1 1. TITLE PAGE 2 Title: Modeling the dental development of fossil hominins through the inhibitory cascade 3 KES SCHROER1,2 and BERNARD WOOD3,4 4 1 5 Dartmouth, 6047 Silsby Hall, Hanover NH 03755, USA, 3Center for the Advanced Study of 6 Hominid Paleobiology, Department of Anthropology, The George Washington University, 2110 7 G St NW, Washington DC 20052, USA, 4Human Origins Program, National Museum of Natural 8 History, Smithsonian Institution. 9 Corresponding author: kes.schroer@gmail.com 10 11 Neukom Institute for Computational Science, Dartmouth, 2Department of Anthropology, 2. SUMMARY The inhibitory cascade is a mathematical model for interpreting the relative size of the 12 occlusal surfaces of mammalian molars in terms of developmental mechanisms. The cascade is 13 derived from experimental studies of mouse molars developed in culture, and has been tested and 14 applied to the dentitions of rodents, ungulates, carnivores, and platyrrhines. Results from such 15 applications have provided new information regarding the origins of plesiomorphic traits in 16 mammalian clade and how derived morphologies may arise. In this study we apply the inhibitory 17 cascade model to the postcanine dentition of a sample of Old World primates that includes fossil 18 hominins. The results of this study suggest that the inhibitory cascade (i.e., M1<M2<M3) 19 describes the relative sizes of the molar occlusal areas of Old World primates and is likely the 20 plesiomorphic condition for this clade. Within that clade, whereas most Old World monkeys 21 have a M1<M2<M3 pattern, most apes have a M1<M2≈M3 pattern. This modified cascade 22 suggests that greater levels of inhibition (or less activation) are acting on the posterior molars of 23 apes, thus facilitating the reduction of M3s within the apes. With the exception of the baboon 1 24 genus Papio, extant congeners typically share the same molar inhibitory cascade. The differences 25 in the relative size relationships observed in the molar and premolar-molar cascades of the 26 species included in the fossil hominin genus Paranthropus suggest that although large postcanine 27 teeth are a shared derived trait within this genus, the developmental basis for postcanine 28 megadontia may not be the same in these two Paranthropus taxa. Our results showthat 29 phenotypic characters like postcanine megadontia may not reflect common development. . 30 3. KEYWORDS 31 Fossil hominin, human evolution, inhibitory cascade, Paranthropus, monophyly, primates, 32 postcanine teeth, molar size. 33 4. INTRODUCTION 34 Evolutionary developmental biologists have begun to determine the regulatory pathways 35 that govern the process of tooth formation and the details of occlusal morphology (Jernvall et al., 36 2000; Jernvall and Thesleff, 2000, 2012; Salazar-Ciudad and Jernvall, 2002, 2004, 2010; 37 Tummers and Thesleff, 2003, 2009; Jarvinen et al., 2006; Munne et al., 2009; Renvoise et al., 38 2009; Michon et al., 2010). This research has helped unravel the complex relationships between 39 the genotype and phenotype of the dentition (Arnold, 1992; Hall, 2003; Polly, 2008) and it has 40 shown how molecular processes can influence macroevolutionary trends (Peterson et al., 2007; 41 Raff, 2007). In particular, understanding the mechanisms underlying tooth development helps 42 quantify potential constraints on tooth evolvability and helps understand how adaptation can 43 result in the modification of regulatory pathways (Renaud et al., 2011; Felix, 2012; Asahara, 44 2013; Bernal et al., 2013; Halliday and Goswami, 2013). 45 46 Fossils are difficult to study within a developmental context. However, the inhibitory cascade model proposed by Kavanagh and colleagues (2007) allows researchers to generate 2 47 hypotheses about how regulatory pathways might have influenced evolutionary trends seen in the 48 postcanine dentition of mammals, including hominins. The inhibitory cascade model is the result 49 of Kavanagh and colleagues’ use of cell culture techniques to investigate mouse dental 50 development. They found that when the lower molars of Mus musculus were isolated from their 51 posterior tail, the rate of initiation of posterior molars was increased and the posterior molars 52 were enlarged. Kavanagh and colleagues hypothesized that the net balance between genetic 53 activation and inhibition during dental development determines the relative size of the teeth in 54 the molar row. Kavanagh and colleague’s simplified model to describe the genotypic-phenotypic 55 relationship between molar position and molar size is: 56 y=1+[(a–i)/i](x–1), 57 where y is the relative molar size estimated from occlusal area, x is the position of the molar in 58 the tooth row, a is the strength of activation, and i is the strength of inhibition. 