Vol 45715 February 2009 doi:10.1038/nature07671 nature LETTERS Giant bold snake from the Palaeocene neotropics reveals hotter past equatorial temperatures Jason J. Head1, Jonathan I. Bloch2, Alexander K. Hastings2, Jason R. Bourque2, Edwin A. Cadena2'3, Fabiany A. Herrera2'3, P. David Polly4 & Carlos A. Jaramillo3 The largest extant snakes live in the tropics of South America and southeast Asia1"3 where high temperatures facilitate the evolution of large body sizes among air-breathing animals whose body tempera- tures are dependant on ambient environmental temperatures (poi- kilothermy)4,5. Very little is known about ancient tropical terrestrial ecosystems, limiting our understanding of the evolution of giant snakes and their relationship to climate in the past. Here we describe a bold snake from the oldest known neotropical rainforest fauna from the Cerrejon Formation (58-60 Myr ago) in northeastern Colombia. We estimate a body length of 13 m and a mass of 1,135 kg, making it the largest known snake6-9. The maximum size of poikilothermic animals at a given temperature is limited by meta- bolic rate4, and a snake of this size would require a minimum mean annual temperature of 30-34 ?C to survive. This estimate is consis- tent with hypotheses of hot Palaeocene neotropics with high con- centrations of atmospheric C02 based on climate models10. Comparison of palaeotemperature estimates from the equator to those from South American mid-latitudes indicates a relatively steep temperature gradient during the early Palaeogene greenhouse, similar to that of today. Depositional environments and faunal composition of the Cerrejon Formation indicate an anaconda-like ecology for the giant snake, and an earliest Cenozoic origin of neo- tropical vertebrate faunas. Serpentes Linnaeus 1758 Boidae Gray 1825 Boinae Gray 1825 Titanoboa cerrejonensis gen. et sp. nov. Etymology. The generic name combines 'Titan (Greek, giant) with 'Bod, type genus for Boinae. The specific name refers to the Cerrejon region, Guajira Department, Colombia. The full translation is 'titanic boa from Cerrejon'. Holotype. UF/IGM 1, a single precloacal vertebra (Fig. la-d). Locality. La Puente Pit, Cerrejon Coal Mine, Guajira Peninsula, Colombia (palaeolatitude 5.5? N; Supplementary Fig. 1). Horizon. Single claystone layer, middle segment of the Cerrejon Formation (Supplementary Fig. 2); middle-late Palaeocene epoch (58-60 Myr ago), palynological zone Cu-02 (ref. 11). Referred material. UF/IGM 2 (paratype), nearly complete precloacal vertebra (Fig. lg, h). UF/IGM 3-UF/IGM 28,184 additional precloa- cal vertebrae and ribs representing 28 individuals (Supplementary Table 1). Figure 11 Titanoboa cerrejonensis precloacal vertebrae, a, Type specimen (UF/IGM 1) in anterior view compared to scale with a precloacal vertebra from approximately 65% along the precloacal column of a 3.4 m Boa constrictor. Type specimen (UF/IGM 1) shown in posterior view (b), left lateral view (c) and dorsal view (d). Seven articulated precloacal vertebrae (UF/IGM 3) in dorsal view (e). Articulated precloacal vertebra and rib (UF/ IGM 4) in anterior view (f). Precloacal vertebra (paratype specimen UF/ IGM 2) in anterior view (g) and ventral view (h). Precloacal vertebra (UF/ IGM 5) in anterior view (i) and posterior view (j). All specimens are to scale. Department of Biology, University of Toronto, Mississauga, Ontario L5L1C6, Canada. Florida Museum of Natural History, University of Florida, Gainesville, Florida 32611-7800, USA. ^Smithsonian Tropical Research Institute, Box 0843-03092, Balboa, Ancon Republic of Panama. ^Department of Geological Sciences, Indiana University, Bloomington, Indiana 47405-1405, USA. 715 ?2009 Macmillan Publishers Limited. All rights reserved LETTERS NATURE|Vol 457|5 February 2009 Diagnosis. Extremely large-bodied boine snake with robust precloa- cal vertebrae possessing a uniquely T-shaped neural spine composed of a transversely expanded posterior margin and distinctly narrow, blade-like anterior process (Fig. la-d, i, j). Subcentral and lateral foramina are extremely reduced. The vertebrae possess a character combination unique to boine snakes. These are: the presence of paracotylar fossae and foramina; straight, posteromedially angled interzygapophyseal ridges; and the vaulted, bi-angled posterior margin of the neural