Ballagh et ai.: Methods for determining length-at-age for two large scombrids 
91 
back-calculation allow the estimation of lengths-at- 
ages that are rarely observed, particularly in the 
absence of a representative sample because of gear 
selectivity (Lopez-Abelian et al., 2008), or to increase 
the amount of length-at-age data to be used in fitting 
a growth curve (e.g., Shafi and Jasim, 1982; Grudtsev 
and Korolevich, 1988). 
Temporal and spatial variation in growth can have 
significant implications for the assessment and man- 
agement of exploited populations (Rahikainen and 
Stephenson, 2004). However, variation in growth 
from estimation error is also likely to have significant 
implications for stock assessment, and accounting 
for bias in growth estimation is not always feasible 
(Gwinn et al., 2010). Substantial differences in growth 
estimates have previously been demonstrated from 
different methods for determining length-at-age from 
otoliths and other hard parts (e.g., Lucena and O’Brien, 
2001; Ballagh et al., 2006). We examine the effects of 
several different methods for determining length-at-age 
from otoliths. 
Here we compared estimates of growth derived from 
several commonly used methods for obtaining length-at- 
age data from otoliths. We applied this approach to the 
otoliths of two large scombrids, narrow-barred Spanish 
mackerel ( Scomberomorus commerson ) and broad-barred 
king mackerel ( Scomberomorus semifasciatus), to test 
for differences in growth attributable to the methods 
used, and to make inferences about which method(s) 
provides the most appropriate estimate of length-at-age 
for growth estimation. Scomberomorus commerson and 
S. semifasciatus are fast growing species and it was 
expected that differences in growth estimates from 
different length-at-age data would be clearer than 
those for slower growing species. We also examined 
the effects on growth estimates when length-at-age data 
from different methods are combined, such as when 
back-calculated and observed length-at-age data are 
combined (e.g., Lopez-Abelian et al., 2008). 
Materials and methods 
Samples of S. commerson were collected from several loca- 
tions along the east coast of Queensland from commercial 
and recreational fishermen using various hook-and- 
line gears, and S. semifasciatus samples were collected 
from the east coast of Queensland, Gulf of Carpentaria, 
and the Northern Territory from commercial fishermen 
using gillnets of various mesh sizes. A small number of 
juveniles of each species were collected by beam trawl 
from the east coast of Queensland. 
Length-at-age and growth 
For each mackerel species five methods of determining 
length-at-age from otoliths were investigated: 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). 
Table 1 
Description of otolith margin categories used in age adjust- 
ment of Scomberomorus commerson and S. semifasciatus. 
Margin category 
Description 
0 
Complete and continuous opaque 
band formed around edge of otolith, 
and no translucent material beyond 
the last opaque band 
I 
Translucent band laid onto the outer 
edge comprising 1/4— 1/3 the width of 
the previous translucent band 
II 
Translucent band laid onto outer 
edge comprising roughly Vi the width 
of the previous translucent band 
III 
Opaque band present on edge; how- 
ever, is not continuous or complete 
Otoliths were aged, measured, and back-calculation 
of previous length-at-age for both species was done by 
using identical methods (Ballagh et al., 2006; Tobin and 
Mapleston 1 ; Welch et al. 2 ). Observed length-at-age was 
defined as the agreed upon count of complete opaque 
increments (annuli) from multiple readings (up to three) 
of each otolith, coupled with the fork length of the fish 
at capture. Back-calculation of previous length-at-age 
was done by using the body proportional hypothesis 
described by Francis (1990) with the parameters from 
linear geometric mean regression of otolith radius on 
fork length (e.g., Ballagh et al., 2006). 
Two methods for age adjustment were investigated 
in this study: category adjustment, and formula 
adjustment. Category adjustment was based on simple 
criteria whereby the observed age of each otolith was 
adjusted for the marginal increment at the outer edge 
of the otolith, which was categorized according to a 
system (margin category, Table 1, Fig. 1). Otoliths for 
which there was agreement in the annuli count were 
assigned a final margin category if any two of the 
margin categories from multiple readings for a single 
otolith were the same. For final margin categories of 
0 or I, no age adjustment was deemed necessary and 
the agreed upon count of annuli was accepted as the 
1 Tobin, A. J., and A. Mapleston. 2004. Exploitation 
dynamics and biological characteristics of the Queensland 
East Coast Spanish mackerel ( Scomberomrous commerson) 
fishery. CRC Reef Research Centre Technical Report No 51, 
61 p. CRC Reef Research Centre, Townsville, Australia. 
2 Welch, D. J., R. C. Buckworth, J. R. Ovenden, S. J. Newman, 
D. Broderick, R. J. G. Lester, A. C. Ballagh, J. M. Stapley, 
R. A. Charters, and N. A. Gribble. 2009. Determination 
of management units for grey mackerel fisheries in northern 
Australia. Final Report, Fisheries Research and Development 
Corporation Project 2005/010. Fishing and Fisheries Research 
Centre Technical Report No. 4, 158 p. Fishing and Fisheries 
Research Centre, James Cook University, Townsville, 
Australia. 
