Table S1. Stomatal sizes (S) and densities (D) for species in Figs. 1, 4, and 5. Type codes correspond to the symbol key in Fig. 1. Species Type code Age, Myr S, µm2 D, mm-2 Ref. Aglaophyton major 1 395 14000 4.5 (1) Sawdonia ornata 2 395 1161 4.3 (1) Horneophyton lignieri 2 395 20700 3.0 (1) Aglayophyton major 1 395 14000 1.0 (1) Rhynia gwynne-vaughanii 2 395 8500 1.8 (1) Nothia aphylla 1 395 9975 5.5 (1) Asteroxylon mackiei 2 395 4550 21 (1) Drepanophycus spinaeformis 2 395 1734 16.6 (1) Hsua deflexa 2 395 3149 n/a (2) Sporathylacium salopense 2 395 1190 42 (3) Sporoginites exuberans 2 395 2475 11 (4) Baragwanathia abitibiensis 2 390 n/a 28 (5) Drepanophycus spinaeformis 2 390 3600 13 (6) Cooksonia pertoni 2 390 2250 n/a (6) Unknown 1 2 390 1054 n/a (6) Unknown 2 2 390 900 n/a (6) Huia gracilis 2 390 n/a 13 (7) Archaeopteris macilenta 4 385 3348 32 (8) Archaeopteris macilenta 4 385 2793 37 (8) Archaeopteris sp. 4 365 1184 n/a (9) Hsua robusta 2 355 5400 5 (10) Swillingtonia denticulata 5 310 300 787.8 (11) Blanzyopteris praedentata 3 305 1650 310 (12) Reticulopteris germarii 3 305 300 300 (13) Barthelpteris germarii 3 305 n/a 304 (13) Neuropteris obliqua 3 305 300 113 (14) Laveineopteris loshii 3 305 250 325 (14) Neuralethopteris schlehanii 3 305 360 300 (14) Neuropteris loshii 3 305 206 200 (15) Neuropteris tenuifolia 3 305 206 300 (15) Neuropteris rarinervi 3 305 300 140 (15) Neuropteris ovata var. simonii 3 305 300 90 (15) Neuropteris ovata var. sarana 3 305 360 28 (15) Neuropteris aconiensis 3 305 120 50 (15) Neuropteris flexuosa 3 305 250 120 (15) Neuropteris scheuchzeri 3 305 200 90 (15) Neuropteris macrophylla 3 305 200 65 (15) Neuropteris britannica 3 305 206 130 (15) Neuropteris subariculata 3 305 297 91 (15) Neuropteris sp. 1 3 305 404 180 (15) Neuropteris sp. 2 3 305 206 180 (15) Alethopteris sullivanti 3 305 702 472 (16) Alethopteris lesquereuxi 3 305 616 250 (17) Lepidodendron obovatum 2 305 1575 200 (18) Lepidodendron dichotomum 2 305 1000 450 (18) Lepidodendron loricatum 2 305 1125 200 (18) Senftenbergia plumosa 3 305 200 200 (19) Laveinopteris tenuifolia 3 305 450 370 (20) Cordaites principalis morph. 1 5 305 104 560 (21) Cordaites principalis morph. 2 5 305 510 104 (21) Cordaites principalis morph. 3 5 305 216 150 (21) Cordaites principalis morph. 4 5 305 540 204 (21) Pecopteris nyranensis 3 305 300 n/a (22) 1 Pecopteris aspidioides 3 305 325 n/a (22) Pecopteris polipodioides 3 305 630 n/a (22) Pecopteris miltonii 3 305 800 n/a (22) Neopteris ovata 3 305 150 343 (23) Lescuropteris genuina 3 305 400 91 (24) Schopfiastrum decussatum 3 305 425 28 (25) Karinopteris spp. 3 300 n/a 38 (26) Lebachia frondosa 5 288 n/a 309 (11) Sphenophyllum apiciserratum 6 270 900 38 (27) Sphenophyllum kaboense 6 270 840 34 (27) Callipteris changii 7 270 n/a 384 (27) Psygmophyllum multipartitum 8 270 n/a 296 (28) Gigantonoclea guizhouensis 9 270 2530 70 (28) Gigantonoclea pubescens 9 260 450 184 (28) Notophytum krauselii 5 225 1700 n/a (29) Eoginkgoites sydneyi 9 200 560 n/a (30) Glossophyllum florinii 8 200 3120 48 (31) Pagiophyllum papillatus 5 200 4510 111 (32) Brachyphyllum comancheanum 5 200 900 63 (33) Eoginkgoites davidsonii 9 200 900 30 (34) Aricycas paulae 10 200 3600 60 (35) Williamsonia nizhonia 9 200 n/a 15 (36) Cladophlebis yazzia 7 200 1296 20 (37) Nilsonia sturii 10 200 741 100 (31) Nilsonia riegeri 10 200 741 n/a (31) Nilsonia lunzensis 10 200 1540 42 (31) Nilsonia neuberi 10 200 945 117 (31) Sphenobaiera huangii 8 190 1216 48 (38) Czekanowskia nizhonia 8 175 n/a 50 (37) Brachyphyllum negevensis 5 170 n/a 40 (39) Brachyphyllum pulcher 5 170 n/a 50 (39) Pagiophyllum peregrinum 5 168 n/a 109 (40) Czekanowskia turneri 8 150 3500 24 (41) Czekanowskia nipponica 8 150 n/a 32 (41) Otozamites archangelski 9 140 5092 n/a (42) Otozamites ornatus 9 140 2652 69 (42) Otozamites parviauriculata 9 140 5022 n/a (42) Otozamites parvus 9 140 2046 n/a (42) Otozamites sanctaecrucis 9 140 2080 n/a (42) Otozamites waltonii 9 140 3000 n/a (42) Ptilophyllum antarcticum 9 140 1350 n/a (42) Ptilophyllum ghiense 9 140 1350 n/a (42) Ptilophyllum hislopi 9 140 2880 n/a (42) Ptilophyllum valvatum 9 140 3672 n/a (42) Frenelopsis varians 5 140 n/a 31 (43) Pseudofrenelopsis dalatzensis 5 140 7125 72 (44) Pseudofrenelopsis heishanensis 5 140 10000 61 (44) Pseudofrenelopsis papillosa 5 140 5829 55 (44) Pseudoctenus ornata 10 140 10000 14 (45) Sagenopteris inequilateralis 11 140 1242 40 (46) Gleichenia chaloneri 7 140 864 n/a (47) Glenrosa texensis 5 130 n/a 48 (48) Glenrosa pagiophylloides 5 130 n/a 28 (48) Tarphyderma glabra 5 120 3744 n/a (49) Tomaxellia biforme 5 120 4900 n/a (50) Pseudoctenis ornata 10 120 10000 n/a (45) Pseudofrenelopsis varians 5 110 10000 n/a (51) Pseudofrenelopsis parceramosa 5 110 6400 n/a (51) Pseudofrenelopsis intermedia 5 110 5000 n/a (51) 2 Pseudofrenelopsis nathorstiana 5 110 4526 n/a (51) Mirovia szaferi 5 110 9900 n/a (52) Mirovia gothanii 5 110 9900 n/a (52) Araucaria grandifolia 5 105 1404 40 (53) Araucaria seorsum 5 105 4700 28 (54) Araucaria lanceolatus 5 105 3800 32 (54) Araucaria acutifoliatus 5 105 3350 42 (54) Araucaria falcatus 5 105 1680 67 (54) Araucaria carinatus 5 105 4375 110 (54) Araucaria otwayensis 5 105 2808 n/a (54) Pseudofrenelopsis nathorstiana 5 100 4526 115 (51) Pseudofrenelopsis parceramosa 5 100 6400 42 (51) Watsoniocladus virginiensis 5 100 5200 46 (51) Nilsonia bohemia 10 95 400 n/a (55) Nilsonia orientalis 10 95 75 n/a (55) Jursia jirusii 10 95 759 n/a (55) Nilsoniopteris pecinovensis 9 95 900 n/a (55) Frenelopsis hogeneggeri 5 95 4900 100 (56) Frenelopsis kaneviensis 5 95 2500 30 (56) Frenelopsis veneta 5 95 8100 90 (56) Brachyphyllum patens 5 95 9000 57 (57) Pagiophyllum bladensis 5 80 594 n/a (58) Pandanites trinervis 12 80 250 144 (59) Sabalites longirachis 12 70 100 n/a (59) Decussocarpus brownei 5 50 558 116 (60) Falcatifolium australis 5 50 1080 158 (60) Dacrycarpus eocinica 5 50 972 252 (60) Prumnopitys tasmanica 5 50 1107 178 (60) Prumnopitys lanceolata 5 50 598 200 (60) Ocotea obtusifolia 12 45 616 364 (61) Knightiophyllum wilcoxianum 12 45 336 n/a (62) Knightia excelsa 12 45 616 596 (62) Sequoia chinensis 5 45 3888 60 (63) Lepidozamia hopei 10 40 2753 n/a (64) Lepidozamia peroffskyana 10 40 2394 n/a (64) Lepidozamia hopeites 10 40 2242 n/a (64) Lepidozamia faveolata 10 40 1734 n/a (64) Metasequoia milleri 5 40 600 n/a (63) Rhodophyllum