
BC-all 
Obsv 
0.41 (0.02) 
1319(17) 
-0.60 (0.07) 
741 
1 
15.0 
0.84 
BC-all 
Adj-cat 
0.43 (0.02) 
1304 (16) 
-0.55(0.07) 
747 
1 
11.0 
0.84 
BC-all 
Adj-frm 
0.44(0.02) 
1295 (15) 
-0.53 (0.07) 
750 
1 
11.9 
0.84 
BC-last 
Obsv 
0.29 (0.03) 
1411 (33) 
-1.30(0.19) 
263 
1 
15.0 
0.87 
BC-last 
Adj-cat 
0.31 (0.03) 
1383(29) 
-1.18 (0.17) 
268 
1 
11.0 
0.87 
BC-last 
Adj-frm 
0.32 (0.03) 
1366 (26) 
-1.14 (0.17) 
271 
1 
11.9 
0.87 
Male 
BC-all 
Obsv 
0.60(0.04) 
1092(12) 
-0.39 (0.08) 
562 
1 
11.0 
0.81 
BC-all 
Adj-cat 
0.63 (0.04) 
1084 (12) 
-0.35(0.08) 
561 
1 
11.0 
0.81 
BC-all 
Adj-frm 
0.64(0.04) 
1081 (11) 
-0.34 (0.07) 
573 
1 
11.0 
0.82 
BC-last 
Obsv 
0.54(0.06) 
1118 (15) 
-0.62(0.17) 
191 
1 
11.0 
0.84 
BC-Last 
Adj-cat 
0.58(0.06) 
1108 (14) 
-0.55 (0.16) 
190 
1 
11.0 
0.84 
BC-Last 
Adj-frm 
0.57 (0.06) 
1103 (13) 
-0.57 (0.15) 
202 
1 
11.0 
0.84 
S. semifasciatus Female 
BC-A11 
Obsv 
1.02 (0.06) 
830(7) 
0.18 (0.04) 
828 
1 
9.0 
0.81 
BC-A11 
Adj-cat 
1.02 (0.05) 
830 (7) 
0.18 (0.04) 
846 
1 
9.0 
0.82 
BC-A11 
Adj-frm 
1.08 (0.06) 
821 (6) 
0.21 (0.04) 
894 
1 
9.0 
0.82 
BC-Last 
Obsv 
0.95 (0.07) 
841 (8) 
0.12 (0.07) 
295 
1 
9.0 
0.80 
BC-Last 
Adj-cat 
0.95 (0.07) 
840(7) 
0.12 (0.07) 
312 
1 
9.0 
0.80 
BC-Last 
Adj-frm 
1.02 (0.07) 
828 (6) 
0.17 (0.06) 
359 
1 
9.0 
0.79 
Male 
BC-A11 
Obsv 
1.03 (0.06) 
790(7) 
0.14 (0.04) 
748 
1 
10.0 
0.80 
BC-A11 
Adj-cat 
1.04(0.06) 
787(7) 
0.15(0.04) 
774 
1 
10.0 
0.80 
BC-A11 
Adj-frm 
1.13 (0.06) 
771 (6) 
0.18 (0.04) 
825 
1 
10.6 
0.79 
BC-Last 
Obsv 
0.96(0.06) 
794(6) 
0.08(0.06) 
306 
1 
10.0 
0.83 
BC-Last 
Adj-cat 
0.96 (0.06) 
791 (6) 
0.07 (0.06) 
332 
1 
10.0 
0.83 
BC-Last 
Adj-frm 
1.00 (0.06) 
776(5) 
0.07 (0.06) 
383 
1 
10.6 
0.78 
Observed length-at-age, although being relatively 
easy to obtain compared to other data, can have the 
most aging error given that any growth beyond a whole 
year is not accounted for. The magnitude and frequency 
of aging error has been shown to be uniform across 
all ages for S. semifasciatus (Marriott et ah, 2010). 
However, given the rapid growth of such species in the 
first few years, aging error for younger ages will have 
more influence on growth estimates than aging error in 
older ages. Although this problem can be exacerbated 
for fast growing species such as S. commerson and S. 
semifasciatus , uniform aging error across age classes 
may be a lesser issue for growth estimation of long- 
lived, slow growing fish, and observed length-at-age 
could be more accurate if samples are collected after the 
period of annuli formation and the opaque increment at 
the edge is included in age estimates. 
Adjustment methods for determining length-at-age 
theoretically provide a more accurate estimate of age 
than observed length-at-age by accounting for growth 
on a finer temporal scale, especially if the spawning 
period and period of annuli formation is discrete (e.g., 
DeVries and Grimes, 1997). The formula-adjustment 
method, however, is useful only if population-specific 
spawning and annuli formation periods are known 
for a given species, and it is less useful if the species 
has a protracted spawning period or if the timing of 
annuli formation varies (e.g., Williams et al., 2005). The 
category-adjustment method is useful for assigning ages 
to cohorts for use in assessment models (Begg et al. 4 ) 
as well as for estimating growth (Shepard et al., 2010). 
Back-calculation is useful for estimating selectivity 
effects (Campana, 1990; Lucena and O’Brien, 2001; 
Ballagh et al., 2006), providing length-at-age estimates 
for younger fish that may not be seen in fishery- 
dependent samples (Campana, 2001; Lopez-Abelian 
et ah, 2008), providing comparisons between different 
populations (Johnson et al., 1983; Fable et ah, 1987; 
Ballagh et al., 2006), and assessing individual growth 
variability (Fossen et ah, 1999; Pilling et al., 2002). 
4 Begg, G. A., C. C.-M. Chen, M. F. O’Neill, and D. B. 
Rose. 2006. Stock assessment of the Torres Strait Spanish 
mackerel fishery. CRC Reef Research Centre Technical 
Report No 66, 81 p. CRC Reef Research Centre, Townsville, 
Australia. 