arch. These charac- ters are also present in some madtsoiid snakes; however, all specimens of Titanoboa possess short, posteriorly angled prezygapophyseal accessory processes as in boines but unlike madtsoiids, and lack the parazygantral foramina and laterally extensive synapophyses that dia- gnose Madtsoiidae12. Among extant boines, Titanoboa is united with Boa constrictor on the basis of dorsolaterally positioned paracotylar fossae and foramina. Vertebrae of Titanoboa are the largest recovered for any extant or fossil snake6"8. Body size can be predicted from vertebral dimensions in taxa where body length evolved by increasing the size of vertebrae instead of their number. This is true for all extant giant boids and pythonids13 and is inferred for Titanoboa because it is united with Boa within Boinae. Vertebral size changes along the vertebral column in snakes, and the position of isolated fossil vertebrae, must be deter- mined before body length can be reconstructed. We estimated verteb- ral position by matching the vertebral shape of two undistorted specimens of Titanoboa to a composite geometric morphometric model vertebral column14 constructed from extant boines (see Methods). Both vertebrae were estimated to be located 60-65% back along the precloacal vertebral column from the axis-atlas complex. Regressions of vertebral width from this region against body lengths for extant boines indicate a snout-vent length (SVL) of 12.01 ? 2.04 m (39 ft) and a total body length (TBL) of 12.82 ? 2.18 m (42 ft) for Titanoboa. Incorporating SVL values of this study into the relationship between length and body mass determined for extant Eunectes murinus (green anaconda)2 and Python natalensis (southern African python)15 results in an estimated mass for Titanoboa of 1,135 kg (1.27 ton) with a range of 652-l,819kg (0.73-2.03 ton). Body size estimates for Titanoboa greatly exceed the largest veri- fiable body lengths for extant Python and Eunectes, which are approximately 9 m and 7 m, respectively1. Maxima for these taxa are extraordinary, however, and surveys of large populations have not recovered individuals exceeding 6 m TBL for Python and 6.5 m TBL for Eunectes2'1"'15'16. Conversely, the record of Titanoboa includes eight individuals represented by vertebrae of approximately the same size as the elements used to estimate TBL (Fig. 1, Supplementary Table 1), indicating that extremely large body size was common in the taxon. Titanoboa is larger than all other giant fossil taxa, including palaeopheids and madtsoiids6,9, making it the largest known snake (Fig. 2). Discovery of Titanoboa extends the known range of body lengths in snakes by more than two orders of magnitude, between TBLs of 10 cm (Leptotyphlops carlae) and 12.8 m. Our estimates of body size also demonstrate that Titanoboa is the largest known non- marine vertebrate from the Palaeocene and early Eocene17. Large body size in Titanoboa provides significant information on equatorial climates during the Palaeogene. Snakes have body tempera- tures that are dependant on their ambient environment (poiki- lothermy), and ambient temperature regulates maximum body size in poikilofhermic vertebrates4,5. Palaeotemperature can be predicted from fossils of poikilofhermic taxa using a model for extant taxa4 that demonstrates that the difference in maximum body size of taxa between two localities is proportional to the difference in ambient temperature for a given mass-specific metabolic rate (see Methods). We used the difference in TBL between Titanoboa and Eunectes murinus, the largest snake in the modern neotropics, to reconstruct the mean annual tem- perature (MAT) for the Palaeocene of equatorial South America. The relationship between TBL and temperature in Eunectes indicates that the approximate minimum MAT under which a 13-m-long boine TBL (m) 7 ! 11 13 15 ?E Elapidae Lamprophiinae i Colubroidea I 1?i Homalopsinae 1 1 Viperidae ? Xenodermatidae ' ? Acrochordus -*H Pareatidae -? Bolyeriidae Boinae -???? Erycinae ??