Letter Doi:10.1038/Nature16972

Home , Ardipithecus, Odontometrics, Paranthropus, Paranthropus robustus

Letter doi:10.1038/nature16972

A simple rule governs the evolution and development of hominin tooth size Alistair R. Evans1,2, E. Susanne Daly3,4, Kierstin K. Catlett3,4, Kathleen S. Paul4,5, Stephen J. King6, Matthew M. Skinner7,8, Hans P. Nesse4, Jean-Jacques Hublin8, Grant C. Townsend9, Gary T. Schwartz3,4 & Jukka Jernvall10

The variation in molar tooth size in humans and our closest the size of subsequently developing molars. Whereas activation is prin relatives (hominins) has strongly influenced our view of human cipally considered to be mesenchymal, previously initiated molars are evolution. The reduction in overall size and disproportionate the source of inhibition, thereby causing a patterning cascade from decrease in third molar size have been noted for over a century, anterior to posterior molars. The model appears to explain a high pro and have been attributed to reduced selection for large dentitions portion of the variation in relative molar size in murines, primates and owing to changes in diet or the acquisition of cooking1,2. The fossil mammaliaforms6,10–15. Mice, however, lack all premolars, but systematic pattern of size variation along the tooth row has been the inhibitory cascade implies that a previously initiated tooth should described as a ‘morphogenetic gradient’ in mammal, and more always inhibit the subsequently developing tooth (for example, the specifically hominin, teeth since Butler3 and Dahlberg4. However, fourth deciduous premolar, dp4, should inhibit the first molar, m1). the underlying controls of tooth size have not been well understood, Here, we test whether the inhibitory cascade explains the mor with hypotheses ranging from morphogenetic fields3 to the clone phogenetic gradient in the primary postcanine tooth size of homin theory5. In this study we address the following question: are there ins and great apes. We partition the lower dentition into triplets: rules that govern how hominin tooth size evolves? Here we propose (1) the third and fourth deciduous premolars, dp3 and dp4, and the first that the inhibitory cascade, an activator–inhibitor mechanism that molar, m1 (dp3–dp4–m1); (2) dp4–m1–m2; and (3) the three molars affects relative tooth size in mammals6, produces the default pattern (m1–m2–m3). If a triplet follows the inhibitory cascade pattern, then of tooth sizes for all lower primary postcanine teeth (deciduous the central tooth is the average size of the two outer teeth. This is math premolars and permanent molars) in hominins. This configuration ematically equivalent to the central tooth being one-third of the total is also equivalent to a morphogenetic gradient, finally pointing to triplet size, a manifestation of the inhibitory cascade6 (Supplementary a mechanism that can generate this gradient. The pattern of tooth Information). As a result, the three teeth show a linear change in size size remains constant with absolute size in australopiths (including with tooth position; hence, linearity of size change is a proxy for the Ardipithecus, Australopithecus and Paranthropus). However, in inhibitory cascade. species of Homo, including modern humans, there is a tight link Our analysis of 58–66 modern human populations for lower between tooth proportions and absolute size such that a single molars and 8 populations for lower deciduous premolars shows a developmental parameter can explain both the relative and absolute linear increase of the average sizes of the first triplet (dp3–dp4–m1; sizes of primary postcanine teeth. On the basis of the relationship ordinary least squares (OLS) regression R2 = 0.9998; Fig. 1). The third of inhibitory cascade patterning with size, we can use the size at one triplet (molars) also follows the inhibitory cascade pattern, but here tooth position to predict the sizes of the remaining four primary size decreases linearly from m1 to m3 (R2 = 0.974). On average, m1 is postcanine teeth in the row for hominins. Our study provides a the largest tooth in the row, with size first increasing and then decreas development-based expectation to examine the evolution of the ing about this central tooth position. The second triplet dp4–m1–m2 unique proportions of human teeth. does not follow the linear pattern predicted by the inhibitory cascade Nearly 80 years ago, Butler3,7 described the morphogenetic gradi because the middle tooth is the largest. We call this change in direction ent in mammalian postcanine teeth. From anterior to posterior, the a reversal of the inhibitory cascade patterning. deciduous premolars and molars increase in size, and in some species Fourteen species of fossil hominins (eight with data on both deciduous the posterior molars then decrease, with only one local maximum of premolars) also follow the inhibitory cascade in the first triplet (Fig. 1 tooth size along the row. Butler3 interpreted this pattern to be gener and Extended Data Fig. 1). The close fit of the dp3–dp4–m1 triplet for ated by a morphogenetic field, where the concentration of a diffusible hominins allows us to predict that the mean size of the undiscovered morphogen determined size. The pattern appeared to apply both to dp4 of Ardipithecus ramidus will be the average of the dp3 and m1 deciduous premolars and to molars, which together are considered sizes, that is, 73 mm2 in area (star in Fig. 1a). In all extinct hominins primary teeth8. Unlike molars, deciduous premolars are replaced with the second or third molar is the largest tooth on average. In most aus a secondary dentition, called the permanent premolars. While several tralopiths (for example, Paranthropus boisei; Fig. 1) the second triplet authors have investigated the morphogenetic gradient in hominins4,9, (dp4–m1–m2) also follows the inhibitory cascade, as the m1 is the they have generally investigated permanent premolars rather than their average of the two adjacent teeth, pushing the reversal position to m2 deciduous predecessors. or m3. This contrasts with a reversal position at m1 in Homo sapiens. In 2007, a developmental mechanism controlling relative molar size Here we used a simple measure of tooth size, length by width rectan in mice either by separating adjacent molars or by applying growth gular area, because it is the most commonly used and, therefore, exten factors in the culture was experimentally discovered6. In the resulting sive data sets are available. To assess alternative measures of size we ‘inhibitory cascade’ model, molar activator/inhibitor ratio determines calculated three additional metrics from micro-computed tomography

