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Supplementary figures: geology of Cerrejón Formation snake localities. Supplementary Figure 1. A. Location of Cerrejón Coal Mine in northern Colombia, image courtesy NASA/JPL-Caltech http://www.jpl.nasa.gov/images/policy/index.cfm. B. Topographic map view of La Puente Pit, Cerrejón Coal Mine, red points indicate Titanoboa cerrejonensis localities. Fossils representing 28 individuals were recovered along a 1.5 km long southeast trending dipslope. C. Aerial photograph of La Puente Pit. D. Vertebra of T. cerrejonensis exposed in footwall of La Puente Pit. E. Articulated vertebral series of T. cerrejonensis in field jackets. www.nature.com/nature 1

Supplementary Figure 2. Stratigraphy of the Cerrejón Formation. Titanoboa fossils were found in a gray claystone layer underlying coal seam 90. Column drawn by German Bayona. www.nature.com/nature 2

Supplementary figures: Online Methods Supplementary Figure 3. 2D homologous landmarks used in morphometric analysis demonstrated on a) Boa constrictor (USNM 220299) precloacal vertebrae 155, and b) Titanoboa cerrejonensis (holotype, UF/IGM 1), in anterior view. Morphology described by individual landmarks is as follows: 1) midline ventral margin of centrum, 2) medial contact between neural arch and centrum, 3) midline dorsal margin of centrum, 4) midline ventral margin of zygosphene, 5) midline dorsal margin of zygosphene, 6) dorsal margin of neural spine, 7) ventromedial margin of zygosphene articular facet, 8) dorsolateral margin of zygosphene articular facet, 9) ventromedial margin of prezygapophyseal articular facet, 10) dorsolateral margin of prezygapophyseal articular facet, 11) lateral margin of prezygapophyseal accessory process, 12) dorsal margin of synapophyseal articular facet, 13) ventral margin of synapophyseal articular facet, 14) contact of synapophysis with centrum. All specimens except for UF/IGM 2 were digitized on both sides of the sagittal plane and landmark coordinates were reflected to one side and averaged to minimize asymmetry and taphonomic distortion to UF/IGM 1. All specimens were digitized using TPSDig 2.1 28. www.nature.com/nature 3

Supplementary Figure 4. A) Regression of vertebral shape on vertebral position for extant boine species. Only the first dimension of the shape space, PC 1, is shown here, though the regression was done. The spline function (red line) runs through the shape mean at each position and is interpolated between positions. We performed the same analysis with a discrete function that runs through the means but is undefined between them. B) Plot of the log likelihood function for an unknown vertebra on the continuous shape gradient function. The log likelihood is highest where the shape of the unknown best fits the shape gradient (here that position is 13.497 [60-65% along the precloacal column], where positions range from 1 to 21). The likelihood function shown here is calculated over all the PC dimensions. The similarity between the likelihood curve and fitted line in part A is coincidental. The discrete likelihood function matches unknown vertebrae only to integer positions along the shape gradient. www.nature.com/nature 4

Institutional abbreviations- UF/IGM, University of Florida/Instituto Nacional de Investigaciones Geologico-Mineras, Bogota, Colombia; ROMV-R, Royal Ontario Museum, Recent Collection; USNM, United States National Museum, Smithsonian Institution Supplementary Table 1. Titanoboa cerrejonensis specimens. The official fossil repository is Instituto Nacional de Investigaciones Geologico-Mineras, Bogota, Colombia. Complete cast collections will also be housed at the Florida Museum of Natural History, University of Florida, Gainesville. Specimen Number # Vertebrae # Ribs Max. vertebral width (mm) UF/IGM 1 1 0 120.0 UF/IGM 2 2 0 119.0 UF/IGM 3 24 21 105.1 UF/IGM 4 13 3 110.5 UF/IGM 5 3 0 124.1 UF/IGM 6 1 0 - UF/IGM 7 3 0 96.6 UF/IGM 8 12 1 105.7 UF/IGM 9 1 0 - UF/IGM 10 1 0 95.9 UF/IGM 11 1 0 - UF/IGM 12 1 0 101.4 UF/IGM 13 12 15 114.0 UF/IGM 14 15 4 54.5 UF/IGM 15 1 0 76.9 UF/IGM 16 26 0 80.2 UF/IGM 17 2 0 115.4 UF/IGM 18 2 0 121.0 UF/IGM 19 1 0 - UF/IGM 20 1 0 - UF/IGM 21 1 0 - UF/IGM 22 1 0 - UF/IGM 23 1 0 - UF/IGM 24 6 0 - UF/IGM 25 2 0 - UF/IGM 26 1 0 72.0 UF/IGM 27 4 0 - UF/IGM 28 1 0 - www.nature.com/nature 5

