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1. TITLE PAGE
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Title: Modeling the dental development of fossil hominins through the inhibitory cascade
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KES SCHROER1,2 and BERNARD WOOD3,4
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Dartmouth, 6047 Silsby Hall, Hanover NH 03755, USA, 3Center for the Advanced Study of
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Hominid Paleobiology, Department of Anthropology, The George Washington University, 2110
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G St NW, Washington DC 20052, USA, 4Human Origins Program, National Museum of Natural
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History, Smithsonian Institution.
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Corresponding author: kes.schroer@gmail.com
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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
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occlusal surfaces of mammalian molars in terms of developmental mechanisms. The cascade is
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derived from experimental studies of mouse molars developed in culture, and has been tested and
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applied to the dentitions of rodents, ungulates, carnivores, and platyrrhines. Results from such
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applications have provided new information regarding the origins of plesiomorphic traits in
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mammalian clade and how derived morphologies may arise. In this study we apply the inhibitory
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cascade model to the postcanine dentition of a sample of Old World primates that includes fossil
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hominins. The results of this study suggest that the inhibitory cascade (i.e., M1<M2<M3)
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describes the relative sizes of the molar occlusal areas of Old World primates and is likely the
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plesiomorphic condition for this clade. Within that clade, whereas most Old World monkeys
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have a M1<M2<M3 pattern, most apes have a M1<M2≈M3 pattern. This modified cascade
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suggests that greater levels of inhibition (or less activation) are acting on the posterior molars of
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apes, thus facilitating the reduction of M3s within the apes. With the exception of the baboon
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genus Papio, extant congeners typically share the same molar inhibitory cascade. The differences
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in the relative size relationships observed in the molar and premolar-molar cascades of the
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species included in the fossil hominin genus Paranthropus suggest that although large postcanine
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teeth are a shared derived trait within this genus, the developmental basis for postcanine
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megadontia may not be the same in these two Paranthropus taxa. Our results showthat
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phenotypic characters like postcanine megadontia may not reflect common development. .
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3. KEYWORDS
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Fossil hominin, human evolution, inhibitory cascade, Paranthropus, monophyly, primates,
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postcanine teeth, molar size.
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4. INTRODUCTION
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Evolutionary developmental biologists have begun to determine the regulatory pathways
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that govern the process of tooth formation and the details of occlusal morphology (Jernvall et al.,
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2000; Jernvall and Thesleff, 2000, 2012; Salazar-Ciudad and Jernvall, 2002, 2004, 2010;
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Tummers and Thesleff, 2003, 2009; Jarvinen et al., 2006; Munne et al., 2009; Renvoise et al.,
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2009; Michon et al., 2010). This research has helped unravel the complex relationships between
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the genotype and phenotype of the dentition (Arnold, 1992; Hall, 2003; Polly, 2008) and it has
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shown how molecular processes can influence macroevolutionary trends (Peterson et al., 2007;
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Raff, 2007). In particular, understanding the mechanisms underlying tooth development helps
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quantify potential constraints on tooth evolvability and helps understand how adaptation can
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result in the modification of regulatory pathways (Renaud et al., 2011; Felix, 2012; Asahara,
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2013; Bernal et al., 2013; Halliday and Goswami, 2013).
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Fossils are difficult to study within a developmental context. However, the inhibitory
cascade model proposed by Kavanagh and colleagues (2007) allows researchers to generate
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hypotheses about how regulatory pathways might have influenced evolutionary trends seen in the
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postcanine dentition of mammals, including hominins. The inhibitory cascade model is the result
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of Kavanagh and colleagues’ use of cell culture techniques to investigate mouse dental
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development. They found that when the lower molars of Mus musculus were isolated from their
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posterior tail, the rate of initiation of posterior molars was increased and the posterior molars
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were enlarged. Kavanagh and colleagues hypothesized that the net balance between genetic
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activation and inhibition during dental development determines the relative size of the teeth in
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the molar row. Kavanagh and colleague’s simplified model to describe the genotypic-phenotypic
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relationship between molar position and molar size is:
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y=1+[(a–i)/i](x–1),
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where y is the relative molar size estimated from occlusal area, x is the position of the molar in
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the tooth row, a is the strength of activation, and i is the strength of inhibition.