1School of Biological Sciences, Monash University, Victoria 3800, Australia. 2Geosciences, Museum Victoria, Victoria 3001, Australia. 3Institute of Human Origins, Arizona State University, Tempe, Arizona 85287, USA. 4School of Human Evolution and Social Change, Arizona State University, Tempe, Arizona 85287, USA. 5Center for Bioarchaeological Research, Arizona State University, Tempe, Arizona 85287, USA. 6Department of Anthropology, University of Massachusetts Amherst, Amherst, Massachusetts 01003, USA. 7School of Anthropology and Conservation, University of Kent, Canterbury CT2 7NR, UK. 8Department of Human Evolution, Max Planck Institute for Evolutionary Anthropology, Leipzig 04103, Germany. 9School of Dentistry, The University of Adelaide, South Australia 5005, Australia. 10Institute of Biotechnology, University of Helsinki 00014, Finland.

a b Tooth position Paranthropus boisei Two-dimensional m3 400 Australopithecus africanus cervix area dp3 dp4 m1 m2 Australopithecus deyiremeda Mesiodistal and Ardipithecus ramidus buccolingual 300 Homo erectus (Asia) crown dimensions M Homo sapiens L ) 2 Homo ﬂoresiensis D B Australopith Two-dimensional 200 Homo crown area

Area (mm 300

100

0 Enamel–dentine junction surface area ) 2 dp3 dp4 m1 m2 m3 200 Tooth

Figure 1 | All hominins show the inhibitory cascade pattern for dp3–dp4–m1 triplet, but species of Homo show greater reduction in size 100 ×

of posterior molars. a, Area (mediodistal length buccolingual width) Area of tooth (mm of each lower postcanine primary tooth for 7 of the 15 hominin species in this study. The inhibitory cascade predicts a linear relationship of the sizes of three adjacent teeth, as seen for dp3–dp4–m1 triplet and dp4–m1–m2 0 triplet for P. boisei. Red dotted line shows expected linear relationship 250 for dp3–dp4–m1 triplet for Ar. ramidus; red star shows predicted size of Area of m1 (mm undiscovered dp4 (73 mm2). Mean ± s.e.m. of populations for H. sapiens 200 (dark blue), and of individuals for fossil hominin species. b, Measurements of tooth area used in this study illustrated on H. erectus Sangiran 1B: 150 mesiodistal length × buccolingual width (the principal measure used in 2 the analyses), 3D enamel–dentine junction area, 2D crown area and 2D ) 100 cervix area. Figure 2 | Prediction surfaces for hominin tooth sizes based on scans using a subset of fossil hominin specimens: tooth occlusal outline inhibitory cascade and scaling of inhibitory cascade reversal with m1 size. Tooth area (vertical axis) for each tooth position (dp3–m3) and area, enamel–dentine junction 3D surface area, and cervical cross- area of m1. Species mean tooth areas (spheres) and prediction surface for sectional area (Fig. 1b). All show the same general pattern of size rela Homo species are plotted in blue, and australopiths in red. Vertical lines tionships (Extended Data Fig. 2). The first two of these were very highly connecting spheres to surface show deviation of the species means from 2 correlated with rectangular area (R > 0.94), cervical area only slightly predicted size. Areas are in square millimetres. See Supplementary Video 5 less so (R2 = 0.86; Extended Data Fig. 3). for 3D rotating graph animation. Expressing the relative size of each tooth in a row as a proportion of the largest tooth in the row reveals a close relationship between abso lute m1 size and relative tooth size for Homo species (Extended Data as contour plots for Homo species and australopiths, showing the sizes Fig. 4). This contrasts with the remaining hominin taxa (that is, the at each tooth position for a given m1 size in that row (see also Extended australopiths), where the proportions are essentially constant with m1 Data Fig. 8). size. Great ape tooth proportions are intermediate to Homo species Given the close fit of almost all australopiths to their prediction sur and australopiths. face (Fig. 2) and a very similar pattern in the great apes, we postulate In a 3D plot combining tooth position, the relative size of each tooth that a tight association between tooth proportions and m1 size existed and the absolute size of m1, all data points generally fall on two dis at the base of the hominin clade (Extended Data Figs 1, 4 and 5). Near tinct planes in 3D space (meaning that relative size has linear relation the origin of the genus Homo, a change in the scaling relationship ships both with m1 size and with tooth position; Extended Data Fig. 5 between m1 size and inhibitory cascade patterning occurs, such that and Supplementary Videos 1 and 2). The tight fit of the teeth to both the reversal position changes with absolute m1 size and shifts mesially the anterior plane A and the posterior plane B reveals two important (Fig. 4). Interestingly, Homo habilis shows proportions more similar to findings: (1) these species follow the expected inhibitory cascade pat australopiths than its congeners, which suggests this shift occurred after tern of linear change for the first three (or four) teeth in the primary the origin of H. habilis, and agreeing with H. habilis perhaps belonging tooth row; (2) there is a strong relationship between tooth position to the genus Australopithecus16. The Dmanisi specimens demonstrate and proportional sizes in all hominins. In Homo the reversal position the heterogeneity present in the early Homo pattern: one specimen (intersection between planes A and B) changes with absolute m1 size, (D2600) resembles the australopith pattern whereas the others are while in the australopiths the reversal position is constant with absolute closer to the Homo pattern (Supplementary Information). m1 size. Using these planar relationships, we can convert proportional The smallest-bodied hominin, Homo floresiensis, is most similar to size to absolute size based on a given m1 size (Extended Data Fig. 6; the smallest-bodied great ape, Pan paniscus, in tooth sizes and propor Supplementary Information). Standardizing m1 size to a straight line in tions and is smaller than tooth rows of human populations with the 3D space produces 3D surfaces that can represent primary postcanine largest tooth at m2 (Extended Data Fig. 1). Among fossil hominins, tooth sizes for australopiths or Homo species (Fig. 2). This diagram H. floresiensis exhibits proportions similar to Homo heidelbergensis essentially shows how absolute tooth sizes and proportions vary with and Homo erectus, but ~40% smaller in absolute area. The recently changes in m1 size. Deviations of the species means from these surfaces described Australopithecus deyiremeda17 and Australopithecus sediba are relatively minor (average and maximum deviation for Homo species both follow the australopith pattern. are 7.1% and 18.0% respectively; for australopiths, 7.6% and 24.5%; H. sapiens is similar to its congeners but at smaller m1 sizes, produc Extended Data Fig. 7). ing disproportionately reduced third molars. For most modern humans For a given tooth position and size, Supplementary Spreadsheet 1 m1 is the largest tooth, but a small proportion of humans have m2 as predicts the sizes of the remaining positions in the primary postcanine the largest tooth (11–19% of individuals in some populations18, and row. These predictions are based on species means and interspecific 8.6% of the population means in our sample). scaling relationships, and so represent sizes and proportions typical of We note that specimen-level predictions can deviate from the species for that m1 size. Figure 3 illustrates the 3D prediction surfaces species-level scaling patterns. When the size of each tooth is used to

