656 
Fishery Bulletin 96(4), 1998 
ses. Elements for which concentrations were signifi- 
cantly correlated with length were corrected for sta- 
tistical analysis as 
AC = C- rL, 
where AC - the corrected concentration, adjusted 
for fish length; 
C = the concentration of a given element 
(mg/Kg) for a fish of fork length L 
(mm); and 
r = the regression coefficient or the “com- 
mon slope” for the covariate length 
(Edmonds et ah, 1989). 
ANCOVA and other subsequent analyses were also 
performed with otolith weight as the covariate, but 
they showed lower power in discriminating among 
groupings of fish. This lower discriminatory power 
was probably a result of the greater measurement 
errors in obtaining otolith weights in relation to mea- 
surement of fish length. Therefore, concentrations 
of elements corrected for length only were used in 
the final discriminant analyses. 
Multivariate analysis of variance (MANOVA) was 
used to compare the mean corrected elemental con- 
centrations of samples from the different areas. One- 
way fixed effects and unbalanced analyses of vari- 
ance (AN OVA) were then used to compare concen- 
trations of individual elements in samples from dif- 
ferent areas to explain differences detected by the 
MANOVAs. Significance levels were corrected for 
multiple testing with the Bonferroni adjustment fac- 
tor. Tukey’s studentized range (HSD) tests were used 
for a posteriori comparisons of the different areas for 
each significant element. 
Principal component analysis (PCA) of the cor- 
rected concentrations of elements was used to inves- 
tigate grouping patterns by area and fish age. AN OVA 
was performed on the first (PC I) and second (PC II) 
principal components to test differences among pro- 
posed groups. Forward stepwise canonical discrimi- 
nant analyses were used to detect differences in the 
length-corrected chemical composition of otoliths for 
school and spotted mackerel from the different ar- 
eas. The significant (P<0.05) canonical variates (CV) 
provided by each analysis represented the optimal 
combination of areas and elements that provided the 
best overall discrimination between the samples. The 
pooled-within-groups correlations of significant 
length-corrected elemental concentrations with each 
canonical variate approximated the contribution of 
the respective element to the discrimination between 
areas. Wilks’s lambda denoted the statistical signifi- 
cance of the discriminatory power of the overall 
model, ranging from 1.0 to 0.0 (perfect discrimina- 
tion). AN OVA and HSD were used on the significant 
discriminant functions to test pairwise comparisons 
among groups detected by the discriminant analy- 
sis. Jack-knifed cross-validation procedures were 
used to give an unbiased estimate of classification 
success (SYSTAT, 1997). 
Results 
School mackerel 
We measured the concentration of 11 trace and mi- 
nor elements in whole otoliths of school mackerel 
(Fig. 2). Iron and lithium were highly variable, often 
at concentrations below the detection limits of the 
spectrometer, and were excluded from data analy- 
ses. Calcium was also excluded because its high con- 
centration (31.4-44.7%) would mask contribution of 
trace elements in the data analyses. The remaining 
elements (Ba, K, Mg, Mn, Na, P, S, and Sr) were 
present in measurable quantities, suitable for sta- 
tistical analyses. ANCOVA indicated that none of 
these eight elements were correlated with fish length 
for school mackerel. However, there was a signifi- 
cant interaction in the concentration of Ba with area 
of collection and fish length (ANCOVA, F= 2.75, df=3, 
76, P<0.05); therefore the Ba data were not used in 
the discriminatory analyses. This interaction was 
caused by an inverse relationship between Ba con- 
centration and fish length for school mackerel from 
Bowen, whereas samples from the other areas all 
showed positive correlations between Ba concentra- 
tion and fish length. 
School mackerel from each age class in each area 
were found to have significantly different mean el- 
emental composition of otoliths (MANOVA, Pillai’s 
trace=1.013, P=5.54, df=21, 228, PcO.OOOl). Mean 
concentrations of individual elements, except for S 
and Sr, varied significantly among school mackerel 
from the different areas and between different age 
classes (Fig. 2). Sodium, P, and Mg concentrations 
differed the most among the study areas, and there 
were significant differences in concentrations of Na 
and P between fish from Bowen and those from 
Rockhampton and Moreton Bay. There were also sig- 
nificantly higher concentrations of K in otoliths of 
Bowen fish, compared with those from Rockhampton 
(HSD, P<0.05). No significant differences in elemen- 
tal composition of otoliths were detected between 
2-year-old school mackerel from Rockhampton and 
Moreton Bay. In contrast, significant differences were 
found for Mg, Mn, Na, and P concentrations between 
1- and 2-year-old fish from Rockhampton, suggest- 
