Bergenius et al Use of otolith morphology to indicate stock structure of Plectropomus leopordus 



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variables and the Fourier harmonics by using a three- 

 way crossed model (outlined below) with fixed factors: 

 cohort, region, and sex. Data were pooled across reefs 

 within regions owing to insufficient sample numbers to 

 test for reef-specific effects. 



A MANOVA was used to test for spatial and temporal 

 differences in otolith shape. A principal component (PC; 

 Tabachnick and Fidell, 1983) analysis was done first on 

 the combined data set of both the shape variables and 

 Fourier harmonics to reduce the number of variables to 

 be incorporated in the MANOVA. The number of PCs to 

 extract and subsequently include in the MANOVA was 

 determined by examining the size of the eigenvalues 

 (representing the variance explained by each PC), as 

 well as their relative contribution to the percent vari- 

 ance explained compared to the other eigenvalues (i.e., 

 scree test; Tabachnick and Fidell, 1983). The latter 

 determines the number of PCs beyond which the addi- 

 tion of more PCs would contribute little to the variance 

 explained by the solution (Tabachnick and Fidell, 1983). 

 Wilk's lambda criterion was used to test for group dif- 

 ferences in the MANOVAs. Sums of squares and de- 

 grees of freedom of interactions were pooled when the 

 F-ratios of interaction effects were <1. Pooling increases 

 the degrees of freedom for the denominator and conse- 

 quently the power of the test of remaining (unpooled) 

 effects in the analyses. 



A posteriori univariate analysis of variance (ANOVA) 

 was used to explore patterns for each of the PCs sepa- 

 rately when significant effects were indicated in the 

 MANOVA. The univariate linear model for the analysis 

 of each PC was 



^ijkl 



 H +C, +R^ +r(R)i^,j,+CR„ + Cr(fl ),,,„,, -He,„^ 



ikn 



where .v ;,, = the PC score for otolith / from cohort /. 



region j and reef k ; 



fi = the estimate of the population mean PC 



score over all cohorts, regions, reefs, and 



otoliths; 



C, = the fixed effect of cohort i averaged over 



regions and reefs; 

 R I = the fixed effect of region j averaged over 

 cohorts and reefs; 

 r{R) I. = the random variation attributable to reef/; 

 within regionj averaged over cohorts; and 

 ^i(:kji ~ unexplained random variation associated 

 with otolith / within cohort ;, region / and 

 reef k. 



Tukey's honestly significant difference (HSD) test 

 was used to determine which means differed following 

 significant effects detected in the ANOVAs. The com- 

 munalities (representing the proportion of the total 

 variance of a variable accounted for by the PC) and 

 variable loadings of the PCs that were significant in 

 the ANOVAs were subsequently examined. A loading 

 below 0.45 indicated that the variable explained less 

 than 207f of the PC and therefore was not interpreted 

 further. 



Finally, two forward stepwise canonical discriminant 

 analyses (CDAs; Tabachnick and Fidell, 1983) were 

 computed by using the shape variables and Fourier 

 harmonics to examine the otolith shape of P. leopardus 

 in multivariate space and to investigate whether otolith 

 shape could be used to classify samples to spatial scale 

 and cohort of origin. The factor used as a separating 

 variable in the CDA depended on the significant effects 

 determined in the MANOVA (i.e., cohort, region, or reef 

 [region], or any interactions between these factors). The 

 CDA was used in this way as a confirmatory technique. 

 Wilk's lambda criterion was used to test for significant 

 differences between the discriminant functions. Jack- 

 knife classification was used to minimize potential bias 

 in the reclassification of individuals. 



Results 



Slopes of the relationship between FL and several oto- 

 lith morphological variables for P. leopardus differed 

 among a range of spatial scales and between cohorts 

 (Table 2). The within-group slope, therefore, was cal- 

 culated for each group according to the level at which 

 the slopes of the relationship differed and was used 

 to correct for the influence of FL (Table 2). For some 

 variables, the common between-group slope was used 

 to correct for the influence of FL because there was 

 a significant overall relationship between the vari- 

 able and FL, which was homogeneous among groups 

 (ANC OVA homogeneity of slopes test,P>0.05; Table 2). 

 No morphological variable was significantly correlated 

 with FL after standardization. Furthermore, shape 

 variables and Fourier harmonics were not significantly 

 different between otoliths of females, males or transi- 

 tional fish (MANOVA, P>0.05). The morphological data, 

 therefore, were pooled across sex for the remainder of 

 the analyses. 



Principal component analysis (PCA) 



Four PCs were extracted from the analysis of the com- 

 bined data set of shape variables and Fourier harmonics 

 and included in the MANOVA (Table 3). The communali- 

 ties ranged between 0.11 and 0.88, and some morphologi- 

 cal variables were better defined by the PC solution than 

 others (Table 3). About 44% of the total variance in the 

 morphological data was explained by the four extracted 

 PCs (17.9%, 10.2%, 9.9% and 5.9% by PC I, II, III, IV, 

 respectively). A combination of higher order harmonics 

 describing the finer details of the otolith outline, and 

 lower order harmonics, perimeter, length, and circular- 

 ity representing the broad shape of otoliths explained 

 most of the variation in PC I and III (Table 3). Variation 

 in the broader details of otolith shape also accounted 

 for most of the variation in PC II and PC IV; otolith 

 area, breadth, perimeter, length, and harmonic eight 

 explained most of the variation in PC II and breadth 

 and harmonic 127 explained most of the variation in 

 PC IV (Table 3). 