** Ungaliophiinae Pythonidae HE --??? Uropeltinae ?M Cylindrophis --t?' Tropidophiinae 1 Anilius scytale t?i Typhlopidae Anomalopedidae *? Leptotyphlopidae Madtsoiidaef Palaeopheidaet Pachyophiidaet Figure 2 | Body size ranges for major snake clades plotted along phylogeny28"30 (Supplementary Table 3). Controversial fossil (dagger) lineages Madtsoiidae, Pachyophiidae and Palaeopheidae were placed as an unresolved polytomy at the base of the snake crown. The size range increase in Boinae based on the Titanoboa cerrejonensis mean TBL estimate is in dark red; maximum TBL estimate for Titanoboa is in pink. snake could survive is 32-33 ?C, ranging between 30 ?C and 34 ?C for body sizes between 11m and 15 m (Fig. 3). These temperature estimates are consistent with hot Palaeogene climate models requiring high atmospheric pco2 concentrations of approximately 2,000 parts per million18, and are slightly higher than temperatures derived from planktonic foraminifer oxygen isotopes by 1-5 ?C19. These estimates exceed MATs derived from coeval Cerrejon palaeofloras by 6-8 ?C20, but palaeotemperatures based on fossil leaf assemblages from riparian and wetland habitats of rain- forests are underestimates21. Palaeotemperature estimates of 30- 34 ?C exceed MAT maxima of modern tropical forests22. However, the high rainfall estimates from the Cerrejon palaeoflora (~4m per year11) combined with increased pco could have maintained forest floras under higher temperature conditions23. Palaeotemperature estimates near the equator allow reconstruction of latitudinal temperature gradients across South America during the Palaeogene. MAT for the middle Palaeocene of Argentina (palaeola- titude -51? S) is 14.1 ?C ? 2.6 ?C24, indicating a latitudinal gra- dient of 13-22 ?C between 5? N and 51? S, with a midpoint of 18 ?C (accounting for taphonomic bias21 suggests MAT of 17.6 ?C ? 3.6 ?C with a gradient midpoint of 15.4 ?C). Our midpoint estimates during the early Palaeogene greenhouse approximate the modern temper- ature difference across South America (Fig. 3) and are not consistent with the climatic thermostat hypothesis that predicts cooler equatorial temperatures and a shallow temperature gradient during greenhouse intervals25. If our Palaeocene estimates are correct, tropical tempera- tures at the slightly younger (55.8 Myr ago) Palaeocene-Eocene ther- mal maximum (PETM) could have reached 38-40 ?C, resulting in widespread equatorial heat-death as recent models and other proxy data have predicted26. However, we still lack empirical evidence of the effects of the PETM on tropical floras and faunas. Remains of Titanoboa were found in depositional environments consisting of coastal plains incised by large-scale river systems within a wet tropical rainforest11'2" and were associated with an aquatic verte- brate fauna including podocnemidid pleurodire turtles, dyrosaurid 716 ?2009 Macmillan Publishers Limited. All rights reserved NATURE|Vol 457|5 February 2009 LETTERS 40 35 30 25 20 15 10 _^-*^X--*~~* ^^* ^^^C?r MAPT 5.5? N ~^? i MAT 5.5? N I >cene rature lent A/ i i Palaec tempe grad 1/ Rec tempe grac ent rature lent \ i MAPT 51? S ' / " MAT 51? S L -?'?i???^ i?,??,?,?i?i?|?,?,?,?i? 10 15 TBL (m) 20 25 Figure 3 | Mean annual palaeotemperature and Palaeocene latitudinal temperature gradients derived from body size of the green anaconda Eunectes mur'mus (light green) and body size estimates of Titanoboa cerrejonensis (dark green). Curves represent model body size increases with temperature in boine snakes based on a maximum TBL for Eunectes of 7.3 m at modern neotropical MAT of 26 ?C (lower curve) and 27 ?C (upper curve). Light red regions indicate error for Titanoboa TBLs and resultant temperature ranges. A MAPT gradient of 18 ?C from equatorial to mid- latitudes at ~58Myr ago is equivalent to the modern gradient (18-19 ?C). Silhouettes are to scale for Titanoboa, Eunectes and a 1.85-m-tall adult human male. mesoeucrocodylians, and elopomorph and dipnoan fishes. Similarities between depositional environments of the Cerrejon Formation and habitats of extant Eunectes together with inferred prey taxa (crocodyliforms) indicate a similar ecology of Titanoboa to mod- ern anacondas2'3. Discovery of Titanoboa and the additional Cerrejon Formation fossil record indicates that components of modern neo- tropical riverine vertebrate faunas were assembled at most six to seven million years after the Cretaceous-Palaeogene extinction event. METHODS SUMMARY We estimated SVL and TBL in Titanoboa by first determining the intracolumnar position of isolated precloacal vertebrae through maximum likelihood iden- tification of quantified vertebral