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doi:10.1038/nature18005 Supplementary Information Table 1. Data of the Phasianinae. Tail length and tarsal spur length as two sexually selected traits and tarsus length and body mass as two body size indices of Phasianinae. All length traits are for males and measured in mm, body mass in g. Data taken from refs. 35 and 51. Species Tail length Spur length Tarsus length Body mass Acryllium vulturinum 272.0 7 109.0 1335.5 Afropavo_congensis 233.0 12 102.0 1418.0 Agelastes meleagrides 152.5 8 84.0 815.0 Agelastes niger 156.0 11 82.0 700.0 Argusianus argus 1240.0 110.0 2322.5 Catreus wallichi 515.0 11 76.0 1588.0 Chrysolophus amherstiae 990.0 9 80.0 762.5 Chrysolophus pictus 697.5 8 75.0 642.5 Crossoptilon auritum 523.0 21 100.0 1923.0 Crossoptilon crossoptilon 337.5 19 87.5 2550.0 Crossoptilon mantchuricum 550.0 14 100.0 2063.0 Gallus gallus 267.5 31 75.0 1061.0 Gallus lafayettii 265.0 30 75.5 965.0 Gallus sonnerati 352.0 28 75.0 963.0 Gallus varius 325.0 26 72.5 1061.0 Guttera plumifera 131.0 83.0 875.0 Guttera pucherani 151.0 93.0 1149.0 Ithaginis cruentus 171.0 10 74.5 568.5 Lophophorus impeyanus 225.0 13 75.0 2180.0 Lophophorus lhuysii 305.0 72.0 2837.0 Lophophorus sclateri 209.0 73.0 2607.5 Lophura bulweri 225.0 18 70.0 1635.0 Lophura diardi 345.0 30 80.0 1420.0 Lophura edwardsi 250.0 25 75.0 1115.0 Lophura erythrophthalma 165.0 26 80.0 1043.0 Lophura hatinhensis 266.5 94.0 1100.0 Lophura ignita 252.5 39 115.0 2202.5 Lophura imperialis 272.0 13 95.0 Lophura inornata 161.0 10 72.5 1070.0 Lophura leucomelana 277.5 17 77.5 975.0 Lophura nycthemera 570.0 32 100.0 1439.0 Lophura swinhoii 455.0 24 90.0 1100.0 Numida meleagris 172.0 84.0 1300.0 Pavo cristatus 1500.0 25 147.5 5000.0 Pavo muticus 1500.0 165.0 4325.0 Phasianus colchicus 540.0 11 71.5 1150.0 Phasianus versicolor 347.5 11 71.0 1000.0 Polyplectron bicalcaratum 375.0 14 77.5 739.0 Polyplectron emphanum 245.0 13 66.0 436.0 Polyplectron germaini 285.0 11 65.0 510.0 Polyplectron inopinatum 360.0 12 65.0 Polyplectron malacense 245.0 17 65.0 567.5 Polyplectron schleiermacheri 195.0 70.0 WWW.NATURE.COM/NATURE 1

Pucrasia macrolopha 249.0 66.0 1275.0 Rheinardia ocellata 1600.0 90.0 Syrmaticus ellioti 430.0 17 70.0 1156.0 Syrmaticus humiae 467.5 18 62.0 1028.0 Syrmaticus mikado 510.0 66.5 1300.0 Syrmaticus reevesii 1300.0 80.0 1529.0 Syrmaticus soemmerringi 618.0 64.0 907.0 Tragopan blythii 200.0 11 80.0 1930.0 Tragopan_melanocephalus 235.0 10 92.5 1975.0 Tragopan satyra 297.0 11 90.0 1850.0 Tragopan temminckii 207.0 11 75.0 1560.0 WWW.NATURE.COM/NATURE 2

Supplementary Information Table 2. Data of the Bovidae. Horn length (in cm) and body mass (in kg) of the 102 Bovidae used for allometry estimates. Data taken from refs. 57 and 58. Male horn Species length Male body mass Addax nasomaculatus 84.5 117.7 Aepyceros melampus 68.4 56.9 Alcelaphus buselaphus 66.0 178.3 Alcelaphus lichtensteini 53.5 178.3 Ammodorcas clarkei 29.0 30.6 Ammotragus lervia 73.6 111.8 Antidorcas marsupialis 26.5 40.7 Antilope cervicapra 57.0 40.2 Bison bison 66.0 795.3 Bos frontalis 73.5 848.4 Bos grunniens 80.0 590.5 Bos javanicus 67.5 750.0 Bos taurus 80.0 680.4 Boselaphus tragocamelus 19.5 253.3 Bubalus bubalis 105.0 1200.0 Bubalus depressicornis 27.8 156.0 Bubalus mindorensis 40.1 274.0 Budorcas taxicolor 41.2 282.7 Capra caucasica 83.0 86.3 Capra cylindricornis 80.0 82.5 Capra falconeri 108.0 92.7 Capra hircus 105.0 53.0 Capra ibex 90.0 80.5 Capra nubiana 100.0 70.0 Capra pyrenaica 74.0 72.5 Capra sibirica 115.1 90.0 Capra walie 102.0 112.5 Capricornis crispus 11.5 35.9 Capricornis sumatraensis 25.0 121.0 Cephalophus adersi 4.5 9.3 Cephalophus callipygus 8.0 18.6 Cephalophus dorsalis 7.0 20.3 Cephalophus natalensis 7.0 13.1 Cephalophus niger 8.5 19.9 Cephalophus nigrifrons 10.0 13.3 Cephalophus ogilbyi 10.0 20.4 Cephalophus rufilatus 7.0 10.1 Cephalophus silvicultor 20.0 52.5 Cephalophus zebra 4.4 13.9 Connochaetes gnou 64.0 166.7 Connochaetes taurinus 68.0 235.3 Damaliscus lunatus 39.5 137.0 WWW.NATURE.COM/NATURE 3