59 Because teeth develop in sequence, the inhibitory cascade model can be used to predict 60 the relative size of the teeth in the molar row. For a typical mammal the above equation predicts 61 that M1=1, M2=a/i, and M3=2a/i-1). The model also predicts a slope of 2.0 and an intercept of - 62 1.0 to describe the ratios between the M2:M1 and M3:M1 occlusal areas. Expressed in another 63 way, the occlusal area of M2 will consistently be 1/3rd the total occlusal area of the molar row 64 since M2/(M1+M2+M3)=(a/i)/[1+a/i +(2a/i–1)]=1/3 (Kavanagh et al., 2007). Weak inhibition 65 (i.e., high a/i) by M1 on the posterior molars results in a molar row that increases in size from 66 anterior to posterior (i.e., the ratio between occlusal areas is >1). Conversely if the ratio is <1, 67 this suggests strong inhibition and results in a molar row that decreases in size from anterior to 68 posterior. A summary schematic of the inhibitory cascade model is provided in Figure 1. 3 69 The inhibitory cascade model also has the potential to help in phylogenetic 70 reconstruction. By applying the model to a large set of fossil and extant mammals, researchers 71 have demonstrated that the relative sizes of most mammalian molars follow the predictions of the 72 inhibitory cascade and may be symplesiomorphic for relative molar sizes in this clade (Halliday 73 and Goswami, 2013). Differences in the relative occlusal areas of postcanine tooth crowns can 74 differentiate the major radiations of mammals (Wilson et al., 2012), and the evolution of 75 specialized teeth such as carnassials is linked with departures from the symplesiomorphic 76 condition of the inhibitory cascade (Asahara, 2013; Halliday and Goswami, 2013). 77 Preliminary analyses suggest that primates generally conform to the inhibitory cascade 78 (Polly, 2007; Halliday and Goswami, 2013) and an in-depth study of platyrrhine (New World) 79 primates suggests that when phylogeny is taken into account their relative occlusal areas do not 80 differ significantly from the pattern predicted by the inhibitory cascade model (Bernal et al., 81 2013). This study applies the inhibitory cascade model to a large sample of catarrhine (Old 82 World) primates that includes fossil hominins. With respect to the molars, we test the hypotheses 83 that most primate groups will have plesiomorphic molar proportions, and that species with 84 specialized dental morphologies will depart from the symplesiomorphic condition. We also test 85 the hypothesis that closely related taxa (e.g., sister taxa) will either share the plesiomorphic 86 condition or depart from it in similar ways. 87 This study also extends the inhibitory cascade model to the premolar tooth row, although 88 the results of this second cascade should be considered preliminary. Premolars are a different 89 developmental class of teeth from molars (Avery, 2001; Ash and Nelson, 2003), and unlike 90 molars, premolars emerge posteriorly to anteriorly in primates (Swindler, 2002). Yet, premolars 91 are functionally similar to molars (Lucas, 2004) and their developmental initiation and crown 4 92 completion patterns are the same as in molars (Swindler, 2002). Evidence of integrative modules 93 in the postcanine dentitions of hominoids (Gomez-Robles and Polly, 2012) and papionins 94 (Hlusko and Mahaney, 2009) suggest links between premolar and molar development. A recent 95 examination of rodent clades with and without the last premolar found that first molar (M1) 96 variation increased in the absence of the P4, suggesting that the presence of a P4 constrains the 97 morphology of the M1 in the way that the M1 inhibits the size of the M2 and M3 in the inhibitory 98 cascade (Labonne et al., 2012). Furthermore, the phenotypic similarity between the molarized 99 posterior premolars and the molars in the species included in the hominin genus Paranthropus 100 (Robinson, 1956; Butler, 1997, 2000; Jernvall et al., 2008) also suggests similarities in genetic 101 control. In this study, we test whether the relative sizes of the series P4, M1, and M2 can be 102 inferred from an inhibitory cascade model. 103 5. MAIN BODY 104 Materials and Methods 105 1. Sample composition 106 In order to provide a comparative context for the analysis of the species within the 107 hominin genus Paranthropus (aka “robust” australopiths) our sample deliberately included Old 108 World monkeys (i.e., cercopithecoids; Cercocebus, Macaca, Papio, and Presbytis), and apes 109 (i.e., hominoids; Hylobates, Gorilla, Pan, and Pongo) genera that have been used previously as 110 morphological and ecological analogues for the postcanine megadontia and robust craniofacial 111 morphology seen in that genus (Strait et al., 2007; Vogel et al., 2008; Cerling et al., 2011; 112 Daegling et al., 2011; Wood and Schroer, 2012). 113 114 Morphological evidence supports the hypothesis that the “robust” australopiths are a clade recognized as the genus Paranthropus (Wood and Chamberlain, 1986, 1987; Wood, 1988; 5 115 Strait et al., 1997; Wood and Richmond, 2000; Kimbel et al., 2004; Strait and Grine, 2004). 