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Supplementary Table 1. Results of Permanovas and Phylogenetic Manovas on Different Vision Models (Defined by Illuminant, Viewing Conditions and Bird Visual System)

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Supplementary Table 1. Results of Permanovas and Phylogenetic Manovas on Different Vision Models (Defined by Illuminant, Viewing Conditions and Bird Visual System) Supplementary table 1. Results of PERMANOVAs and phylogenetic MANOVAs on different vision models (defined by illuminant, viewing conditions and bird visual system). Dependent Visual Illuminant Viewing condition Test Statistic p-value variable system PERMANOVA F9 = 6.88 0.001 *** UVS phylogenetic MANOVA approx-F9 = 2.97 < 0.001 *** against a leaf PERMANOVA F9 = 6.93 0.001 *** VS phylogenetic MANOVA approx-F9 = 3.05 < 0.001 *** forest shade PERMANOVA F9 = 5.38 0.001 *** UVS phylogenetic MANOVA approx-F9 = 3.07 < 0.001 *** against the sky PERMANOVA F9 = 5.38 0.001 *** VS phylogenetic MANOVA approx-F9 = 3.36 < 0.001 *** PERMANOVA F9 = 7.04 0.001 *** UVS phylogenetic MANOVA approx-F9 = 3.01 < 0.001 *** against a leaf PERMANOVA F9 = 7.07 0.001 *** VS phylogenetic MANOVA approx-F9 = 3.10 < 0.001 *** xyzL woodland shade PERMANOVA F9 = 5.33 0.001 *** UVS phylogenetic MANOVA approx-F9 = 3.12 < 0.001 *** against the sky PERMANOVA F9 = 5.34 0.002 ** VS phylogenetic MANOVA approx-F9 = 3.39 < 0.001 *** PERMANOVA F9 = 7.24 0.001 *** UVS phylogenetic MANOVA approx-F9 = 3.00 < 0.001 *** against a leaf PERMANOVA F9 = 7.24 0.001 *** VS phylogenetic MANOVA approx-F9 = 3.07 < 0.001 *** large gap PERMANOVA F9 = 5.37 0.001 *** UVS phylogenetic MANOVA approx-F9 = 3.14 < 0.001 *** against the sky PERMANOVA F9 = 5.37 0.001 *** VS phylogenetic MANOVA approx-F9 = 3.38 < 0.001 *** x, y and z are the mean coordinates in the tetrahedral colour space of transparent areas for each species and L is the mean luminance. For phylogenetic analyses, p-value is calculated based on simulations. Dependent Visual Illuminant Viewing condition Test Statistic p-value variable system PERMANOVA F9 = 2.52 0.029 * UVS phylogenetic MANOVA approx-F9 = 2.04 0.074 . against a leaf PERMANOVA F9 = 2.47 0.021 * VS phylogenetic MANOVA approx-F9 = 2.11 0.063 . forest shade PERMANOVA F9 = 1.99 0.062 *** UVS phylogenetic MANOVA approx-F9 = 2.30 0.035 * against the sky PERMANOVA F9 = 2.03 0.045 * VS phylogenetic MANOVA approx-F9 = 2.69 0.004 ** PERMANOVA F9 = 2.27 0.034 * UVS phylogenetic MANOVA approx-F9 = 2.07 0.057 . against a leaf PERMANOVA F9 = 2.27 0.037 * VS phylogenetic MANOVA approx-F9 = 2.15 0.051 . xyz woodland shade PERMANOVA F9 = 2.05 0.037 * UVS phylogenetic MANOVA approx-F9 = 2.44 0.017 * against the sky PERMANOVA F9 = 2.03 0.051 . VS phylogenetic MANOVA approx-F9 = 2.81 0.002 ** PERMANOVA F9 = 2.37 0.028 * UVS phylogenetic MANOVA approx-F9 = 2.07 0.051 . against a leaf PERMANOVA F9 = 2.35 0.028 * VS phylogenetic MANOVA approx-F9 = 2.13 0.046 * large gap PERMANOVA F9 = 1.97 0.071 . UVS phylogenetic MANOVA approx-F9 = 2.38 0.018 * against the sky PERMANOVA F9 = 2.01 0.052 . VS phylogenetic MANOVA approx-F9 = 2.73 0.004 ** x, y and z are the mean coordinates in the tetrahedral colour space of transparent areas for each species. For phylogenetic analyses, p- value is calculated based on simulations. Dependent Visual Illuminant