Supplementary Table 2. Examined specimens (extant). Taxon Specimen # SVL (mm) TBL (mm) Vertebral width 60% (mm) Vertebral width 65% (mm) Acrantophis dumerili USNM 497683 1423 1535 6.38 6.53 Acrantophis dumerili ROMV-R 7864 1900 2040 19.66 19.04 Acrantophis dumerili ROMV-R 7833 2390 2480 23.50 21.42 Boa constrictor USNM-348597 1355 1606 12.92 12.64 Boa constrictor ROMV-R 7182 2970 3220 27.69 27.08 Boa constrictor USNM 220299 3129 3434 28.20 28.01 Candoia carinata USNM 348502 803 867 11.22 10.96 Corallus caninus ROMV-R7498 1216 1450 12.20 11.80 Corallus enhydris ROMV-R 4075 1360 1734 10.79 10.54 Epicrates anguilifer ROMV-R 7842 1960 2330 17.61 17.97 Epicrates cenchria ROMV-R 7902 1195 1380 11.54 11.27 Epicrates cenchria ROMV-R 5345 1070 1210 10.65 10.22 Epicrates inornatus ROMV-R 7900 1450 1700 11.66 11.58 Epicrates striatus ROMV-R 7901 1385 1770 11.20 10.85 Epicrates striatus UF63866 1950 2250 15.09 15.08 Epicrates subflavus UF69268 1490 1720 10.80 10.66 Eunectes murinus ROMV-R 7340 2110 2470 17.10 17.26 Eunectes murinus ROMV-R 7285 2910 3320 24.32 23.99 Eunectes notaeus ROMV-R 7307 2190 2510 17.67 17.24 Eunectes notaeus ROMV-R 7286 2310 2690 24.33 23.12 Sanzinia madagascarensis USNM 220313 1610 1760 16.15 15.69 Supplementary Table 3. Total Body length (TBL) minima and maxima of major snake taxa. Only maxima are reported for monotypic Anilius scytale. TBLs for pachyophiids are based on observations by J.J.H. Reported maximum TBLs for extant Boines and Pythonids are poorly constrained and are often anecdotal. We relied on the maximum verifiable first-hand measurements for both Eunectes and Python 1 Two fossil records of giant boids are not considered here: Chubutophis 29 is represented by a vertebrae estimated to be from a juvenile individual 5-7 meters in TBL with adult lengths for the taxon estimated to be 10-12 meters 7,29. The ontogenetic status of the specimen is poorly constrained, however, because the characters used to assign juvenile status (poor development of a haemal keel, angle of centrum, thickness of zygosphene) are subject to considerable intracolumnar and interspecific variation. The specimen additionally includes somatically mature vertebral morphology, including a tall, well-developed neural spine. A large partial vertebral centrum from Paleogene sediments of Argentina was considered to represent a snake 15-20 meters TBL 7. The specimen is approximately 60% the size of the Titanoboa paratype UF/IGM 2 (centrum length of partial centrum = ~3.2 cm, centrum length of UF/IGM 2 = 5.4 cm), but is too incomplete to determine intracolumnar position or systematic interrelationships. Methods for calculating TBL from vertebral size in both Chubutophis and the partial centrum were not defined. Size data for other recent and fossil snakes from literature sources 6,8,9,30-47. Taxon Minimum TBL Maximum TBL www.nature.com/nature 6

