Geometric morphometric and statistical analyses
Right forewings were carefully removed from 75% alcohol-preserved specimens and temporarily mounted on micro-slides. Photographs with the same scale were taken with a digital camera attached to the Nikon SMZ1500 stereo zoom microscope (Nikon, Tokyo, Japan).
Twenty-three homologous landmarks (LMs) at vein intersections or terminations that could be reliably identified were selected (Fig. 2), and can be considered type I landmarks (Bookstein, 1991). Data for wing size and shape were obtained by positioning landmarks on digitized wings using tpsDig2 (Rohlf, 2004).
Measurement error. An analysis of measurement error was conducted on a subsample of 30 specimens of D. magna, which were chosen randomly and repeated 2 times to obtain landmark data. Procrustes ANOVA (analysis of variance) was performed for landmark data in MorphoJ v1.05c (Klingenberg and McIntyre, 1998; Klingenberg, 2011). All measurements were taken by the same person to reduce experimenter effect. The averaged error of wing centroid size did not exceed 0.18% of the total variation (F = 0.01, P = 1.0000), and 0.49% (F = 0.12, P = 1.0000) for wing shape variables. This means that the measurement error explained a negligible percentage of variance.
Size variation. Wing size variation was examined using centroid size (the square root of the sum of squared distance between each landmark and the wing centroid), which was uncorrelated with any shape variable and was not influenced by landmark variation (Bookstein, 1991, 1996). Centroid size was calculated using tpsRelw 1.44 (Rohlf, 2006) and tested for normality using the Shapiro-Wilk test. Leven’s test was used to test homogeneity of the variance (Milliken and Johnson, 2009). One-way analysis of variance (ANOVA) was used to test the difference in centroid size between the sexes and among populations. A post hoc test (LSD test) after Bonferroni correction on centroid size defined pair-wise differences in centroid size of populations. All statistical analyses were performed in IBM SPSS statistics software version 19.0 for windows (IBM Corporation, 2010).
Shape variation. For wing shape variation, the 258 landmark configurations were scaled, translated, and rotated against the consensus configuration using Generalized Procrustes Analysis (GPA) procedure to remove the nonshape effects of size, position and orientation (Rohlf and Slice, 1990; Dryden and Mardia, 1998). The resulted matrix (w; ‘weight matrix’ sensu Rohlf et al., 1996) was used for shape analysis. For a shape, a principal component analysis (PCA) was carried out to determine the explained percentage of each principal component (PC) of the total variation. The total shape variables were used for the multivariate analysis of variance (MANOVA) to test wing shape differences within and among species/population. Canonical variate analysis (CVA) and linear discriminant analysis (LDA) were used to discriminate populations and provide shape variations associated with canonical variates (CVs). The percentages of correct classification (hit ratio, HR sensu Gerard et al., 2015; Huberty and Olejnik, 2006) based on a leave-one-out cross-validation procedure in LDA were used to evaluate the discriminatory power of the wing. The allometric effect or the change in shape associated with size differences was evaluated with a multivariate regression of shape variables onto size. Morphometric and statistical analyses were computed using the IMP series software (Sheets, 2012), MorphoJ v1.05c (Klingenberg, 2011) and R version 3.0.2 (R Core Team, 2013).