abc 101175 250 *319322 250 250 325 * 250 300 dp3 dp4 m1 m2 m3 275 ) ) 2 200 250 Similar to Paranthropus boisei 200 2 * (mm 175 (mm 225 * dp3 dp4 m1 m2 m3 200 200 175 150 Similar to Australopithecus africanus 150 175 150 125 62 93 125 130 119 Area of m1 * Area of m1 75 150 dp3 dp4 m1 m2 m3 75 125

50 100 125 Similar to Homo neanderthalensis 100 100 50 100 100 * * dp3 dp4 m1 m2 m3 dp3 dp4 m1 m2 m3 Figure 3 | Hominin prediction plot for primary postcanine rows. then move horizontally (green arrows) to the other tooth positions (green a, c, Contour plot of prediction surfaces in Fig. 2. Contours show tooth crosses) and read off sizes from the red contours. Asterisks and dashed areas in square millimetres. Red contours are for australopiths (a), blue lines indicate position of inhibitory cascade reversal. b, Predicted tooth for Homo species (c). To predict the mean sizes of remaining four teeth row sizes for mean m1 areas of 175 and 250 mm2 for australopiths and in a row from the mean size of one tooth position (for example, an 125 mm2 for Homo, which are similar in size to the species listed below australopith m1 of 250 mm2), start at the known tooth’s position (x axis), each tooth row. Lines above tooth rows indicate triplets that follow the move vertically (orange arrow) to the red contour of the measured size, inhibitory cascade (deviation from inhibitory cascade less than 5%). predict the other teeth in the same specimen, the average error is 10.3% Developmentally, in the activator–inhibitor model, higher or and 7.9% for Homo and australopiths, respectively (Supplementary lower relative inhibition yields smaller or larger posterior molars, Information). The largest prediction errors (above 30%) are found respectively. Absolute tooth size was independent of the inhibitory in H. erectus (D211, Thomas I), H. heidelbergensis (Arago 1) and cascade in the mouse-derived model (ref. 6 and Extended Data H. neanderthalensis (KMH1, Krapina 1,7,79 and Krapina 64). Some Fig. 9), whereas size and proportions are linked in hominins of the discrepancies are probably related to errors in size estimation (Extended Data Fig. 4). The simplest way to incorporate size into the owing to developmental age, preservation and wear, and potential inhibitory cascade is through the activation, because the first tooth identification inaccuracies in making composite specimens. Increased in a developmental series is unimpeded by the inhibition by other intraspecific variation in Homo species could also result from relaxed teeth. Therefore, we hypothesize a decrease in mesenchymal activa selection, implicated by the increased fluctuating asymmetry found in tion drives the change in tooth proportions in Homo. The mechanism most Homo dentitions compared with australopiths and great apes19,20, controlling reversal position, however, remains to be determined. or multiple selection pressures. Another possibility is developmental While the inhibitory cascade has been invoked to account for pat instability when molars in a tooth row approach equal size: for example, terns in vertebrate limbs, digits and somites21, a link between abso extra molar presence in mouse experiments seems linked to the molars lute size and patterning in multiple vertebrate systems remains to be being of equal size6. established.