morphology against morphological change along a model boine vertebral column. We regressed SVL and TBL of extant taxa onto vertebral width (postzygapophyseal width) for the intracolumnar regions corresponding to the positions determined for the fossil elements, and used the resulting equations to calculate SVL and TBL for fossil specimens. We estimated mean annual palaeotemperatures (MAPT) by solving the equation describing size differences across a temperature gradient at a standard coefficient of metabolism [Qi0]27, TBLs for Titanoboa of 10.6-14.9m, maximum TBL for Eunectes murinus of 7.3 m1, and MAT values for modern neotropical lowland rainforests of 26-27 ?C22. Full Methods and any associated references are available in the online version of the paper at www.nature.com/nature. Received 11 October; accepted 26 November 2008. 1. Murphy, J. C. & Henderson, R. W. Tales of Giant Snakes: A Natural History of Anacondas and Pythons (Krieger, 1997). 2. Rivas, J. The Life History of the Green Anaconda (Eunectes murinus), with Emphasis on its Reproductive Biology. Dissertation, Univ. Tennessee (1999). 3. Dirksen, L. Anakondas: monographische Revision der Gattung Eunectes Wagler 7830 (Serpentes, Boidae) (Natur und Tier, 2002). 4. Makarieva, A. M., Gorshkov, V. G. & Li, B.-L Gigantism, temperature and metabolic rate in terrestrial poikilotherms. Proc. R. Soc. Lond. B 272, 2325-2328 (2005). 5. Makarieva, A. M., Gorshkov, V. G. & Li, B.-L. Temperature-associated upper limits to body size in terrestrial poikilotherms. Oikos 111, 425-436 (2005). 6. Rage, J.-C. Palaeophis colossaeus nov. sp. (le plus grand Serpent connu?) de I'Eocene du Mali et le probleme du genre chez les Palaeopheinae. C.R. Acad. Sci. Ser. 2,1741-1744 (1983). 7. Albino, A. M. Serpientes gigantes en la Patagonia. Ciencia Hoy 3, 58-63 (1991). 8. Scanlon, J. D.& Mackness, B. S. A new giant python from the Pliocene Bluff Downs local fauna of northeastern Queensland. Alcheringa 25, 425-437 (2002). 9. Head, J. J. & Polly, P. 0. They might be giants: morphometric methods for reconstructing body size for the World's largest snakes. J. Vertebr. Paleontol. 24 (suppl. 3), 68A (2004). 10. Sloan, L. C. & Shellito, L. J. in Causes and Consequences of Globally Warm Climates in the Early Paleogene (eds Wing, S. L, Gingerich, P. 0., Schmitz, B. & Thomas, E.) 25-47 (Geological Society of America Special Paper, 369, 2003). 11. Jaramillo, C. et al. Palynology of the upper Paleocene Cerrejon Formation, Northern Colombia. Palynology 31,153-189 (2007). 12. Scanlon, J. D. Skull of the large non-macrostomatan snake Yurlunggur from the Australian Oligo-Miocene. Nature 439, 839-842 (2006). 13. Head, J. J. & Polly, P. 0. Dissociation of somatic maturity from segmentation drives gigantism in snakes. Biol. Lett. 3, 296-298 (2007). 14. Polly, P. D. & Head, J. J. in Morphometrics-Applications in Biology and Paleontology (ed. Elewa, A. M. T.) 197-222 (Springer, 2004). 15. Alexander, G. J. in Biology of the Boas and Pythons (eds Henderson, R. W. & Powell, R.) 51-75 (Eagle Mountain Publishing, 2007). 16. Shine, R., Harlow, P. S., Keogh, J. S. & Boeadi. The influence of sex and body size on food habits of a giant tropical snake, Python reticulatus. Fund. Ecol. 12, 248-258 (1998). 17. Alroy, J. Cope's rule and the dynamics of body mass evolution in North American fossil mammals. Science 280, 731-734 (1998). 18. Shellito, C. J., Sloan, L. C. & Huber, M. Climate model sensitivity to atmospheric C02 levels in the Early-Middle Paleogene. Palaeogeogr. Palaeclimatol. Palaeoecol. 193,113-123(2003). 19. Pearson, P. N. et al. Stable warm tropical climate through the Eocene epoch. Geology 35, 211-214 (2007). 20. Herrera, F., Wing, S. & Jaramillo, C. Warm (not hot) tropics during the Late Paleocene. First Continental Evidence. Eos Trans. AGU 86 (Suppl.), PP51C-0608 (2005). 21. Kowalski, E. A. & Dilcher, D. L. Warmer paleotemperatures for terrestrial ecosystems. Proc. Natl Acad. Sci. USA 100,167-170 (2003). 22. Burnham, R. J. & Johnson, K. R. South American paleobotany and the origins of neotropical rainforests. Phil. Trans. R. Soc. Lond. B 359,1595-1610 (2004). 23. Hogan, K. P., Smith, A. P. & Ziska, L. H. Potential effects of elevated C02 and changes in temperature on tropical plants. Plant Cell Environ. 14,763-778 (1991). 