pasekovicum 12 40 750 n/a (65) Rhodophyllum sinuata 12 40 750 n/a (65) Rhodophyllum sinuata var. engelhardti 12 40 1800 n/a (65) Rhodophyllum tristanioides 12 40 625 n/a (65) Rhodophyllum rossmasslerii 12 40 600 n/a (65) Rhodophyllum psidioides 12 40 750 n/a (65) Rhodophyllum sinuatum 12 40 529 n/a (65) Rhodophyllum reticulosum 12 40 1050 n/a (65) Sequoia sempevirens 5 15 3162 85 (63) Unknown Arundinoideae 13 10 26 285 (66) Unknown graminoid 13 0.037 67 155 (67) Unknown graminoid 13 0.036 81 132 (67) Unknown graminoid 13 0.035 70 112 (67) Unknown graminoid 13 0.034 74 116 (67) Unknown graminoid 13 0.032 65 100 (67) Unknown graminoid 13 0.031 54 143 (67) Unknown graminoid 13 0.031 57 109 (67) Unknown graminoid 13 0.029 60 149 (67) Unknown graminoid 13 0.029 59 108 (67) Unknown graminoid 13 0.028 68 149 (67) Unknown graminoid 13 0.027 60 156 (67) 3 Unknown graminoid 13 0.026 71 121 (67) Unknown graminoid 13 0.026 50 174 (67) Unknown graminoid 13 0.025 67 177 (67) Unknown graminoid 13 0.024 65 132 (67) Unknown graminoid 13 0.024 59 113 (67) Unknown graminoid 13 0.024 53 135 (67) Unknown graminoid 13 0.023 59 197 (67) Unknown graminoid 13 0.023 63 120 (67) Unknown graminoid 13 0.023 54 140 (67) Unknown graminoid 13 0.023 59 135 (67) Unknown graminoid 13 0.022 65 172 (67) Unknown graminoid 13 0.022 62 230 (67) Unknown graminoid 13 0.021 72 96 (67) Unknown graminoid 13 0.021 66 124 (67) Unknown graminoid 13 0.021 65 146 (67) Unknown graminoid 13 0.021 70 152 (67) Unknown graminoid 13 0.02 77 162 (67) Unknown graminoid 13 0.02 63 147 (67) Unknown graminoid 13 0.019 64 214 (67) Unknown graminoid 13 0.019 66 160 (67) Unknown graminoid 13 0.018 59 141 (67) Unknown graminoid 13 0.018 58 167 (67) Unknown graminoid 13 0.017 66 151 (67) Unknown graminoid 13 0.017 59 200 (67) Unknown graminoid 13 0.016 59 198 (67) Unknown graminoid 13 0.016 59 163 (67) Unknown graminoid 13 0.016 56 214 (67) Unknown graminoid 13 0.015 55 143 (67) Unknown graminoid 13 0.015 55 163 (67) Unknown graminoid 13 0.015 62 97 (67) Unknown graminoid 13 0.014 66 147 (67) Unknown graminoid 13 0.014 63 121 (67) Unknown graminoid 13 0.014 58 106 (67) Unknown graminoid 13 0.014 56 150 (67) Unknown graminoid 13 0.014 55 114 (67) Unknown graminoid 13 0.013 58 124 (67) Unknown graminoid 13 0.013 62 86 (67) Unknown graminoid 13 0.013 64 107 (67) Unknown graminoid 13 0.013 62 128 (67) Unknown graminoid 13 0.011 65 182 (67) Unknown graminoid 13 0.011 62 135 (67) Unknown graminoid 13 0.01 60 83 (67) Unknown graminoid 13 0.009 62 145 (67) Unknown graminoid 13 0.009 61 123 (67) Unknown graminoid 13 0.008 55 166 (67) Unknown graminoid 13 0.008 56 89 (67) Unknown graminoid 13 0.008 55 167 (67) Unknown graminoid 13 0.007 58 154 (67) Unknown graminoid 13 0.006 61 82 (67) Unknown graminoid 13 0.005 56 95 (67) Unknown graminoid 13 0.005 66 73 (67) Unknown graminoid 13 0.004 71 84 (67) Unknown graminoid 13 0.003 59 125 (67) Unknown graminoid 13 0.002 60 154 (67) Unknown graminoid 13 0.001 62 163 (67) Unknown graminoid 13 0.001 59 117 (67) Abies normanniana 5 0 1372 110 (68) Cedrus deodara 5 0 1178 85 (68) Pinus sylvestris 5 0 784 120 (68) 4 Picea pungens 5 0 2205 39 (68) Larix decidua 5 0 1092 16 (68)