P. pygmaeus G. gorilla P. troglodytes P. paniscus

Ar. ramidus

Au. anamensis

Key Au. afarensis dp3 dp4 m1 m2 m3 ***Au. deyiremeda P. robustus

Largest tooth (or teeth) in species P. boisei Largest tooth (or teeth) in individuals Au. africanus with m1–m3 Predicted tooth size Au. sediba H. habilis Australopiths Homo species H. ﬂoresiensis Great apes H. erectus (Africa) Scale (mm2) H. erectus (Asia) H. heidelbergensis 50 100 150 200 250 300 350 H. neanderthalensis H. sapiens

18 17 10 9 8 7 6 5 4 3 2 1 0 Millions of years ago Figure 4 | Phylogenetic distribution of tooth sizes and proportions in largest tooth. The largest tooth/teeth for fossil individuals with all three hominins shows an origin of the Homo pattern shortly after the origin molars preserved are indicated with a white circle. The phylogeny is of the genus. Tooth sizes plotted to scale for all species in the current modified from ref. 28 to include only taxa represented in this study, with study. Supplementary Spreadsheet 1 was used to predict measurements the addition of P. paniscus, Pongo pygmaeus and Au. deyiremeda (***) for unavailable tooth positions. The largest tooth for the species mean (Supplementary Information). is filled black, as is any other tooth that is within 5% of the size of the

