Appendixes Table S1. Univariate linear (βuni) and nonlinear (γuni), and multivariate linear (βmulti) and nonlinear (γmulti) selection gradients for all traits and populations together with the sample sizes of mated males (m) and of unmated males (um). Note that for some populations sample sizes are lower than the others. With the inclusion of these populations our aim was to test for the consistency of the documented patterns rather than quantifying selection gradients in separate populations. Sample size m um Flight speed γmulti CA BKP HC PM DNZ PR -0.53 0.87 0.24 0.06 0.28 -0.06 -0.61 0.86 0.79 -0.12 0.15 -0.49 -0.52 -0.12 0.29 0.03 0.26 -0.07 -0.54 -3.01 0.77 -0.17 0.15 0.13 12 3 19 24 19 8 12 6 19 18 21 12 Flight endurance βmulti CA BKP HC PM DNZ PR 0.21 1.74 0.46 -0.12 0.26 1.19 -2.39 2.34 0.10 0.23 -0.14 0.11 0.13 1.78 0.50 -0.11 0.21 1.19 -1.95 3.78 0.22 0.27 -0.13 0.09 12 3 19 24 19 8 12 6 19 18 21 12 Phenoloxidase activity γuni CA BKP HC PM DNZ PR -0.03 -0.35 -0.15 0.14 -0.03 0.46 0.24 -0.56 -0.04 0.31 -0.46 -0.16 0.08 -0.84 -0.11 -0.04 -0.25 0.45 0.27 -0.39 0.22 0.06 0.09 -0.68 26 13 36 33 28 13 31 19 40 23 34 22 Relative fat content βuni CA BKP HC PM DNZ PR 0.33 0.27 0.53 0.05 0.27 0.20 -0.03 -0.02 -0.14 -0.63 -0.36 0.63 -0.07 0.32 0.34 0.25 0.71 0.14 -0.19 -0.04 -0.12 -1.44 -0.51 1.06 28 13 38 32 28 13 32 19 43 27 35 24 1 βuni γuni βmulti γmulti Sample size m um Flight muscle ratio CA BKP HC PM DNZ PR -0.23 -0.31 0.08 0.30 0.26 -0.31 0.53 -1.31 0.56 0.06 -0.55 -0.19 -0.24 -0.16 0.33 0.60 0.43 -0.06 0.81 -1.23 0.61 0.10 -0.33 -0.65 29 13 38 33 28 13 33 19 42 27 34 24 Wing length CA BKP HC PM DNZ PR -0.54 -0.48 -0.42 -0.63 0.30 0.67 -0.21 0.27 0.12 0.04 0.38 0.33 -0.54 -0.19 -0.42 -0.70 0.17 0.81 -0.54 -0.47 0.25 0.05 0.25 -1.01 29 13 36 31 28 13 33 19 43 27 32 24 Aspect ratio CA BKP HC PM DNZ PR 0.11 -0.78 -0.08 0.14 0.01 -0.02 -1.08 0.28 0.16 0.04 -0.17 0.48 0.51 -0.80 0.15 0.48 -0.17 -0.26 -1.36 -0.90 0.14 -0.47 -0.13 0.54 28 13 36 29 27 12 33 18 41 26 31 24 Wing loading Continuation of Table S1. CA BKP HC PM DNZ PR 0.25 0.09 0.39 -0.51 0.00 0.06 0.68 1.20 -0.14 0.03 0.45 0.60 0.15 0.37 0.25 -0.55 -0.18 -0.04 0.26 0.86 -0.38 -0.02 0.25 0.45 26 13 35 29 27 12 32 18 41 26 31 23 2 Table S2. Multivariate results of the generalized linear model analyses examining sexual selection on the two flight performance traits in the set of six study populations of the damselfly C. puella. Significant p-values are indicated in bold. Population (Pop) Flight speed (PC1) Flight speed (PC1)2 Flight speed (PC1) × Pop Flight speed (PC1)2 × Pop Flight endurance (PC2) Flight endurance (PC2)2 Flight endurance (PC2)× Pop Flight endurance (PC2)2 × Pop df 5 1 1 5 5 1 1 5 5 Mating success χ2 p 3.9641 0.55 0.6614 0.42 0.2878 0.59 3.9546 0.56 6.6027 0.25 5.8360 0.016 0.1924 0.66 6.3597 0.27 1.6723 0.89 3 Table S3. Multivariate results of the generalized linear models examining sexual selection on the set of six phenotypic traits in the set of six study populations of the damselfly C. puella. Significant p-values are indicated in bold. Mating success χ2 p 11.1845 0.048 0.0886 0.77 Population (Pop) Phenoloxidase activity df 5 1 Phenoloxidase activity2 Phenoloxidase activity × Pop 1 5 0.0341 6.5812 0.85 0.25 Phenoloxidase activity2 × Pop Relative fat content 5 1 5.9323 4.0091 0.31 0.045 Relative fat content2 Relative fat content × Pop 1 5 0.4040 2.8340 0.53 0.73 Relative fat content 2 × Pop Flight muscle ratio 5 1 7.7972 1.9615 0.17 0.16 Flight muscle ratio2 Flight muscle ratio × Pop 1 5 0.3459 6.3463 0.56 0.27 Flight muscle ratio2 × Pop Wing length 5 1 13.8766 1.0029 0.016 0.32 Wing length2 Wing length × Pop 1 5 0.2425 12.1824 0.62 0.032 Wing length2 × Pop Aspect ratio 5 1 2.1499 0.1330 0.83 0.72 Aspect ratio2 Aspect ratio × Pop 1 5 0.5591 8.3618 0.45 0.14 Aspect ratio2 × Pop Wing loading 5 1 4.0946 0.9412 0.54 0.33 Wing loading2 Wing loading × Pop 1 5 2.7655 7.0017 0.096 0.22 Wing loading2 × Pop 5 6.6951 0.24 4 Figure S1. The left hind wing of a C. puella male with the 18 digitalized landmarks. Wing size was measured as the distance between landmark 1 and 9. 5