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Because teeth develop in sequence, the inhibitory cascade model can be used to predict
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the relative size of the teeth in the molar row. For a typical mammal the above equation predicts
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that M1=1, M2=a/i, and M3=2a/i-1). The model also predicts a slope of 2.0 and an intercept of -
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1.0 to describe the ratios between the M2:M1 and M3:M1 occlusal areas. Expressed in another
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way, the occlusal area of M2 will consistently be 1/3rd the total occlusal area of the molar row
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since M2/(M1+M2+M3)=(a/i)/[1+a/i +(2a/i–1)]=1/3 (Kavanagh et al., 2007). Weak inhibition
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(i.e., high a/i) by M1 on the posterior molars results in a molar row that increases in size from
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anterior to posterior (i.e., the ratio between occlusal areas is >1). Conversely if the ratio is <1,
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this suggests strong inhibition and results in a molar row that decreases in size from anterior to
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posterior. A summary schematic of the inhibitory cascade model is provided in Figure 1.
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The inhibitory cascade model also has the potential to help in phylogenetic
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reconstruction. By applying the model to a large set of fossil and extant mammals, researchers
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have demonstrated that the relative sizes of most mammalian molars follow the predictions of the
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inhibitory cascade and may be symplesiomorphic for relative molar sizes in this clade (Halliday
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and Goswami, 2013). Differences in the relative occlusal areas of postcanine tooth crowns can
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differentiate the major radiations of mammals (Wilson et al., 2012), and the evolution of
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specialized teeth such as carnassials is linked with departures from the symplesiomorphic
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condition of the inhibitory cascade (Asahara, 2013; Halliday and Goswami, 2013).
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Preliminary analyses suggest that primates generally conform to the inhibitory cascade
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(Polly, 2007; Halliday and Goswami, 2013) and an in-depth study of platyrrhine (New World)
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primates suggests that when phylogeny is taken into account their relative occlusal areas do not
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differ significantly from the pattern predicted by the inhibitory cascade model (Bernal et al.,
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2013). This study applies the inhibitory cascade model to a large sample of catarrhine (Old
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World) primates that includes fossil hominins. With respect to the molars, we test the hypotheses
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that most primate groups will have plesiomorphic molar proportions, and that species with
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specialized dental morphologies will depart from the symplesiomorphic condition. We also test
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the hypothesis that closely related taxa (e.g., sister taxa) will either share the plesiomorphic
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condition or depart from it in similar ways.
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This study also extends the inhibitory cascade model to the premolar tooth row, although
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the results of this second cascade should be considered preliminary. Premolars are a different
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developmental class of teeth from molars (Avery, 2001; Ash and Nelson, 2003), and unlike
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molars, premolars emerge posteriorly to anteriorly in primates (Swindler, 2002). Yet, premolars
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are functionally similar to molars (Lucas, 2004) and their developmental initiation and crown
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completion patterns are the same as in molars (Swindler, 2002). Evidence of integrative modules
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in the postcanine dentitions of hominoids (Gomez-Robles and Polly, 2012) and papionins
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(Hlusko and Mahaney, 2009) suggest links between premolar and molar development. A recent
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examination of rodent clades with and without the last premolar found that first molar (M1)
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variation increased in the absence of the P4, suggesting that the presence of a P4 constrains the
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morphology of the M1 in the way that the M1 inhibits the size of the M2 and M3 in the inhibitory
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cascade (Labonne et al., 2012). Furthermore, the phenotypic similarity between the molarized
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posterior premolars and the molars in the species included in the hominin genus Paranthropus
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(Robinson, 1956; Butler, 1997, 2000; Jernvall et al., 2008) also suggests similarities in genetic
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control. In this study, we test whether the relative sizes of the series P4, M1, and M2 can be
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inferred from an inhibitory cascade model.