Viewing condition Test Statistic p-value variable system Kruskal Wallis 9 = 31.1 < 0.001 *** UVS phylogenetic ANOVA F9 = 7.26 0.002 ** against a leaf Χ Kruskal Wallis 9 = 30.9 < 0.001 *** VS phylogenetic ANOVA F9 = 7.26 0.001 *** forest shade Χ Kruskal Wallis 9 = 30.9 < 0.001 *** UVS phylogenetic ANOVA F9 = 5.38 0.002 ** against the sky Χ Kruskal Wallis 9 = 30.8 < 0.001 *** VS phylogenetic ANOVA F9 = 5.38 0.003 ** Χ Kruskal Wallis 9 = 30.9 < 0.001 *** UVS phylogenetic ANOVA F9 = 7.23 0.001 *** against a leaf Χ Kruskal Wallis 9 = 30.9 < 0.001 *** VS phylogenetic ANOVA F9 = 7.23 0.001 *** L woodland shade Χ Kruskal Wallis 9 = 30.6 < 0.001 *** UVS phylogenetic ANOVA F9 = 5.33 0.002 ** against the sky Χ Kruskal Wallis 9 = 30.7 < 0.001 *** VS phylogenetic ANOVA F9 = 5.34 0.002 ** Χ Kruskal Wallis 9 = 30.8 < 0.001 *** UVS phylogenetic ANOVA F9 = 7.24 0.001 *** against a leaf Χ Kruskal Wallis 9 = 30.8 < 0.001 *** VS phylogenetic ANOVA F9 = 7.24 0.001 *** large gap Χ Kruskal Wallis 9 = 30.8 < 0.001 *** UVS phylogenetic ANOVA F9 = 5.37 0.002 ** against the sky Χ Kruskal Wallis 9 = 30.8 < 0.001 *** VS phylogenetic ANOVA F9 = 5.37 0.001 *** Χ L is the mean luminance. For phylogenetic analyses, p-value is calculated based on simulations. Supplementary table 2. Phylogenetic signal for structural features and transmission properties. Phylogenetic Variable p-value signal 72 < 0.001 *** Mean scale length K = 0.419 0.001 *** λ = 0.6 < 0.001 *** Mean scale width K = 1.17 0.001 *** λ = 1.00574 0.0529 . Mean scale density K = 0.238 0.003 ** λ = 0. <0.001 *** Mean membrane width K = 0.563 0.001 *** Mean nanostructure λ = 0.996903 <0.001 *** density K = 0.935 0.001 *** λ = 0. 3 <0.001 *** Mean transmittance K = 1.06 0.001 *** Nanostructure type λ = 0.9744 < 0.001 *** Scale type and insertion 41 < 0.001 *** δ = 4. Scale colour (coloured vs. p(D = 1) = 0 D = δ-0.0 = 5.945 transparent) p(D = 0) = 0.583 for multicategorial D for binary traits) of the different features associated to micro- and nanostructures and of mean transmittance. 0,Measure the trait of isthe distributed phylogenetic randomly signals across (Pagel’s λ and Blomberg’s K for quantitativeare traits; equal δ to 1 the trait evolvestraits according and Purvis to a and Brownian Fritz’s motion model along the phylogeny. When D is equal to 1, the trait is randomly distributed across the phylogeny whereasWhen λ or when K are D equalis equal to to 0, the trait evolves according to Brownianthe motion phylogeny model whereas along the when phylogeny. λ or K The value of delta, the more the trait evolve according to the phylogeny. For , to determine whether the distribution of the trait is different from a random distribution we randomized the trait 1000 times along the phylogeny, and we calculated forδ each can be randomisation. any positive real We number then compared and the higher the value of to the distribution of values of under the randomδ hypothesis and we calculated a p-value as the number of simulations in which is higher than the value obtained for the real distribution of the trait. δ δ δ δ Supplementary table 3. Informations about specimens used for optical and structural measurements. mean standard mean standard mean standard relative x error for x relative y error for y relative z error for z standard coordinate coordinate coordinate coordinate coordinate