24. Iglesias, A. et al. A Paleocene lowland macroflora from Patagonia reveals significantly greater richness than North American analogs. Geology 35, 947-950 (2007). 25. Crowley, T. J. & Zachos, J. C. in Warm Climates in Earth History (eds Huber, B. T., MacLeod, K. G. & Wing, S. L) 50-76 (Cambridge Univ. Press, 2000). 26. Huber, M. A hotter greenhouse? Science 321, 353-354 (2008). 27. Chappell, M. A. & Ellis, T. M. Resting metabolic rates in bold snakes: allometric relationships and temperature effects. J. Comp. Physiol. B157, 227-235 (1987). 28. Vidal, N. & Hedges, S. B. Higher-level relationships of snakes inferred from four nuclear and mitochondrial genes. C.R. Biol. 325, 977-985 (2002). 29. Lawson, R., Slowinski, J. B. & Burbrink, F. T. A molecular approach to discerning the phylogenetic placement of the enigmatic snake Xenophidion schaeferi among the Alethinophidia. J. Zool. (Lond.) 263, 285-294 (2004). 30. Vidal, N. et al. The phylogeny and classification of caenophidian snakes inferred from seven nuclear protein-coding genes. C.R. Biol. 330,182-187 (2007). Supplementary Information is linked to the online version of the paper at www.nature.com/nature. Acknowledgements We thank C. Bell, R. Ghent, E. Kowalski, A. M. Lawing, B. MacFadden, R. Reisz and S. Wing for advice and discussion, K. Seymour, K. Krysko, K. deQueiroz and G. Zug for access to comparative specimens, A. Rincon and M. Carvalho for fieldwork, J. Mason, K. Church, J. Mathis and J. Nestler for fossil preparation, and K. Krysko and J. Nestler for photographic assistance. We thank Carbones del Cerrejon, L. Teicher, F. Chavez, C. Monies and G. Hernandez for logistical support and access to the Cerrejon mine. This research was funded by the National Science Foundation, Fondo para Investigaciones del Banco de la Republica de Colombia, Smithsonian Tropical Research Institute Paleobiology Fund, the Florida Museum of Natural History, a Geological Society of America Graduate Student Research Grant to A.K.H., and a National Sciences and Engineering Research Council of Canada Discovery Grant to J.J.H. Author Contributions J.J.H., J.I.B., C.A.J., P.D.P., A.K.H. and J.R.B. contributed to project planning. J.J.H. and J.I.B. contributed to systematic palaeontology. J.J.H., P.D.P., JIB., A.K.H., J.R.B. and E.A.C. contributed to body size estimation. J.J.H., J.I.B., F.A.H., P.D.P. and C.A.J. contributed to palaeoclimatic analysis. J.I.B., A.K.H., E.A.C, F.A.H. and C.A.J. contributed to fieldwork. J.I.B., A.K.H., C.A.J. and J.J.H. contributed to financial support. All authors contributed to manuscript and figure preparation. Author Information Reprints and permissions information is available at www.nature.com/reprints. Correspondence and requests for materials should be addressed to J.J.H. (jason.head@utoronto.ca). 717 ?2009 Macmillan Publishers Limited. All rights reserved doi:10.1038/nature07671 nature METHODS Position estimation of fossil vertebrae. We used a maximum-likelihood algo- rithm to find the most likely position of isolated vertebrae along an anterior-posterior shape gradient derived from the vertebrae of representative extant taxa, a procedure modified from ref. 14. The anterior-posterior morphological gradient was estimated by measuring the shape of vertebrae between the first and last precloacal vertebrae. Vertebral shape was quantified using two-dimensional geometric landmarks that represent morphology in anterior view (Supplementary Fig. 3). The anterior view was chosen because it provides height and width information as well as the most complex vertebral morphology. The number of precloacal vertebrae varies within Boinae13 (Supplementary Table 2), so we sampled vertebral morphology at 5% intervals along the column for all specimens to standardize comparisons across taxa. We projected the vertebral landmarks of all the extant species and the isolated fossil specimens into the same shape space by Procrustes superimposition to minimize shape differences among specimens, with orthogonal projection into tangent space. Shapes were rotated to their principal components (PC) axes using singular value decomposition to find the eigenvectors and eigenvalues. The PC axes have the valuable property that the shape variation described by each one is statistically uncorrelated with the shape variation described by the others. Variance is therefore additive across