90 
Abstract — Fish growth is commonly 
estimated from length-at-age data 
obtained from otoliths. There are 
several techniques for estimating 
length-at-age from otoliths including 
1) direct observed counts of annual 
increments; 2) age adjustment based 
on a categorization of otolith margins; 
3) age adjustment based on known 
periods of spawning and annuli for- 
mation; 4) back-calculation to all 
annuli, and 5) back-calculation to the 
last annulus only. In this study we 
compared growth estimates (von Ber- 
talanffy growth functions) obtained 
from the above five methods for esti- 
mating length-at-age from otoliths for 
two large scombrids: narrow-barred 
Spanish mackerel (Scomberomorus 
commerson) and broad-barred king 
mackerel (Scomberomorus semifascia- 
tus). Likelihood ratio tests revealed 
that the largest differences in growth 
occurred between the back-calcula- 
tion methods and the observed and 
adjusted methods for both species of 
mackerel. The pattern, however, was 
more pronounced for S. commerson 
than for S. semifasciatus , because of 
the pronounced effect of gear selectiv- 
ity demonstrated for S. commerson. 
We propose a method of substituting 
length-at-age data from observed or 
adjusted methods with back-calcu- 
lated length-at-age data to provide 
more appropriate estimates of popu- 
lation growth than those obtained 
with the individual methods alone, 
particularly when faster growing 
young fish are disproportionately 
selected for. Substitution of observed 
or adjusted length-at-age data with 
back-calculated length-at-age data 
provided more realistic estimates of 
length for younger ages than observed 
or adjusted methods as well as more 
realistic estimates of mean maximum 
length than those derived from back- 
calculation methods alone. 
Manuscript submitted 6 January 2010. 
Manuscript accepted 25 October 2010. 
Fish. Bull. 109:90-100 (2011). 
The views and opinions expressed 
or implied in this article are those of the 
author (or authors) and do not necessarily 
reflect the position of the National Marine 
Fisheries Service, NOAA. 
Integrating methods for determining 
length-at-age to improve growth estimates 
for two large scombrids 
Aaron C. Ballagh (contact author ) 1 * 
David Welch 1 2 
Ashley J. Williams ' 3 
Amos Mapleston 1 
Andrew Tobin 1 
Nicholas Marton 4 
Email address for contact author: aaron.ballagh@jcu.edu.au 
1 Fishing and Fisheries Research Centre 
School of Earth and Environmental Sciences 
James Cook University 
Townsville, Queensland 4811, Australia 
'Present address for contact author: Research Services 
James Cook University 
Townsville, Queensland 4811 Australia 
3 Oceanic Fisheries Programme 
Secretariat of the Pacific Community BP D5 
98848 Noumea CEDEX, New Caledonia 
4 Australian Bureau of Agricultural and 
Resource Economics-Bureau of Rural Sciences 
Department of Agriculture, Fisheries and Forestry 
GPO Box 1563 
Canberra, Australian Capital Territory 2601, Australia 
age estimates are not always col- 
lected or treated in the same way, 
either because of sampling bias or 
differences in aging protocols, and it 
is often unknown to what degree dif- 
ferences in length-at-age estimation 
methods affect parameter estimates 
from growth models. 
Obtaining length-at-age data from 
otoliths is not always as simple as 
counting the number of growth 
increments (Francis et al., 1992; 
Campana, 2001), and many methods 
have been used to obtain length- 
at-age data such as image analysis 
(e.g., Fablet, 2006), back-calculation 
(e.g., Campana, 1990; Secor and 
Dean, 1992), otolith weight and 
morphometric relationships (e.g., Lou 
et al., 2005; Steward et al., 2009), 
length-mediation (e.g., Francis et 
al., 2005), and age adjustment (e.g., 
DeVries and Grimes, 1997; Williams 
et al., 2005; Williams et al., 2008). 
A combination of methods have 
been used in studies to estimate 
growth, where methods such as 
Growth is perhaps the most studied 
of all parameters used to describe the 
life history of exploited fish. Growth is 
usually expressed as a mathematical 
equation describing the mean growth 
of a population and relating size to 
age (Katsanevakis and Maravelias, 
2008). An understanding of growth is 
fundamental for population modeling, 
stock assessments, and managing 
exploited species (Gulland, 1988). The 
methods used to estimate growth in 
fish vary significantly with the type of 
data being used. The most commonly 
used data for estimating fish growth 
is length-at-age data, although 
length-frequency data and mark 
recapture data are also used (Francis, 
1988; Labelle et al., 1993). Counts of 
periodic growth increments observed 
in otoliths or other hard parts are 
predominantly used to estimate fish 
age (Begg et al., 2005; Campana, 
2005), and a range of growth models 
have been developed to be fitted to 
length-at-age data (e.g., Ricker, 1979; 
Schnute, 1981). However, length-at- 
2 Queensland Primary Industries 
and Fisheries 
Department of Employment, Economic 
Development and Innovation 
P.O. Box 1085 
Oonoonba, Queensland 4811, Australia 