coordinate standard Measure Transmitt Average error for in in in in in in mean error for points used Mean ance over mean mean tetrahedri tetrahedra tetrahedri tetrahedra tetrahedri tetrahedra relative relative for link Scale transmitta 300-700 transmitta transmitta c colour l colour c colour l colour c colour l colour luminanc luminanc between length Scale Mean Mean nce over nm for the nce over nce over space for space for space for space for space for space for e for UVS e for UVS mean Mean measurem Scale Mean density membran Membrane nanostruct Nanostructu 300-700 chosen 300-700 300-700 UVS vision UVS vision UVS vision UVS vision UVS vision UVS vision vision vision Specimen ID transmitta scale ent Mean scale width scale standard e thickness ure re density nm for the veins for the 5 for the 5 model model model model model model model model mimicry for Specimen Year of nce and Scale Scale Scale length standard width standard density error (mm- thickness standard Nanostruct densité standard chosen standard measure measure presented presented presented presented presented presented presented presented Family Subfamily Tribe Genus species ssp ring Tip label in MCCtree transmission ID for MEB Collection location collection structures type insertion colour (µm) error (µm) (µm) error (µm) (mm-²) ²) (nm) error (nm) ure type (µm-²) error (µm-²) veins (%) error (%) points (%) points (%) in table 1 in table 1 in table 1 in table 1 in table 1 in table 1 in table 1 in table 1 Erebidae Arctiinae Arctiini Dysschema sp. confusa ME15_88_DYSSSP1 ME15-88 ME15-88 Peru, San Martin, Carachamera 2015 v2 scale erected coloured 111.54 2.37 31.55 3.65 301.93 3.43 1225.74 410.38 nipples 0.32 0.15 32.99 NA 12.59 11.81 0.14139 0.01134 0.17564 0.00392 -0.23115 0.00276 0.07010 0.11800 Erebidae Arctiinae Arctiini Hyalurga egeon lerida ME16_67_HYALEGE ME16-67 ME16-67 Peru, San Martin, Chazuta 2016 v2 scale erected coloured 82.09 4.57 21.87 1.44 650.30 77.43 690.48 224.88 nipples 0.71 0.13 2.56 NA 14.98 12.06 0.16493 0.01352 0.16082 0.00971 -0.23399 0.00197 0.09205 0.09876 Erebidae Arctiinae Arctiini Hyalurga grandis agnosia TR17_17_HYALGRA TR17-17 TR17-17 Peru, San Martin, Shapaja 2015 v3 scale erected coloured 107.42 30.68 11.97 2.63 725.66 63.44 583.04 133.18 nipples 1.77 0.01 5.80 NA 7.65 5.81 0.17607 0.02232 0.14851 0.01671 -0.23296 0.00281 0.02200 0.02241 Erebidae Arctiinae Arctiini Hypocrita strigifera blue ME16_58_HYPOSTRI ME16-58 ME16-58 Peru, San Martin, Chazuta 2016 v2, v3, v5 scale flat transparent 107.36 1.66 84.45 5.30 152.34 20.27 1010.80 148.42 nipples 1.23 0.98 2.31 1.07 2.34 0.89 0.29273 0.01983 0.09498 0.01736 -0.24778 0.00063 0.00234 0.00165 Erebidae Arctiinae Arctiini Notophyson tiresias confusa ME16_63_NOTOTIR ME16-63 ME16-63 Peru, San Martin, Urahuasha 2016 v2 scale flat coloured 85.32 6.12 108.47 5.00 144.10 21.36 1864.49 602.64 absent 0.04 0.04 6.10 NA 7.23 0.72 0.26345 0.01114 0.13710 0.00959 -0.24777 0.00038 0.02194 0.00397 Erebidae Arctiinae Arctiinae1 eurimedia TR17_7_MOTH1 TR17-7 TR17-7 Peru, Loreto, Shucushyacu 2015 v2, v3 scale flat coloured 71.49 3.92 87.67 5.09 276.84 13.58 3085.06 454.88 absent 0.07 NA 0.43 0.39 2.91 4.61 0.39068 0.07407 -0.01859 0.08548 -0.24821 0.00051 0.01015 0.02201 Erebidae Arctiinae Arctiinae2 lerida 11_1065_MOTH2 11-1065
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