116 However, there is debate about whether the species presently included within this genus are 117 sister taxa (Wood, 1988; McCollum, 1999; Constantino and Wood, 2007; Wood and Schroer, 118 2012; Foley, 2013). The temporally-earlier of the two main species within Paranthropus, 119 Paranthropus boisei, has several derived features compared to Paranthropus robustus, which the 120 current fossil record suggests is nearly half a million years younger (Wood and Richmond, 121 2000). The morphology of P. boisei is so derived that when the first fossil evidence of the 122 species was discovered, its morphology warranted the formation of a new genus, Zinjanthropus 123 (Leakey et al., 1964). In this study, we maintain the taxonomic designations P. boisei and P. 124 robustus to highlight their overall similarities, but we use the inhibitory cascade model to test the 125 hypothesis of “robust” australopith monophyly. 126 In addition to Paranthropus, two other fossil hominin genera were included in the analysis: 127 Homo, the genus that includes modern humans, and Australopithecus, the likely ancestral clade 128 of both Paranthropus and Homo (Strait et al., 1997). Because there is much debate about the 129 taxonomic significance of the variation seen in early Homo (e.g. Miller 1991, 2000; Wood, 1992; 130 Kramer, 1993; Kramer et al., 1995; Lieberman et al., 1996; Kennedy, 1999; Wood and Collard, 131 1999a,b; Anton, 2003; Gilbert et al., 2003; Leakey et al., 2012; Lordkipanidze et al., 2013) 132 specimens of Homo were divided into just two inclusive groups. This first, Homo habilis sensu 133 lato, includes some specimens that have been referred to Homo rudolfensis (e.g., Lieberman et 134 al., 1996; Wood and Collard, 1999a,b; Strait and Grine, 2004; Leakey et al., 2012). The second 135 group, Homo erectus sensu lato, includes some specimens that have been referred to Homo 136 ergaster (e.g., Wood and Collard, 1999a,b; Wood, 1992; Wood and Richmond, 2000, Strait and 137 Grine, 2004). This group also includes the southern African specimen SK 15 and the Dmanisi 6 138 fossil hominins, which were initially referred to Homo georgicus (Gabounia et al., 2002), but 139 more recently they have been assigned to Homo erectus (Lordkipanidze et al., 2013). The 140 specimen numbers and the sources of measurements for the fossil hominins are given in Table 141 S1.2. Materials and methods 142 Lower jaws of the extant primate genera were obtained from the collections of the 143 American Museum of Natural History in New York City, National Museum of Natural History 144 in Washington DC, and Natural History Museum in London. All specimens were adult and from 145 wild populations. The species samples were sex balanced. The representative species of each 146 genus are equally sampled, except in the case of Pan where specimens of Pan paniscus were 147 unavailable for study. 148 Measurements of fossil hominin postcanine teeth were obtained from precision casts in 149 the collections at The George Washington University and the University of Arkansas, with the 150 balance taken from the literature. All specimens were from individuals with erupted M3s, but sex 151 was not controlled. The representative species of each genus are equally sampled 152 Only individuals with complete M1-M3 or P4-M2 series were analyzed. Specimens with 153 occlusal wear that masked the identification of individual cusps, or with interproximal wear that 154 affected >20% of the occlusal margin, were not included in the extant sample. For teeth with 155 moderate interstitial wear, the worn margin was reconstructed by approximating the curvature of 156 the margin from overall crown shape (Wood and Uytterschaut, 1987; Bailey and Lynch, 2005). 157 Specimens were photographed using a Canon Digital Rebel XT camera fitted with a 60 158 mm macro lens. A scale was set and leveled in the occlusal plane of the teeth, and levels on the 159 camera and photography stand were used to make sure that the occlusal plane was parallel to the 160 lens of the camera. Maximum mesiodistal and buccolingual diameters for each postcanine tooth 7 161 were obtained via scaled measurements in TPSDig (Figure S1; Rohlf, 2009), and occlusal areas 162 were computed by multiplying these diameters (Kavanagh et al., 2007; Polly, 2007; Wilson et 163 al., 2012; Halliday and Goswami, 2013). Mesiodistal and buccolingual diameters for all extant 164 primate and fossil hominin specimens are available at 165 http://dx.doi.org/10.6084/m9.figshare.1181983. 