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the factor and otolith length as the covariate. Both oto- 
lith length and fish TL have been used as covariates 
in similar analyses and were expected to yield similar 
results. However, Campana and Casselman (1993) rec- 
ommended the use of otolith length because this mea- 
sured variable is more robust to collection and preser- 
vation effects, in addition to its strong correlation with 
fish TL (in our study, correlation coefficient [r]=0.90). 
In the ANCOVA model, if the interaction of region and 
otolith length was significant (P<0.05), the shape index 
was excluded from the analysis because it could not be 
corrected (Tracey et al., 2006). When the interaction 
was not significant but the effect of otolith size was 
significant, the shape index was corrected through the 
use of the common within-group slope (6), whereby the 
product of the slope and otolith length was subtracted 
from the shape variable. One-way analysis of variance 
(ANOVA), followed by Tukey’s honest significant differ- 
ence (HSD) post-hoc comparisons and Welch’s t-tests 
(with significance for both tests assessed at a=0.05), 
was used to examine differences in shape indices and 
to identify those indices that could be used in a dis- 
criminant analysis. 
To identify the optimal number of harmonics for 
analysis, we ran cross-validation analyses to explore 
the descriptive power of harmonics. For this analysis, 
we started with the first 2 harmonics and subsequently 
added harmonics until the rate of jackknife reclassi- 
fication success declined or plateaued, indicating that 
the additional harmonics no longer were increasing 
discriminatory power. Preliminarily, we evaluated sepa- 
rately 15 and 20 harmonics to examine the sensitivity 
of the analysis to the number of harmonics. With 15 
and 20 harmonics, the mean (and standard deviation 
of the mean) reclassification success rate was nearly 
identical to or slightly worse — although not statistical- 
ly significant — than the result from our original analy- 
sis with 10 harmonics, and, therefore, we limited our 
analysis to 10 harmonics. In addition to the statistical 
justification, we viewed 10 harmonics as a compromise 
between the parsimony of fewer harmonics indicated 
by cross validation and a larger number of harmonics 
based on the notion that fine-scale description is of- 
ten contained in higher-order harmonics (Cadrin et al., 
2005) and that cross validation might not detect these 
small differences. 
Linear discriminant analyses were used to examine 
differences between geographical subsamples (i.e., pu- 
tative stocks) at all 3 spatial scales. Ideally, the con- 
struction of discriminant functions for otolith shape 
benefits from the inclusion of both EFC and shape in- 
dices (Agiiera and Brophy, 2011); therefore, any signifi- 
cant shape indices were considered for inclusion in the 
discriminant analysis. 
Finally, jackknife reclassification (i.e., leave-one-out 
cross validation) was used to examine the classification 
success of the discriminant functions when classifying 
known-origin otoliths. Rates of reclassification success 
were compared with the null classification expectation 
(i.e., no structure) of l/g, where g was the number of 
groups or putative stocks in the analysis (White and 
Ruttenberg, 2007). Because unbalanced sample sizes 
can be problematic in discriminant function analysis 
(DFA) and result in a high rate of reclassification suc- 
cess by chance (White and Ruttenberg, 2007), we bal- 
anced our sample sizes on the basis of the smallest 
sample size in each analysis, and then we ran 1000 
DFAs with all groups (except the smallest) randomized 
without replacement. We also conducted randomization 
tests of samples so that we would have not only a null 
point estimate but also a distribution (i.e., an expected 
range) to provide greater inference for our empirical 
results. 
Results 
Otolith shape indices 
Circularity was the only otolith shape index that was 
not normally distributed, nor could it be normalized 
through transformation, and it was, therefore, dropped 
from the analysis of this study. With analysis of covari- 
ance, we detected no significant interactions between 
otolith length and location for any of the 4 remaining 
shape variables, which then were slope adjusted appro- 
priately. At the basin level, all shape variables, except 
rectangularity, were significantly different (Table 2; 
Fig. 3). At the within-basin level, form function in the 
Gulf of Mexico was the only shape index that showed 
significant differences between states; no differences in 
shape indices were detected among Atlantic states. At 
a finer spatial scale (areas within North Carolina), dif- 
ferences in otolith shape indices were largely absent, 
with the exception of form function (Table 2). 
Elliptical Fourier analysis 
On the basis of the large number of EFCs (N= 37) 
that were extracted in this study and a lack of high 
cumulative Fourier power (<70%, including all EFCs; 
Pothin et al., 2006), the descriptive power of harmonics 
was explored with analyses of cross validation. In the 
cross-validation analyses for each geographic scale, the 
rate of jackknife reclassification success plateaued al- 
most immediately, indicating that each additional EFC 
provided minimal explanatory power. This result is in 
agreement with the finding of low Fourier power. Ulti- 
mately, all 4 discriminant analyses included the first 
10 EFCs and any significant shape indices (Table 3). 
Our basin-scale rate of reclassification success was 
nearly 80%, the highest level of reclassification success 
that we detected in any analysis and well outside the 
upper range of the null distribution (45-56%). Both 
within-basin reclassifications and the within-North 
Carolina reclassifications were marginally above — 
about a 6% improvement in classification — the range 
of the null expectation distribution (Table 3); however, 