In conclusion, previous work comparing relative molar sizes using 23. Wolpoff, M. H.Metric Trends in Hominid Dental Evolution. Case Western Reserve 22 23 University Studies in Anthropology 2 (Case Western Reserve Univ. Press, step indices and ratios identified significant changes in these pro 1971). portions throughout hominin evolution; here we explain such changes 24. Lucas, P. W. Dental Functional Morphology (Cambridge Univ. Press, 2004). based on the developmental inhibitory cascade mechanism. Whereas 25. Greaves, W. S. The jaw lever system in ungulates: a new model. J. Zool. selective pressures emphasizing function, such as changing bite force, 184, 271–285 (1978). 24–27 26. Spencer, M. A. Force production in the primate masticatory system: have been used to explain the variation in tooth proportions , only electromyographic tests of biomechanical hypotheses. J. Hum. Evol. 34, by including development can one explain the details of the changes. 25–54 (1998). By providing a development-based expectation for the evolution of 27. Lucas, L. Variation in Dental Morphology and Bite Force along the Tooth Row in Anthropoids. PhD thesis, Arizona State Univ. (2012). the hominin dentition, the inhibitory cascade framework moves this 28. Dembo, M., Matzke, N. J., Mooers, A. O. & Collard, M. Bayesian analysis of a research towards a predictive science, further testable with additional morphological supermatrix sheds light on controversial fossil hominin fossils. relationships. Proc. R. Soc. B 282, http://dx.doi.org/10.1098/rspb.2015.0943 (2015). Online Content Methods, along with any additional Extended Data display items and Source Data, are available in the online version of the paper; references unique to Supplementary Information is available in the online version of the paper. these sections appear only in the online paper. Acknowledgements This contribution is dedicated to the late Professor received 5 July 2015; accepted 7 January 2016. Percy Butler, the inspiration for much of this work and discoverer of the morphogenetic gradient in teeth, who unfortunately did not see this work 1. Brace, C. L. Environment, tooth form, and size in the Pleistocene. J. Dent. Res. completed. We thank M. Fortelius, G. Evans, A.-L. Khoo, F. Grine, P. Trusler, 46, 809–816 (1967). J. Adams, J. Clutterbuck, L. Chieu, D. Hocking, M. McCurry, Q. Nasrullah, 2. Bermúdez de Castro, J. M. & Nicolas, M. E. Posterior dental size reduction in T. Park and the Evans EvoMorph Laboratory for discussions and criticism hominids: the Atapuerca evidence. Am. J. Phys. Anthropol. 96, 335–356 of the manuscript. Thanks to M. Collard for supplementary information on (1995). the hominin phylogeny. We thank the Powell-Cotton Museum (M. Harman), 3. Butler, P. M. Studies of the mammalian dentition. Differentiation of the American Museum of Natural History, Cleveland Museum of Natural History post-canine dentition. Proc. R. Soc. Lond. B 109, 1–36 (1939). (L. 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Mbua), Ditsong National ecaudatus and its allies. Proc. R. Soc. Lond. B 107, 103–132 (1937). Museum of Natural History (S. Potze), University of Witwatersrand (C. Menter 8. Owen, R. Odontography (Hippolyte Bailliere, 1840–1845). and B. Zipfel), Senckenberg Natural History Museum (F. Schrenk and O. 9. Townsend, G. C. & Brown, T. Morphogenetic fields within the dentition. Kullmer) and the Royal Belgian Institute of Natural Sciences (M. Toussaint). Aust. Orthod. J. 7, 3–12 (1981). This study was made possible by use of material from the Burlington Growth 10. Polly, P. D. Evolutionary biology: development with a bite. Nature 449, Centre, Faculty of Dentistry, University of Toronto, which was supported by funds 413–415 (2007). provided by grant (1) (number 605-7-299) National Health Grant (Canada), 11. Renvoisé, E. et al. Evolution of mammal tooth patterns: new insights from a (data collection); (2) Province of Ontario Grant PR 33 (duplicating); and (3) the developmental prediction model. Evolution 63, 1327–1340 (2009). Varsity Fund (for housing and collection). All research protocols were reviewed 12. Wilson, L. A. B., Madden, R. H., Kay, R. F. & Sanchez-Villagra, M. R. Testing a and granted exemption by Arizona State University’s (ASU) Institutional Review developmental model in the fossil record: molar proportions in South Board and the Burlington Growth Centre, and informed consent was obtained American ungulates. Paleobiology 38, 308–321 (2012). for all human subjects. This research was financially supported by grants from 13. Bernal, V., Gonzalez, P. N. & Ivan Perez, S. Developmental processes, the Australian Research Council Future Fellowship (A.R.E., FT130100968), evolvability, and dental diversification of New World monkeys.Evol. Biol. 40, Academy of Finland (J.J.), National Science Foundation (GRFP number 532–541 (2013). 2011121784; K.S.P.), Max Planck Society (M.M.S.), Wenner-Gren Foundation 14. Halliday, T. J. D. & Goswami, A. Testing the inhibitory cascade model (K.K.C.), Graduate and Professional Student Association at ASU (E.S.D., K.K.C.), in Mesozoic and Cenozoic mammaliaforms. BMC Evol. Biol. 13, 79 and ASU Sigma XI chapter (E.S.D., K.K.C.). This research was also facilitated (2013). in part by a grant (48952) from the John Templeton Foundation (G.T.S.). The 15. Schroer, K. & Wood, B. Modeling the dental development of fossil hominins opinions expressed in this publication do not necessarily reflect the views of the through the inhibitory cascade. J. Anat. 226, 150–162 (2015). John Templeton Foundation. 16. Wood, B. & Collard, M. The human genus. Science 284, 65–71 (1999). 17. Haile-Selassie, Y. et al. New species from Ethiopia further expands Middle Author Contributions J.J. and A.R.E. conceived the project. A.R.E., E.S.D., Pliocene hominin diversity. Nature 521, 483–488 (2015). K.K.C., K.S.P., S.J.K., M.M.S., G.C.T., G.T.S. and J.J. collected data. E.S.D. and 18. Garn, S. M., Lewis, A. B. & Kerewsky, R. S. Molar size sequences and fossil K.K.C. independently validated application of the inhibitory cascade model taxonomy. Science 142, 1060 (1963). to deciduous premolars. G.T.S. performed hominin taxonomic classification. 19. Kieser, J. A. & Groeneveld, H. T. The assessment of fluctuating odontometric M.M.S. conducted the computed tomography scanning and measurements. asymmetry from incomplete hominid fossil data. Anthropol. Anz. 44, 175–182 J.-J.H. and G.C.T. provided materials. A.R.E. performed the analyses. H.P.N. (1986). implemented individual-level prediction accuracy and confidence interval 20. Kegley, A. D. T. & Hemingway, J. in Voyages in Science: Essays by South African calculations. A.R.E. and J.J. took the lead in writing the paper with contributions Anatomists in Honour of Phillip V. Tobias’ 80th birthday (eds G. Strkalj, N. Pather, & from all co-authors. B. Kramer) 35–49 (Content Solutions, 2005). 21. Young, N. 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Methods in Row. For hominins and great apes separately, we used R version 3.1.3 (ref. 31) to Tooth size data. Human lower primary postcanine tooth sizes, defined as rectan perform multiple linear regression for Prop Max in Row ~ Tooth Position + Area gular areas of mesiodistal length × maximum buccolingual width, were collated of m1, and linear regression for Max Area in Row ~ Area of m1. For hominins, from the literature, and measured from dental casts at the Burlington Growth Prop Max in Row was converted to Area by multiplying it by Max Area in Row Centre, Toronto, Canada. All research protocols were reviewed and granted for the given m1 size. This function was then divided by the ratio of the expected exemption by Arizona State University’s Institutional Review Board and the Area of m1 to that calculated for m1 to give m1 size a 1:1 relationship with Area Burlington Growth Centre, and informed consent was obtained for all human in the predictive surface (see Supplementary Information and Extended Data subjects. Population-level means of molar sizes were collated from studies where Fig. 10 for calculations and plots). Individual-level fossil data were used for the pre all three molars were measured and wear was not excessive, largely from compi diction error calculation using the relevant Homo or australopith prediction sur lations23,29 (see Supplementary Information). No statistical methods were used face. Prediction error was calculated as 100 × |(observed − predicted)|/observed. to predetermine sample size. Fossil hominin tooth size measurements were com Three-dimensional tooth size data. X-ray microtomographic scans of six hominin piled at the specimen level and assigned to taxonomic groups (see Supplementary specimens with three sufficiently unworn lower molars were performed at the Max Information), using measurements adjusted for wear when available. H. erectus Planck Institute for Evolutionary Anthropology, Leipzig, Germany. Three-dimensional specimens from Asia and Africa were grouped separately. Ape tooth size measure tooth models were measured for rectangular area, tooth occlusal outline area, enamel– ments were obtained from the literature30 or measured from museum specimens dentine junction 3D surface area, and cervical cross-sectional area (Fig. 1b). (see Supplementary Information). For all individual-level data, measurements taken from both sides of the same individual were averaged. Individuals of the 29. Kieser, J. A. Human Adult Odontometrics (Cambridge Univ. Press, 1990). 30. Johanson, D. C. Some metric aspects of the permanent and deciduous same sex were averaged, then sexes were averaged to obtain a population or species dentition of the pygmy chimpanzee (Pan paniscus). Am. J. Phys. Anthropol. mean size for each tooth. 41, 39–48 (1974). Analyses. For each primary tooth row (mean of sex, population or species), all 31. R Development Core Team. R: a language and environment for statistical teeth were scaled so that the largest tooth in the row equalled 1, called Prop Max computing (R Foundation for Statistical Computing, 2015).