Elapidae Simoselaps anomalus (21 cm) Ophiophagus hannah (~5.5 m) Lamprophiinae Aparallactus jacksonii (26 cm) Mehelya capensis (1.6 m) Colubridae Tantilla atriceps (23 cm) Pytas mucosus (~3.5 m) Homalopsinae Enhydris indica (35 cm ) Homalopsis buccata (1.3 m) Viperidae Bitis scheideri (20 cm) Lachesis muta (2.5 m) Xenodermatidae Achalinus rufescens (39 cm) Xenodermus javanicus (67 cm) Acrochordus A. granulatus (1.6 m) A. dehmi (~3 m) Pareatidae Pareas margaritophorous (43 cm) Alopeltura boa (87 cm) Bolyeriidae Bolyeria multicarinata (95 cm) Casarea dussumieri (1.28 m) Tropidophiinae Tropidophis pardalis (34 cm) Tropidophis melanurus (1.06 m) Ungaliophiinae Exiliboa placata (41 cm) Ungaliophis continentalis (75 cm) Boinae Candoia carinata (paulsoni) (137 cm) Titanoboa cerrejonensis (12.8 m) Pythonidae Antaresia stimsoni (87 cm) Python reticulatus (~8.3 m)/ Liasis dubudingala (~9 m) Erycinae Eryx millaris (50 cm) Lichanura trivirgata (112 cm) Uropeltinae Rhinophis travancoricus (18 cm) Uropeltis macrorhynchus (74 cm) Cylindrophis C. maculatus (60 cm) C. rufus (87 cm) Anilius scytale - ~1 m Typhlopidae Typhlops zenkeri (13 cm) Rhinotyphlops schlegelii (82 cm) Anomalopedidae Helminthophis petersi (11 cm) Liotyphlops albirostris (30 cm) Leptotyphlopidae Leptotyphlops carlae (10 cm) Leptotyphlops humilis (40 cm) Madtsoiidae Patagoniophis australiensis (50 cm) Gigantophis garstini (10.7 m) Palaeopheidae Palaeophis casei (50 cm) Palaeophis colossaeus (~9 m) Pachyophiidae Pachyophis woodwardi (~50 cm) Pachyrhachis problematicus (~1.5 m) Supplementary Notes Additional references cited in Supplementary information. 31. Rohlf, F. TpsDig, version 2.1 (Stony Brook Department of Ecology and Evolution, State University of New York at Stony Brook, 2006). 32. Albino, A. M. Snakes from the Paleocene and Eocene of Patagonia (Argentina): Paleoecology and coevolution with mammals. Hist. Biol. 7, 51-69 (1993). 33. Pope, C. H. The reptiles of China (The American Museum of Natural History, New York, 1935). 34. Smith, M. A. Fauna of British India, Ceylon and Burma, including the whole of the Indo-Chinese sub-region. Reptilia and Amphibia. Volume III, Serpentes. (Taylor and Francis, London, 1943). 35. Hoffstetter, R. Les serpents du Néogène du Pakistan (couches des Siwaliks). Bull. Soc. Géol. France, Sér. 7 6, 467-474 (1964). 36. Bogert, C. M. A new genus and species of dwarf boa from southern Mexico. Amer. Mus. Novit. 2354, 1-38 (1968). 37. Gyi, K. K. A revision of colubrid snakes of the subfamily Homalopsinae. Univ. Kan. Pub. Mus. Nat. Hist. 20, 47-223 (1970). 38. Pitman, C. R. S. A guide to the snakes of Uganda (Revised edition) (Wheldon & Wesley Ltd, Codicote, Hertfordshire, 1974). www.nature.com/nature 7

39. Roux-Estève, R. Révision systématique des Typhlopidae d Afrique Reptilia- Serpentes. Mém. Mus. Natl. Hist. Natur. 87, 1-313 (1974). 40. Tolson, P. J., & R. W. Henderson. The Natural History of West Indian boas (R & A Publishing, Ltd., Tauton, Somerset, 1993). 41. Coborn, J. The Mini-atlas of Snakes of the World (T.F.H. Publications, Neptune City, New Jersey, 1994). 42. Greene, H. W. Snakes, the evolution of mystery in nature. University of California Press, Berkeley, California, 1997). 43. Greer, A. E. The biology and evolution of Australian snakes (Surrey Beatty & Sons, Chipping Norton, New South Wales, 1997). 44. Starace, F. Guide des serpents et amphisbènes de Guyane (IBIS Rouge, Guadeloupe, Guyane, 1998). 45. Holman, J. A. The fossil snakes of North America (Indiana University Press, Indianapolis, Indiana, 2000). 46. Smith, H. M., Chiszar, D., Tepedelen, K. & van Breukelen, F. A revision of bevelnosed boas. Hamadryad 26, 283-315 (2001). 47. Boback, S. M. & Guyer, C. Empirical evidence for an optimal body size in snakes. Evolution 57, 345-351 (2003). 48. Ernst, C. H. & Ernst, E. M. Snakes of the United States and Canada (Smithsonian Institution Press, Washington D.C., 2003). 49. Scanlon, J. D. Australia s oldest known snakes: Patagoniophis, Alamtiophis, and cf. Madtsoia (Squamata: Madtsoiidae) from the Eocene of Queensland. Mem. Queensl. Mus. 51, 215-235 (2005). 50. Hedges, S. B. At the lower size limit in snakes: two new species of threadsnakes (Squamata: Leptotyphlopidae: Leptotyphlops) from the Lesser Antilles. Zootaxa 1841, 1-30 (2008). www.nature.com/nature 8