166 To investigate intra-observer error, 45 individuals (i.e., c. 20 % of the extant sample) 167 were drawn from among all of the extant taxa in the study and re-measured two months after the 168 initial set of measurements. Intra-observer error for linear measurements was ±0.4 mm. 169 3. Analysis 170 Two different postcanine cascades, the standard M1-M3 and the P4-M2, were tested 171 against the murine inhibitory cascade model. We used two inter-tooth ratios for each analysis, 172 M2:M1 and M3:M1 for the molar cascade and M1:P4 and M2:P4 for the premolar-molar cascade. 173 Reduced major axis regression (RMA) was used to examine the nature of any 174 correlations between relative occlusal areas. There are reservations about the use of RMAs for 175 anything other than the ratios of the standard deviations of y on x (Smith, 2009), but RMA is 176 used in the inhibitory cascade model because a single line defines the ratio between x and y (i.e., 177 the relationship of the data is symmetrical). Data were considered to falsify the predictions of the 178 inhibitory cascade model when the 95% confidence interval of the slope does not include 2.00. 179 Because RMA regressions have the tendency to drive small sample sizes toward a slope of 1, the 180 use of the RMA makes it more likely that the prediction that groups will fall within the 181 boundaries of the inhibitory cascade model will be falsified. 182 183 RMA regressions were performed in software developed in the C programming language with standard linear regression error estimates (Bohonak, 2004). Data were bootstrapped 1000 8 184 times and the resulting regression compared to the predictions of the murine inhibitory cascade. 185 Even when the significance values for r2 were low, regressions with confidence intervals that 186 included the 2.0 slope and -1.0 intercept predicted by the inhibitory cascade model were 187 determined “validated” as is prior practice (Renvoise et al., 2009; Wilson et al., 2012; Halliday 188 and Goswami, 2013). 189 Means and standard deviations of the occlusal areas of each postcanine tooth, P4-M3, are 190 reported for the extant genera in Table S2. The individual measurements from each fossil tooth 191 are given in Table S3. Results of a MANOVA conducted in R indicated that the ratios of 192 occlusal areas for all taxa are significantly distinct from one another (Table S4). A Pillai trace 193 was applied to protect against Type I errors for small samples. Small samples were of a 194 particular concern for the interpretation of the slopes of P. boisei and P. robustus, and Student’s 195 t-test was employed to test whether the slopes of the regression lines for the relative molar sizes 196 of P. boisei and P. robustus were statistically different (Table S5). 197 Results 198 1. RMA regressions 199 In most extant primates, RMA regressions of the molar ratios at both the species and 200 genus levels have 95% confidence intervals that include the slope and intercept predicted by the 201 murine inhibitory cascade (Table 1). Thus, based on the results of this analysis, the inhibitory 202 cascade model can be generally applied to the extant primates included in this study. The 203 exceptions among extant primates include Cercopithecus, which is not validated by the model at 204 either the species or genus level, and Papio ursinus, which unlike its congeners does not fit the 205 model. All other extant congeners share similar fits to the inhibitory cascade. 9 206 Among the fossil hominin genera, the molar ratios of Australopithecus and Homo 207 conform to the predictions of the murine inhibitory cascade model at the species level. At the 208 genus level, the relationship between the occlusal areas of the molars of Homo can be described 209 by the intercept of the inhibitory cascade but not by its slope. The maximum confidence interval 210 of the slope of Homo in this study is 1.96 as opposed to the 2.00 dictated by the parameters of the 211 inhibitory cascade, which may relate to the variation observed in the relative occlusal areas of H. 212 habilis sensu lato. Within the genus Paranthropus, the congeners P. robustus and P. boisei differ 213 notably. While the relative occlusal areas of P. robustus are well described by the inhibitory 214 cascade, neither the intercept nor slope of P. boisei fit the model. 215 There is no evidence of a consistent pattern for the premolar-molar cascade among extant 216 or fossil genera (Table 2). Among the extant primates, the molarized premolars of Cercocebus fit 217 the proposed premolar-molar cascade, but the proposed premolar-molar cascade also fits some 218 taxa with no evidence of molarization (e.g., Cercopithecus mitis and Hylobates albibarbis). 219 Within Paranthropus, both P. robustus and P. boisei are considered to have molarized 220 premolars, but only P. robustus fits the proposed premolar-molar cascade. 221 2. Regression plots 222 The results of the RMA are summarized in linear regression plots of the molar cascade 223 and the proposed premolar-molar cascade. The proportions of the molar occlusal areas of extant 224 primates are weakly correlated (r2 = 0.55). The cercopithecoids in the extant sample conform to 225 the slope of murine inhibitory cascade model more closely than the hominoids (Figure 2). 