98 
Fishery Bulletin 109(1 ) 
Table 5 
Chi-squared values for overall likelihood ratio tests between growth estimates from different combinations of substituted meth- 
ods (observed [Obsv], category adjusted [Adj-cat], formula adjusted [Adj-frm], back-calculation to all annuli [BC-all], and back- 
calculation to the last annulus only [BC-last]) of estimating length-at-age for Scomberomorus commerson and S. semifasciatus 
(* indicates significant difference at P<0.0033, a was Bonfferoni adjusted for multiple comparisons, df=3). 
Species Sex 
Methods 
BC-all- 
Adj-cat 
X 2 
BC-all- 
Adj-frm 
X 2 
BC-last- 
Obsv 
X 2 
BC-last- 
Adj-cat 
X 2 
BC-last- 
Adj-frm 
X 2 
S. commerson Female 
BC-all-Obsv 
0.087 
0.434 
13.8* 
13.0 
12.6 
BC-all- Adj-cat 
0.138 
15.3* 
14.4* 
13.7 
BC-all-Adj-frm 
16.5 * 
15.4* 
14.3* 
BC-last-Obsv 
0.073 
0.680 
BC-last-Adj-cat 
0.349 
Male 
BC-all-Obsv 
0.193 
0.428 
11.2 
10.4 
9.6 
BC-all-Adj-cat 
0.050 
12.7 
11.6 
10.5 
BC-all-Adj-frm 
14.0* 
12.6 
11.3 
BC-last-Obsv 
0.203 
0.719 
BC-last-Adj-cat 
0.220 
S. semifasciatus Female 
BC-all-Obsv 
0.001 
0.709 
0.957 
0.853 
0.103 
BC-all-Adj-cat 
0.802 
0.992 
0.879 
0.110 
BC-all-Adj-frm 
3.6 
3.5 
0.538 
BC-last-Obsv 
0.020 
1.8 
BC-last-Adj-cat 
1.6 
Male 
BC-all-Obsv 
0.199 
5.5 
0.529 
1.346 
8.8 
BC-all-Adj-cat 
3.9 
0.581 
0.934 
6.7 
BC-all-Adj-frm 
6.2 
4.9 
1.9 
BC-last-Obsv 
0.374 
9.0 
BC-last-Adj-cat 
6.3 
years (Gwinn et al., 2010). Recently, several different 
methods for reducing bias in growth estimates from 
length-at-age data from size-selective samples have 
been proposed, including multinomial estimation models 
(Taylor et al., 2005), multigrowth model inference 
(Thorson and Simpfendorfer, 2009) and biologically 
based von Bertalanffy fitting procedures (Gwinn et al., 
2010 ). 
Substitution was shown to be a potentially useful 
method for providing more accurate estimates of popu- 
lation growth than the individual methods alone in 
the presence of selectivity pressure for faster grow- 
ing young fish. Given that a significant difference in 
growth was observed between data substituted with 
the two different back-calculation methods for S. com- 
merson, it is presumed that back-calculating data to all 
annuli would be the most appropriate back-calculation 
method to use in substitution in this instance given the 
selectivity bias observed in the young age classes. We 
therefore recommend that back-calculated length-at-age 
data from all annuli for young age classes be combined 
with observed or adjusted length-at-age data from older 
age classes to estimate population growth in the pres- 
ence of selectivity favoring faster growing younger fish. 
Further studies should be undertaken to investigate the 
appropriateness of different methods for length-at-age 
determination and the effectiveness of substitution for 
species with different growth characteristics and under 
different selectivity regimes of fisheries. 
Acknowledgments 
The authors would like to thank members of the Fish- 
ing and Fisheries Research Centre for their support. 
The Fisheries Research and Development Corporation 
(projects 2001/019 and 2005/010), the School of Earth 
and Environmental Sciences of James Cook University, 
and the CRC Reef Research Centre provided funding 
and support for this study. This manuscript was greatly 
improved by thorough reviews from anonymous reviewers. 
Literature cited 
Ballagh, A. C., G. A. Begg, A. Mapleston, and A. Tobin. 
2006. Growth trends of Queensland east coast Spanish 
mackerel ( Scomberomorus commerson ) from otolith back- 
calculations. Mar. Freshw. Res. 57:383-393. 
Begg, G. A., S. E. Campana, A. J. Fowler, and I. M. Suthers. 
2005. Otolith research and application: current direc- 
tions in innovation and implementation. Mar. Freshw. 
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