Dorcatragus megalotis 10.0 10.0 Eudorcas rufifrons 40.4 27.0 Eudorcas thomsoni 34.0 22.7 Gazella cuvieri 31.0 29.4 Gazella dorcas 31.5 16.3 Gazella gazella 31.0 23.3 Gazella leptoceros 36.0 27.2 Gazella spekei 28.0 21.3 Gazella subgutturosa 30.0 27.4 Hemitragus jemlahicus 29.5 103.3 Hippotragus equinus 85.0 274.4 Hippotragus niger 122.5 235.2 Kobus ellipsiprymnus 75.0 236.8 Kobus kob 54.5 97.5 Kobus leche 70.0 104.3 Kobus megaceros 68.7 105.5 Kobus vardoni 47.0 76.0 Litocranius walleri 38.0 35.0 Madoqua guentheri 7.5 3.7 Madoqua kirkii 7.5 4.6 Madoqua saltiana 5.0 2.3 Naemorhedus goral 14.5 32.0 Nanger dama 40.0 68.0 Nanger granti 65.0 72.1 Neotragus batesi 3.0 2.4 Neotragus moschatus 9.0 4.8 Neotragus pygmaeus 2.8 2.0 Oreamnos americanus 23.2 95.9 Oryx dammah 150.0 165.0 Oryx gazella 88.3 178.0 Ourebia ourebi 13.5 14.1 Ovis ammon ammon 118.1 120.7 Ovis aries 80.0 66.9 Ovis canadensis canadensis 65.6 83.4 Ovis dalli 97.5 80.4 Ovis nivicola 74.0 103.2 Pantholops hodgsonii 61.0 42.3 Pelea capreolus 22.5 24.0 Philantomba maxwellii 3.5 6.5 Philantomba monticola 4.5 4.4 Procapra gutturosa 23.0 31.5 Raphicerus campestris 14.5 10.9 Raphicerus melanotis 8.0 10.7 Raphicerus sharpei 6.5 7.4 Redunca arundinum 37.5 58.3 Redunca fulvorufula 26.0 30.1 Redunca redunca 30.5 51.6 Rupicapra rupicapra 23.2 40.3 WWW.NATURE.COM/NATURE 4

Saiga tatarica 29.0 42.5 Sylvicapra grimmia 9.9 18.3 Syncerus caffer 100.0 642.9 Tragelaphus derbianus 95.0 680.0 Tragelaphus angasii 65.0 110.2 Tragelaphus buxtoni 86.0 232.0 Tragelaphus euryceros 80.0 300.0 Tragelaphus imberbis 75.0 95.6 Tragelaphus oryx 54.0 647.3 Tragelaphus scriptus 41.0 49.7 Tragelaphus spekii 66.0 102.3 Tragelaphus strepsiceros 120.0 240.8 WWW.NATURE.COM/NATURE 5

Supplementary Information Table 3. Data and phylogeny of the Zalmoxis harvestmen. Body size indicators and hind-leg data of the Zalmoxis harvestmen, which we collected from various sources. The phylogenetic relationships are indicated by the tree on the left, which is based on the molecular phylogeny of ref. 71. Species Body Prosoma Hind-leg length width length Ref. Z. ziblethiurdos 1.50 0.66 2.93 66 Z. gebeleizis 2.55 0.96 3.49 66 Z. cuspanalis 3.00 8.00 67 Z. mitobatipes 3.50 11.00 67 Z. bendis 1.38 0.68 2.84 66 Z. kotys 2.36 0.92 6.30 66 Z, sabazios 2.60 0.94 5.41 66 Z. insularis 1.54 4.65 68 Z. princeps 3.18 1.05 6.67 69 Z. mendax 3.43 1.44 10.14 69 Z perditus 1.96 0.76 3.33 69 Z. kaktinsae 2.04 0.86 4.36 69 Z. pygmaeus 2.50 6.00 70 Z. robustus 4.50 12.00 70 Z. falcifer 2.28 1.00 5.45 69 Z. carwellensis 2.86 7.88 68 Z. furcifer 2.26 1.04 17.84 69 WWW.NATURE.COM/NATURE 6