226 Hominoids, including fossil hominins, have similarly-sized M2s and M3s compared to 227 cercopithecoids (Figure 3). That is, most hominoids are described by the occlusal relative size 228 order, M1<M2≈M3. 10 229 The regression of molar sizes in P. boisei differs from that of its congener P. robustus 230 (Figure 4). Whereas P. robustus shares the M1<M2<M3 pattern seen in the majority of primates 231 in this study, P. boisei is unusual because of the relative sizes of its M2s and M3s, which are 232 much larger than predicted from the occlusal area of M1. The area of the M2 is especially large 233 given the size of the M1. 234 If we accept a working hypothesis that P4 development influences the size of the M1 and 235 M2, we can report a few patterns from an examination of premolar-molar ratios. The premolar- 236 molar ratios of extant primates are very weakly correlated (r2 = 0.27). Catarrhine primates have a 237 P4-M2 relative size sequence (P4<M1<M2) that resembles that for M1-M3. At the level of the 238 superfamily, cercopithecoids tend to have premolar-molar proportions above the trajectory 239 predicted on the basis of the molars (Figure 5), whereas extant hominoids consistently fall below 240 this trajectory. This is because, when P4 crown size is normalized, cercopithecoids tend to have 241 larger M2s than hominoids. Among the fossil hominins, although Au. africanus, H. habilis s.l., H. 242 erectus s.l., and P. robustus resemble extant hominoids (Figures 6 and 7), most P. boisei 243 specimens tend to follow the cercopithecoid pattern. 244 11 245 Discussion 246 1. Molar cascade 247 The murine inhibitory cascade predicts the relative occlusal areas of extant primate 248 molars, and we suggest that it is the plesiomorphic condition for catarrhine primates. The 249 catarrhines are broadly described by a molar row in which the relative occlusal areas increase in 250 size. Hominoids tend to have more similarly-sized M2s and M3s than cercopithecoids. Based on 251 the murine experiments, this suggest that hominoids have a derived developmental pathway in 252 which there is less activation on the posterior molars, more inhibition on the posterior molars, or 253 some combination of these effects. The M1<M2≈M3 pattern may relate to the timing of the 254 emergence of the M1, which occurs later in Pan than in cercopithecoids (Kelley and Smith, 255 2003). Late emergence of the M1 may delay the initiation of posterior molars and subsequently 256 affect the final size of posterior molars. If late emergence of the M1 is the plesiomorphic 257 condition of hominoids, this would account for the reduced M3s described in several hominoid 258 lineages (Nanda, 1954; Garn, 1962, 1963; Garn et al., 1964; Frisch, 1967, 1973; Lavelle, 1970; 259 Lavelle and Moore, 1973; Mahler, 1973; Kinzey, 1984; Plavcan and Gomez, 1993; Smith, 1994; 260 Swindler, 1998; Dean and Lucas, 2009). This condition may also be the precursor to the much 261 delayed emergence of the M1 in H. erectus s.l. and later Homo (Dean et al., 2001). 262 Our null hypothesis, which is that closely-related taxa will share the same inhibitory 263 cascade, is supported by the observation that in all but one extant primate genera, congeners 264 share the same inhibitory cascade. The exception, Papio, has a complex evolutionary history 265 featuring substantial introgression (Keller et al., 2010; Jolly et al., 2011) and paraphyletic species 266 (Zinner et al., 2009). Rather than divisions along traditionally recognized species lines, 267 mitochondrial DNA studies have detected a major division between Papio groups in East and 12 268 southern Africa (Newman et al., 2004; Zinner et al., 2009). This division is also found in this 269 study, with specimens of Papio from East Africa (Papio anubis and Papio cynocephalus) sharing 270 the same inhibitory cascade, while the southern African group (Papio ursinus) did not. 271 The results from the analysis of extant primates provide a comparative context for 272 interpreting the relationships between fossil hominins. Paranthropus robustus shares the 273 plesiomorphic condition of extant primates, in which M3 is predictably the largest tooth in the 274 molar series. Conversely, P. boisei has much larger M2s than predicted by the occlusal areas of 275 the M1 and, as a taxon, has the absolutely and relatively largest M2:M1 ratio in this study. A 276 distinct M1<M2>M3 molar size sequence is rare among mammals, requiring both low inhibition 277 levels and a premature stop to M3 development (Kavanagh et al., 2007; Polly, 2007; Labonne et 278 al., 2012); such genetic constraints may be one of the determinants of the relative size of the M2 279 in P. boisei. 