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Fig. S1. Behaviour of mean and variance of bilateral distances (average r and l distances, separately) with respect to size across the skulls in the African fruit bats Eidolon helvum and Rousettus egyptiacus. (A) Non-transformed distances; (B) log-transformed distances; (C) size-adjusted distances (residuals from a linear regression r ? l against PC1 of all 74 variables). Spearman's rank correlation value, its probability and the regression line are shown for each analysis.

Fig. S2. Relationship between asymmetry (as populational variance of r ? l) and 'size' (as PC1 from a principal component analysis on log-transformed data) for 74 cranial characters in the African fruit bats Eidolon helvum and Rousettus egyptiacus. (A) Non-transformed data (r ? l); (B) log-transformed data (log r ? log l); (C) size-adjusted residuals. Spearman's rank correlation value, its probability and the regression line are shown for each analysis.

Fig. S3. Results by species of Shapiro-Wilk's test for non-normality on 74 asymmetry (r ? l) characters of skull and mandible in Eidolon helvum and Rousettus egyptiacus. y-axis, values of Shapiro-Wilks 'W' test statistic; x-axis, associated P value. Short-dashed lines mark the significance cutting point at a = 0.05; long-dashed lines indicate the significance cutting point after Bonferroni adjustment.

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