a b Taxon Homo sapiens 400 Homo sapiens Ardipithecus ramidus Australopithecusafarensis Australopithecusafricanus 300 Australopithecusanamensis Australopithecusdeyiremeda 300 Australopithecussediba Homo erectus (Asia) Homo erectus (Africa) Homo floresiensis 200 )

2 Homo habilis Homo heidelbergensis Homo neanderthalensis Paranthropus boisei 200 Paranthropus robustus 100 (m m Australopith Homo 0

Area dp3dp4 m1 m2 m3 100

dp3dp4 m1 m2 m3 Tooth c 400 Ardipithecus ramidus 400 Australopithecus afarensis 400 Australopithecus africanus 400 Australopithecus anamensis

300 300 300 300

200 200 200 200

100 100 100 100 ) 2 0 0 0 0

dp3dp4 m1 m2 m3 dp3dp4 m1 m2 m3 dp3 dp4 m1 m2 m3 dp3 dp4 m1 m2 m3

400 Australopithecus deyiremeda 400 Australopithecus sediba 400 Paranthropus boisei 400 Paranthropus robustus Area (mm

300 300 300 300

200 200 200

200 100 100 100

0 0 100 0

dp3dp4 m1 m2 m3 dp3dp4 m1 m2 m3 dp3 dp4 m1 m2 m3 dp3 dp4m1m2m3 d 400 Homo erectus (Africa) 400 Homo erectus (Asia) 400 Homo floresiensis 400 Homo habilis

300 300 300 300

200 200 200 200

100 100 100 100 ) 2

0 0 0 0

dp3dp4 m1 m2 m3 dp3dp4 m1 m2 m3 dp3 dp4 m1 m2 m3 dp3 dp4m1m2m3

400 Homo heidelbergensis 400 Homo neanderthalensis Area (mm

300 300

200 200

100 100

0 0

dp3dp4 m1 m2 m3 dp3dp4 m1 m2 m3 e 400 Gorillagorilla 400 Panpaniscus 400 Pantroglodytes 400 Pongopygmaeus ) 2 300 300 300 300

200 200 200 200

Area (m m 100 100 100 100

0 0 0 0

dp3dp4 m1 m2 m3 dp3dp4 m1 m2 m3 dp3 dp4 m1 m2 m3 dp3 dp4 m1 m2 m3 f 150 150 400 Gorilla gorilla males 400 Gorillagorilla females ) 2 300 300 100 100

200 200

50 50 Area (m m 100 100 Pantroglodytes males Pantroglodytes females 0 0 0 0

dp3dp4 m1 m2 m3 dp3dp4 m1 m2 m3 dp3 dp4m1m2m3 dp3 dp4 m1 m2 m3 Extended Data Figure 1 | Homo species and australopiths differ in populations. c, Eight australopith species and (d) six fossil Homo species; their pattern of tooth sizes, but all hominins and great apes follow black points and lines represent individual tooth rows (left and right rows the inhibitory cascade for dp3–dp4–m1 triplet. The inhibitory cascade of each specimen plotted separately). e, Four great ape species; black points predicts that there is a linear relationship among three adjacent teeth. Area and lines represent means of each sex. f, Two great ape species; black (in square millimetres) of each lower postcanine primary tooth. a, Mean points and lines represent individuals, red points and lines are means for area of each tooth for 15 hominin species. b–e, Red points and lines are each sex. Sex and species means show clearer inhibitory cascade patterns species means. b, H. sapiens; black points and lines represent means of than most individuals.