280 13 281 282 2. Premolar-molar cascade There was no consistent evidence of a premolar-molar cascade among the primate genera 283 and species examined here, even within taxa described by molarized premolars. However, when 284 the data are considered at the superfamily level, there is a difference in the P4-M2 relative size 285 relationships between cercopithecoids and hominoids. Cercopithecoid taxa tend to fall above the 286 predictions of this model, whereas the hominoid taxa tend to fall below this prediction. That is to 287 say, for similar M1:P4 occlusal area ratios, cercopithecoids tend to have larger M2s than 288 hominoids. This is consistent with the results of the molar cascade, which suggests that 289 hominoids have reduced M3s compared to cercopithecoids. Rather than assume that the 290 principles of the molar cascade can be applied to premolars and molars without any 291 modification, experimental work using mouse mutants with artificially induced premolars 292 (Peterkova et al., 2005; Klein et al., 2006; D’Souza et al., 2007) could help develop a model 293 specific to the P4-M2 sequence. This would also help researchers better understand the factors 294 that contribute to premolar molarization. 295 6. CONCLUSION 296 This study is an example of how models derived from the principles of evolutionary 297 development can help improve our understanding of macroevolutionary trends. By determining 298 how postcanine crown area may be influenced by an inhibitory cascade, it is possible to evaluate 299 dependent relationships between dental morphologies that may otherwise appear as independent 300 traits. Thus, on the basis of the inhibitory cascade, the taxa within the fossil hominin genus 301 Paranthropus do not share the same molar size relationships. Relative molar size is not 302 consistent with the hypothesis of Paranthropus monophyly. This study adds to other 303 morphological differences seen in the megadont postcanine dentitions of P. boisei and P. 14 304 robustus (Wood, 1988; Suwa et al., 1994, McCollum, 1999) and suggests that it may no longer 305 be prudent to assume that postcanine megadontia is a synapomorphy of Paranthropus. If the 306 results of the analyses conducted here are confirmed, they affect our understanding of the 307 evolutionary significance of postcanine megadontia and premolar molarization. Developmental 308 biology continues to illuminate the details of the complex relationships between genotype and 309 phenotype, and by doing so it improves our ability to generate more reliable hypotheses about 310 early hominin taxonomy and phylogeny. 311 7. ACKNOWLEDGEMENTS 312 The manuscript was greatly improved by comments from Drs. Patricia Hernandez, Aida Gomez- 313 Robles, and Mark Grabowski (George Washington University), Matthew Skinner (University 314 College London), Paul Constantino (Marshall University), and two anonymous reviewers. Brian 315 Richmond provided comments on an early version of the manuscript. This study was conceived 316 while under the supervision of Dr. Jukka Jernvall (University of Helsinki) and benefited from his 317 comments. Dr. Peter Ungar (University of Arkansas) provided access to many fossil casts. 318 Access to extant species was made possible through Linda Gordon, Darrin Lunde, and Dr. 319 Matthew Tocheri (NMNH), Eileen Westwig (AMNH), and Roberto Portela Miguez (BMNH). 320 Kristen Ramirez (CUNY) and Christine Foltz assisted with photography. David Otten 321 (University of Arkansas), Michael Frick, Teresa Girolamo, and David Cobey provided 322 hospitality during museum visits. Funding for this research was provided by the NSF-IGERT 323 DGE-0801634, an NSF-GRF to KS, a Cosmos Club Scholars Award to KS, and a special gift 324 from the Council of Scientific Society Presidents to KS. The authors declare no conflict of 325 interest. 326 15 327 Author contributions: KS conceived of the application of the inhibitory cascade to fossil 328 hominins, and BW encouraged the application of the model to reinterpreting the relationships 329 among Paranthropus taxa. BW assisted with arranging visits to extant and fossil collections. All 330 measurements and analyses were performed by KS. The initial manuscript was drafted by KS 331 with critical revisions by both authors. 332 8. REFERENCES 333 Anton, S.C., 2003. Natural history of Homo erectus. Am. J. Phys. Anthropol., 122, pp. 126-70. 334 Arnold, S.J., 1992. Constrains of phenotypic evolution. Am. Nat., 130, pp. 85-107. 335 Asahara, M., 2013. 