the axes, allowing the PC scores to be used as uncorrelated variables in multivariate statistical analysis. A multivariate regression of vertebral shape onto position in the vertebral column was used to extract a species-independent anterior-posterior shape gradient from the extant data set. Both a discrete function and a continuous spline function were fit. The discrete function runs through the multivariate means of each of the 5% vertebral positions and is undefined between them. The spline function runs through the 5% multivariate means and is interpolated between them (Supplementary Fig. 4). These multivariate regression functions and their residual variation were used as likelihood models for estimating the position of the fossil vertebrae. The following function describes the likelihood distribution of shape at vertebral position (pos) fc L(post\z,z,G2)= IT ^2nak/ (1) where i is the number of principal components, k,i is the score of the unknown vertebra on PQ, zki is the expectation of shape at vertebral position k on PQ along the shape gradient defined by the extant species, and a2j is the residual variance around the estimated shape gradient at position k on PC,. If the variance is pre- sumed to be equal along the length of the shape gradient, which it is approximately in our data, then the variance term becomes a constant and can be dropped: L(posk\z,z) = n g-b-w The log likelihood equation is then simply: l(pOSk\z,z)= ^(Zj-Zkj)2 (2) (3) Maximizing this equation for position k gives the best estimate of the position of the unknown vertebrae given its shape (z) and the estimated shape gradient of the extant snakes (z). Standard errors (s.e.) for the positional estimates were obtained by cross validation. Isolated vertebrae with a known position were systematically selected from the sample of extant snakes. Each vertebra was submitted to the maximum likelihood procedure and the distance of the estimated position from the true position was noted, s.e. is the mean distance from the true value for the entire sample. Regression of body size onto vertebral size. We estimated body length for Titanoboa by regressing SVL and TBL measured in millimetres onto postzyga- pophyseal width measured in millimetres for precloacal vertebrae between 60% and 65% intervals along the precloacal vertebral column for the examined sam- ple of extant boines (n = 21, Supplementary Table 2), based on results of posi- tion estimation, and applying the resultant equation to the holotype (UF/IGM 1, width = 120 mm) and paratype (UF/IGM 2, width =119 mm) specimens. SVL, TBL and vertebral width data were not log-transformed because they were approximately normally distributed (SVL skewness = 0.63, TBL skew- ness = 0.49, postzygapophyseal width skewness = 0.64, s.e. skewness for all = 1.07). Least-squares linear regression models produced positive, significant relationships between SVL and width (60%: slope = 95.9, intercept = 262.6, P< 0.001, R2 = 0.85; 65%: slope =100.4, intercept = 226.5, P< 0.001, R2 = 0.87), and TBL and width (60%: slope = 100.7, intercept = 436.2, P< 0.001, R2 = 0.81; 65%: slope =106.0, intercept = 390.0, P< 0.001, R2 = 0.83). The estimated means of 12.04 m SVL and 12.82 m TBL were obtained by averaging the 60% and 65% estimates. The error for size estimates was deter- mined by subtracting the averaged regression coefficients from a perfect fit for extant taxa. Palaeotemperature estimation. We estimated palaeotemperature from body size using the equation of ref. 4: = Q' ,(Ar/l(TC)/3z (4) where I[ is length of the largest taxon, L2 is length of the smallest taxon, 10 ?C is interval of temperature change associated with metabolic rate change (Qi0; ref. 5), and AT= temperature; ? temperature^. We solved for the temperature associated with the larger taxon (Titanoboa; Fig. 3) as follows: MAPT = MAT + 3al0 C log10(TBLT/TBLE) logioQio (5) where MAPT is mean annual palaeotemperature (temperature; in equation (4)), MAT is modern mean annual temperature (temperature^ of equation (4)), TBLp is total body length of Titanoboa (I; in equation (4)), TBLE is total body length of Eunectes (L2 of equation (4)), Q10 is mass-specific metabolic rate of 2.65 for bold snakes27, and i = 0.33 (ref. 5): MAPT = MAT + 9.9?C iog10(TBLT/TBLE) 0.42 (6) ?2009 Macmillan Publishers Limited. All rights reserved