400 Australopithecus anamensis KNM-KP 29286 400 Homo erectus Sangiran 1B

300 300

200 200 Measurement CervixArea 100 EDJ3DArea 100 MDBLArea OES2DArea 0 0

dp3dp4 m1 m2 m3 dp3 dp4 m1 m2 m3

400 Homo neanderthalensis Scladina 4A I 400 Paranthropus boisei KNM-ER 15930

300 300

200 200

100 100

0 0

dp3dp4 m1 m2 m3 dp3 dp4 m1 m2 m3

400 Paranthropus robustus DNH 8 400 Paranthropus robustus SK 6

300 300

200 200

100 100

0 0

dp3dp4 m1 m2 m3 dp3 dp4 m1 m2 m3 Extended Data Figure 2 | Two- and three-dimensional measures of tooth size for six fossil hominin specimens. Rectangular area (mesiodistal length × buccolingual width, MDBLArea), 3D area of the enamel–dentine junction (EDJ3DArea), cross-sectional area of the tooth at the cervix (CervixArea) and outline area of the outer enamel surface (OES2DArea) for each tooth position.

CervixArea EDJ3DArea MDBLArea

400 R2 = 0.811 3 2 3 a a 350 1 3 1 2 2 300 12 2 1 250 3 3

EDJ3DAre 1 1 200 2 3 EDJ3DAre

150 100 150 200 CervixArea

350 2 300 2 33 2 300 R = 0.863 3 3 R = 0.945 3 2

a 3 a 250 2 1 250 2 2 12 1 1 200 2 200 2 3 3 21 3 12 3 1 1 MDBLAre MDBLAre 150 1 150 1 1 32 3 21 MDBLAre a 100 100

100 150 200 200 250 300 350 CervixArea EDJ3DArea

250 250 2 2 33 2 33 R = 0.876 R = 0.962 2 R = 0.992 2 250 3 3 2 3 3 a a a 3 200 22 1 1 1 200 22 200 2 2 1 1 1 2 2 3 3 150 21 2 150 12 3 3 1 3 1 150 21 1 3 OES2DAre 1 OES2DAre OES2DAre 1 2 1 100 1 3 100 3 21

OES2DAre a 100 132

100 150 200 200250 300350 150200 250300 CervixArea EDJ3DArea MDBLArea

Species Australopithecus anamensis KNM-KP 29286 Homo erectus Sangiran 1b Homo neanderthalensis Scladina 4A I Paranthropus boisei KNM-ER 15930 Paranthropus robustus DNH 8 Paranthropus robustus SK 6

Tooth 1 m1 2 m2 3 m3 Extended Data Figure 3 | Two- and three-dimensional measures at the cervix (CervixArea) and outline area of the outer enamel surface of tooth size are highly correlated. Bivariate plots for planar area (OES2DArea). R2 shown for each plot. Blue line and shaded area, OLS (mesiodistal length × buccolingual width, MDBLArea), 3D area of the regression and 95% confidence interval; red line and shaded area, loess enamel–dentine junction (EDJ3DArea), cross-sectional area of the tooth smoothing and 95% confidence interval.

1.00 dp3 dp4 0.75

0.50

0.25

0.00

w 1.00

0.75

0.50

0.25 m1 m2 0.00 Prop Max in Ro 100 150 200 250 1.00

0.75

0.50

0.25 m3 0.00 100 150 200 250 Area of m1 (mm2) Extended Data Figure 4 | The proportional size of each tooth shows row) versus area of m1 (in square millimetres) for 15 hominin and 4 great a tight relationship with absolute size of the first molar, with the ape species. Blue triangles and solid line, OLS regression for Homo species; relationship differing between Homo species, australopiths and great red circles and dashed line, OLS for australopiths; yellow squares and apes. Proportional size of each tooth (proportion of the largest tooth in the dotted line, OLS for great apes.

a Tooth position

Homo B

Homo B w

Prop Max in Row

n Ro n

i ax ax

Homo A M Homo A

Area of m1 Prop Prop

Area

o f m1

Tooth position

b Tooth position Area of m1

Aust B

Prop Max in Row Aust B

w Ro in x Aust A Ma Prop

Area of m1 Aust A

Tooth position c Tooth position w

Ape B ow R Prop Max in Ro Ape B

Ape A Prop Max in in Max Prop

A rea of m1 Ape A

Area of m1

Tooth position d

position Tooth position Tooth A rea of m1

x in

rop Ma

P w

Area of m1

Prop Max in Ro in Max Prop Aust B Ape B Homo B

Homo A Aust B Homo A Homo B Ape A Ape B Ape A Aust A Aust A

Extended Data Figure 5 | See next page for figure caption.