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TABLES 546 25 547 548 549 550 551 552 553 Table 1. Reduced major axis (RMA) regression results for the molar cascade (M1-M3) in extant primates and fossil hominins. INT is the intercept, and C.I. is the 95% confidence interval. For the criterion “Fits IC?”, values denote whether or not the sample could be described by the predictions of the inhibitory cascade as applied to a murine sample (Kavanagh et al., 2007; Renvoise et al., 2009). “Y” denotes yes, and “N” denotes no. Each genus sample is equally weighted by representative species. All extant samples are equally weighted by sex. Taxon N IC murine prediction INT C.I. Min C.I. Max -1.00 C.I. Min Slope C.I. Max 2.00 R2 C.I. Min C.I. Max Fits IC? 1.00 Cercopithecoids Cercocebus C. atys C. torquatus Cercopithecus C. diana C. mitis Colobus C. angolensis C. guereza Lophocebus L. albigena L. johnstoni Macaca M. cyclopis M. fascicularis M. nemestrina Papio P. anubis P. cynocephalus P. ursinus Presbytis P. potenziani P. rubicunda 8 4 4 24 12 12 24 12 12 16 8 8 30 10 10 10 24 8 8 8 32 16 16 -0.49 -0.14 -1.34 0.16 0.46 -0.30 -1.10 -0.66 -0.69 -2.27 -1.22 -3.51 -0.89 -2.85 -2.10 -0.21 -0.21 -1.53 -0.54 -0.06 -0.39 -1.39 -0.24 -2.78 -2.40 -14.21 -0.33 -0.05 -0.90 -2.08 -2.22 -2.00 -7.07 -5.89 -18.28 -1.53 -5.20 -5.24 -1.71 -0.61 -3.71 -2.24 -0.60 -1.07 -2.87 -1.00 0.61 2.07 7.64 0.48 0.97 3.09 4.58 5.35 3.45 -0.81 0.37 14.56 -0.26 6.96 -0.30 2.96 0.16 1.01 0.92 0.60 0.15 4.96 3.22 1.48 1.23 2.07 0.86 0.65 1.20 2.18 1.76 1.92 2.95 2.17 3.93 2.07 3.43 3.08 1.55 1.52 2.56 1.74 1.42 1.50 2.35 1.37 0.68 -0.46 -4.50 0.60 0.26 -1.44 -2.34 -2.93 -1.35 1.83 0.93 -10.54 1.56 -3.44 1.55 -1.06 1.27 0.78 0.65 1.02 1.01 -3.11 -1.91 3.10 2.80 11.33 1.26 1.04 1.69 3.01 3.07 2.98 6.82 5.91 15.74 2.56 5.10 5.70 2.67 1.82 4.37 2.86 1.80 2.09 3.65 2.07 0.42 0.64 0.19 0.30 0.29 0.25 0.07 0.06 0.22 0.39 0.34 0.11 0.52 0.20 0.56 0.24 0.78 0.56 0.45 0.88 0.26 0.03 0.02 0.09 0.04 0.03 0.03 0.02 0.00 0.00 0.00 0.00 0.08 0.05 0.00 0.31 0.00 0.06 0.00 0.56 0.04 0.01 0.70 0.11 0.00 0.00 0.91 1.00 1.00 0.58 0.65 0.76 0.47 0.62 0.86 0.69 0.91 0.64 0.73 0.71 0.91 0.69 0.90 0.96 0.92 0.99 0.50 0.48 0.27 Y Y Y N N N Y Y Y Y Y Y Y Y Y Y N Y Y N Y Y Y 24 12 12 24 12 12 18 16 8 8 -1.28 -0.46 -2.17 -0.61 -0.64 -0.89 -0.70 -0.66 -1.49 -0.26 -3.12 -3.31 -5.27 -1.29 -1.49 -2.31 -1.50 -1.15 -2.59 -1.57 -0.14 3.80 4.28 0.00 2.19 2.78 -0.21 0.20 0.12 2.72 2.06 1.39 2.77 1.52 1.56 1.76 1.52 1.59 2.23 1.24 1.14 -2.05 -2.48 0.98 -1.16 -1.52 1.07 0.82 0.88 -1.50 3.56 3.72 5.22 2.14 2.39 3.03 2.22 2.01 3.11 2.44 0.07 0.02 0.15 0.28 0.15 0.11 0.48 0.62 0.53 0.38 0.00 0.00 0.00 0.05 0.00 0.00 0.19 0.31 0.08 0.01 0.36 0.53 0.69 0.53 0.51 0.52 0.75 0.91 0.95 0.94 Y Y Y Y Y Y Y Y Y Y 12 6 6 12 6 6 12 6 6 -1.12 -4.39 0.14 -0.45 -0.04 3.38 0.30 0.69 -0.57 -3.77 -6.93 -1.84 -1.13 -1.08 -29.80 -0.35 0.11 -1.56 0.15 17.32 0.52 3.43 3.02 9.63 0.69 1.51 0.52 1.90 4.37 0.85 1.46 1.09 -1.92 0.86 0.59 1.59 0.87 12.48 0.57 -2.03 -1.96 -7.12 0.59 -0.03 0.69 3.93 6.18 2.48 1.96 2.23 25.24 1.41 0.94 2.48 0.39 0.41 0.73 0.03 0.54 0.11 0.72 0.65 0.82 0.10 0.00 0.11 0.00 0.03 0.00 0.38 0.03 0.52 0.80 0.93 1.00 0.85 1.00 1.00 0.91 1.00 1.00 Y Y Y N Y Y N N Y Hominoids Gorilla G. beringei G. gorilla Hylobates H. agilis H. lar Pan troglodytes Pongo P. abelii P. pygmaeus Fossil hominins 554 Australopithecus Au. afarensis Au. africanus Homo H. erectus s.l. H. habilis s.l. Paranthropus P. boisei P. robustus 26 555 556 557 558 559 560 561 Table 2. Reduced major axis (RMA) regression results for the premolar-molar cascade (P4-M2) in extant primates and fossil hominins. INT is the intercept, and C.I. is the 95% confidence interval. For the criterion “Fits IC?”, values denote whether or not the sample could be described by the predictions of the inhibitory cascade as applied to a murine sample (Kavanagh et al., 2007; Renvoise et al., 2009). “Y” denotes yes, and “N” denotes no. Each genus sample is equally weighted by representative species. All extant samples are equally weighted by sex. Taxon N IC prediction (molar) INT C.I. Min C.I. Max -1.00 C.I. Min Slope C.I. Max 2.00 R2 C.I. Min C.I. Max Fits IC? 1.00 Cercopithecoids Cercocebus C. atys C. torquatus Cercopithecus C. diana C. mitis Colobus C. angolensis C. guereza Lophocebus L. albigena L. johnstoni Macaca M. cyclopis M. fascicularis M. nemestrina Papio P. anubis P. cynocephalus P. ursinus Presbytis P. potenziani P. rubicunda 8 4 4 24 12 12 24 12 12 16 8 8 30 10 10 10 24 8 8 8 32 16 16 0.26 0.86 -0.81 0.11 0.28 -0.54 0.26 0.57 0.21 -0.17 -1.15 0.00 -0.46 0.63 -0.19 -1.16 -0.69 0.38 0.28 -2.65 -0.03 0.20 -0.23 -0.14 -27.39 -7.84 -0.37 -0.43 -1.10 -0.08 -0.24 -0.46 -1.46 -10.38 -0.45 -1.13 -0.14 -0.91 -2.80 -2.08 -0.35 -1.55 -5.91 -0.50 -0.12 -1.09 0.58 4.10 0.30 0.54 3.66 0.24 0.53 2.79 0.64 0.53 1.07 0.45 0.02 1.07 0.13 4.89 0.41 1.10 1.11 8.42 0.34 0.54 0.28 1.05 0.74 2.09 1.20 1.08 1.66 1.05 0.84 1.08 1.38 2.07 1.24 1.61 0.95 1.32 2.16 1.87 1.04 1.26 3.38 1.12 0.97 1.21 0.82 -1.55 1.10 0.88 -1.63 1.07 0.85 -0.68 0.75 0.92 0.56 0.93 1.27 0.62 1.07 -2.90 1.15 0.62 0.78 -4.57 0.89 0.80 0.86 1.35 20.00 8.00 1.54 1.65 2.03 1.32 1.44 1.59 2.25 8.06 1.55 2.11 1.55 1.77 3.50 2.83 1.50 2.53 5.63 1.43 1.25 1.78 0.67 0.41 0.98 0.48 0.25 0.72 0.67 0.28 0.79 0.51 0.26 0.85 0.43 0.72 0.83 0.08 0.15 