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. 25 FEBRUARY 2016 | VOL 530 | NATURE | 477 © 2016 Macmillan Publishers Limited. All rights reserved RESEARCH LETTER 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.