Extended Data Figure 5 | Tooth proportions of hominins are of planes. c, Great apes, plane A (yellow; R2 = 0.98) formula: constrained by the inhibitory cascade and size of m1. Three- ApeAPropMaxinRow = 0.268 × ToothPos − 0.0727 × AreaM1 + 0.173. dimensional space of tooth position (horizontal axis, numbered 1–5 for plane B (light brown; R2 = 0.63) formula: ApeBPropMaxinRow = dp3–m3), area of m1 (axis into page) and proportion of maximum in −0.0837 × ToothPos + 0.000337 × AreaM1 + 1.29. While the R2 values tooth row (vertical axis). The proportional sizes of all teeth lie on two are substantially lower for the plane B regressions, the average deviations planes in 3D space. For all groups, plane A is fitted to dp3–dp4–m1, and from plane B for Homo and australopiths are 0.026 and 0.022 respectively, plane B to m2–m3. a, Homo species, plane A (cyan; R2 = 0.96) formula: which are lower than the equivalent values of 0.046 and 0.036 for plane A. HomoAPropMaxinRow = 0.238 × ToothPos − 0.00166 × AreaM1 + 0.441. Therefore, the low R2 values do not reflect the close fit of the data to the Plane B (blue; R2 = 0.62) formula: HomoBPropMaxinRow = −0.0822 × planes. d, Comparison of Homo, australopith and great ape planes shows ToothPos + 0.000690 × AreaM1 + 1.23. Thick blue line shows intersection that the corresponding planes and intersections for the first two groups of planes. b, Australopiths, plane A (light red; R2 = 0.93) formula: diverge at smaller m1 sizes. The great ape planes fall between those of the AustAPropMaxinRow = 0.0810 × ToothPos + 0.230 × AreaM1 + 2.38 × 10−6. other two groups. See Supplementary Videos 1–4 for 3D rotating graph Plane B (dark red; R2 = 0.07) formula: AustBPropMaxinRow = 0.00963 × animations. ToothPos + 0.000168 × AreaM1 + 0.906. Thick red line shows intersection

350 Australopiths 300 Homo species

250

200

150

Max Area in Row (mm²) 100

100 150200 250 Area of m1 (mm²) Extended Data Figure 6 | The size of the largest tooth in the row is closely related to the size of the m1 in hominins. OLS regressions. HomoMaxAreaInRow = 1.312 × AreaM1 − 30.44, P = 0.001, R2 = 0.90; AustMaxAreaInRow = 1.298 × AreaM1 + 0.150, P = 0.0003, R2 = 0.90.

ab 25 25 Tooth dp3 dp4 m2 ) 20 20 m3

15 15

10 10 Prediction Error (% 5 5

0 0 icanus (Africa ) iremed a halensis ustu s arensis oise i sedib a fr namensis af ey ob amidus habilis sb sa sapien s sa sd sr floresiensi s erectus (Asia) erectus heidelbergensis neande rt Homo Homo Homo ranthropu Homo Homo Homo ranthropu stralopithecus Homo Pa stralopithecu Ardipithecu sr Pa ustralopithecus Au ustralopithecu ustralopithecu A Au A A Extended Data Figure 7 | Percentage error in estimates of each tooth compared with the prediction surfaces in Fig. 2. Prediction surface is calculated so that m1 always has zero prediction error, therefore it is excluded from error calculations. a, Homo species; b, australopiths.

62 93 125 130 119 50 88 156 158 100 10 01

dp12343 dp4 m1 m2 m35 Extended Data Figure1 8 | Detailed contour plot (contour2345 step = 5 mm2) the measured size, then moving horizontally to the other tooth positions for prediction surfaces of hominin tooth size. Area of m1 and areas on (cyan line and crosses) to read off the sizes according to the contours. contour in mm2. Blue contours are for Homo species, red for australopiths. When mean m1 size is 125 mm2, dp3, dp4, m2 and m3 are 62, 93, 130 and From the mean size of one tooth position (for example, m1 at 125 mm2), 199 mm2 respectively for a Homo species and 50, 88, 156 and 158 mm2 the mean sizes of the remaining four teeth in the row can be predicted by respectively for an australopith species. following the tooth position vertically (orange line) to meet the contour of

a 1.00

0.75

0.50

Prop Max in Row 0.25

0.00

m1 m2 m3 Tooth

b 1.00

0.75

0.50

0.25 m3 Prop Max in Row

0.00

0102030 m1 Area (mm2) Extended Data Figure 9 | Slope of the inhibitory cascade in murines plotted against absolute size of first molar (in square millimetres) shows is weakly related to absolute size, unlike in hominins where there is a a weak relationship (cf. Extended Data Fig. 4). Blue line and shaded area, strong relationship. a, Relative sizes of molars for the 29 species of murine OLS regression and 95% confidence interval. rodents in ref. 6. b, Relative size of third molar to first molar (m3/m1)

ab c T T

AM1

A PropAre

AM1

Extended Data Figure 10 | Planes and surfaces for equations of tooth plane A or AreaAH on the left of the intersection and plane B or AreaBH position T (horizontal) versus area of m1 AM1 (into page) versus on the right of the intersection of the two planes or surfaces, respectively. proportion of area or area (vertical). a, Regression plane A (cyan) c, Prediction of m1 area using formulae for AreaAH (cyan) when T = 3 and plane B (green) with proportion of area PropArea as calculated in compared with the expected 1:1 relationship (black) using equation 11 in equations 2 and 3 in Supplementary Information. b, Surfaces AreaAH the Supplementary Information. If the cyan formula were standardized by (cyan) and AreaBH (green) as calculated in equations 11 and 12 in the expected value (black), the standardized surface will correctly predict Supplementary Information. The two regions that represent the data are m1 size (equation 17 in the Supplementary Information).