0.57 0.61 0.00 0.42 0.83 0.53 0.29 0.00 0.84 0.12 0.00 0.13 0.29 0.02 0.40 0.21 0.06 0.43 0.20 0.19 0.43 0.00 0.00 0.10 0.22 0.00 0.18 0.58 0.20 0.86 1.00 1.00 0.75 0.72 0.94 0.87 0.71 0.96 0.89 0.75 0.99 0.69 0.94 0.98 0.65 0.44 0.90 0.90 0.63 0.65 0.94 0.78 N Y Y N N Y N N N N Y N Y N N Y Y N Y Y N N N 24 12 12 24 12 12 18 16 8 8 -0.10 -0.17 -0.02 0.22 -0.57 -0.89 0.56 -0.10 0.74 0.27 -0.46 -0.79 -0.55 -0.20 -1.64 -2.36 0.22 -0.54 0.40 -0.71 0.24 0.30 0.59 0.54 3.57 2.62 1.04 2.84 1.68 0.70 1.29 1.34 1.24 0.92 1.36 1.76 0.77 1.23 0.63 0.86 1.07 1.01 0.82 0.70 -1.11 -1.34 0.47 -1.13 -0.13 0.52 1.55 1.74 1.58 1.18 1.96 3.09 1.01 1.54 0.88 1.63 0.63 0.56 0.64 0.59 0.28 0.11 0.36 0.24 0.60 0.65 0.32 0.13 0.14 0.36 0.01 0.00 0.03 0.00 0.02 0.23 0.86 0.93 0.89 0.80 0.70 0.49 0.67 0.63 0.97 0.95 N N N N N Y N N N N 14 7 7 10 5 5 14 7 7 0.13 0.59 -0.91 -0.90 -0.27 -7.01 0.31 3.09 0.09 3.09 -1.25 0.17 -5.63 -4.77 -1.93 -16.57 -0.33 -1.25 -1.08 -1.25 2.45 1.13 6.20 7.27 3.23 14.76 0.85 4.11 0.69 4.11 1.21 0.93 1.84 1.57 1.11 5.37 0.98 -1.42 1.10 -1.42 -0.40 0.56 -2.55 -3.25 -0.89 -7.50 0.63 -2.26 0.74 -2.26 2.18 1.18 4.94 3.94 1.93 11.08 1.46 2.51 1.96 2.51 0.26 0.80 0.02 0.06 0.60 0.23 0.50 0.01 0.77 0.01 0.01 0.08 0.00 0.00 0.04 0.01 0.01 0.00 0.15 0.00 0.79 1.00 0.97 0.57 1.00 1.00 0.84 0.69 1.00 0.69 Y N Y Y N Y N Y N Y Hominoids Gorilla G. beringei G. gorilla Hylobates H. agilis H. lar Pan troglodytes Pongo P. abelii P. pygmaeus Fossil hominins Australopithecus Au. afarensis Au. africanus Homo H. erectus s.l. H. habilis s.l. Paranthropus P. boisei P. robustus 27 562 11. FIGURE LEGENDS 563 Figure 1. The inhibitory cascade is presented as a dashed line plotting the function y = 1 + [(a – 564 i)/i](x – 1), which describes how the rates of activation and inhibition affect molars as they 565 develop in sequence. M2:M1 and M3:M1 are ratios of relative molar size. As the ratio of M2:M1 566 ratio increases, the ratio of M3:M1 also increases, showing a high degree of activation acting 567 along the molar row. The opposite, a decrease in molar ratios, denotes high rates of inhibition. 568 Gray shading indicates areas of general size reduction or increase in the postcanine tooth row 569 and is bounded by cases where M1=M2 and M1=M3. 570 Figure 2. Regression of the relative occlusal areas of the molars of extant primates, faceted by 571 genus. The line represents the function of the inhibitory cascade. Gray solid circles = 572 cercopithecoids; black solid diamonds = hominoids. 573 Figure 3. Regression of the relative occlusal areas of the molars of fossil hominins and extant 574 primates. The solid line represents the function of the inhibitory cascade and the dashed line is a 575 least squares regression of the extant specimens. Solid symbols = extant taxa; unfilled symbols = 576 fossil hominins. Gray solid circles = cercopithecoids; black solid diamonds = hominoids. 577 Unfilled squares = Australopithecus; unfilled circles = Homo, unfill upward triangles = 578 Paranthropus boisei and unfilled downward triangles = Paranthropus robustus. 579 Figure 4. Regression of the relative occlusal areas of the molars of fossil hominins, faceted by 580 taxon. The solid line represents the function of the inhibitory cascade, and the dashed line is a 581 least squares regression of the extant specimens. Unfilled squares = Australopithecus; unfilled 582 circles = Homo, unfilled upward triangles = Paranthropus boisei and unfilled downward 583 triangles = Paranthropus robustus. Specimens which deviate notably from the inhibitory cascade 584 are labeled. 28 585 Figure 5. Regression of the relative occlusal areas of the last premolar and first two molars of 586 extant primates, faceted by genus. The line represents the function of the inhibitory cascade. 587 Gray solid circles = cercopithecoids; black solid diamonds = hominoids. 588 Figure 6. Regression of the relative occlusal areas of the last premolar and first two molars of 589 fossil hominins and extant primates. The line represents the function of the inhibitory cascade. 590 Solid symbols = extant taxa; unfilled symbols = fossil hominins. Gray solid circles = 591 cercopithecoids; black solid diamonds = hominoids. Unfilled squares = Australopithecus; 592 unfilled circles = Homo, unfilled upward triangles = Paranthropus boisei and unfilled downward 593 triangles = Paranthropus robustus. 594 Figure 7. Regression of the relative occlusal areas of the last premolar and first two molars of 595 fossil hominins, faceted by taxon. The line represents the function of the inhibitory cascade. 596 Solid symbols = extant taxa; unfilled symbols = fossil hominins. Gray solid circles = 597 cercopithecoids; black solid diamonds = hominoids. Unfilled squares = Australopithecus; 598 unfilled circles = Homo, unfilled upward triangles = Paranthropus boisei and unfilled downward 599 triangles = Paranthropus robustus. 29