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5. MAIN BODY
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Materials and Methods
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1. Sample composition
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In order to provide a comparative context for the analysis of the species within the
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hominin genus Paranthropus (aka “robust” australopiths) our sample deliberately included Old
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World monkeys (i.e., cercopithecoids; Cercocebus, Macaca, Papio, and Presbytis), and apes
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(i.e., hominoids; Hylobates, Gorilla, Pan, and Pongo) genera that have been used previously as
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morphological and ecological analogues for the postcanine megadontia and robust craniofacial
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morphology seen in that genus (Strait et al., 2007; Vogel et al., 2008; Cerling et al., 2011;
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Daegling et al., 2011; Wood and Schroer, 2012).
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Morphological evidence supports the hypothesis that the “robust” australopiths are a
clade recognized as the genus Paranthropus (Wood and Chamberlain, 1986, 1987; Wood, 1988;
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Strait et al., 1997; Wood and Richmond, 2000; Kimbel et al., 2004; Strait and Grine, 2004).
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However, there is debate about whether the species presently included within this genus are
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sister taxa (Wood, 1988; McCollum, 1999; Constantino and Wood, 2007; Wood and Schroer,
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2012; Foley, 2013). The temporally-earlier of the two main species within Paranthropus,
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Paranthropus boisei, has several derived features compared to Paranthropus robustus, which the
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current fossil record suggests is nearly half a million years younger (Wood and Richmond,
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2000). The morphology of P. boisei is so derived that when the first fossil evidence of the
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species was discovered, its morphology warranted the formation of a new genus, Zinjanthropus
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(Leakey et al., 1964). In this study, we maintain the taxonomic designations P. boisei and P.
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robustus to highlight their overall similarities, but we use the inhibitory cascade model to test the
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hypothesis of “robust” australopith monophyly.
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In addition to Paranthropus, two other fossil hominin genera were included in the analysis:
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Homo, the genus that includes modern humans, and Australopithecus, the likely ancestral clade
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of both Paranthropus and Homo (Strait et al., 1997). Because there is much debate about the
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taxonomic significance of the variation seen in early Homo (e.g. Miller 1991, 2000; Wood, 1992;
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Kramer, 1993; Kramer et al., 1995; Lieberman et al., 1996; Kennedy, 1999; Wood and Collard,
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1999a,b; Anton, 2003; Gilbert et al., 2003; Leakey et al., 2012; Lordkipanidze et al., 2013)
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specimens of Homo were divided into just two inclusive groups. This first, Homo habilis sensu
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lato, includes some specimens that have been referred to Homo rudolfensis (e.g., Lieberman et
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al., 1996; Wood and Collard, 1999a,b; Strait and Grine, 2004; Leakey et al., 2012). The second
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group, Homo erectus sensu lato, includes some specimens that have been referred to Homo
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ergaster (e.g., Wood and Collard, 1999a,b; Wood, 1992; Wood and Richmond, 2000, Strait and
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Grine, 2004). This group also includes the southern African specimen SK 15 and the Dmanisi
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fossil hominins, which were initially referred to Homo georgicus (Gabounia et al., 2002), but
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more recently they have been assigned to Homo erectus (Lordkipanidze et al., 2013). The
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specimen numbers and the sources of measurements for the fossil hominins are given in Table
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S1.2. Materials and methods
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Lower jaws of the extant primate genera were obtained from the collections of the
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American Museum of Natural History in New York City, National Museum of Natural History
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in Washington DC, and Natural History Museum in London. All specimens were adult and from
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wild populations. The species samples were sex balanced. The representative species of each
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genus are equally sampled, except in the case of Pan where specimens of Pan paniscus were
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unavailable for study.
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Measurements of fossil hominin postcanine teeth were obtained from precision casts in
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the collections at The George Washington University and the University of Arkansas, with the
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balance taken from the literature. All specimens were from individuals with erupted M3s, but sex
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was not controlled. The representative species of each genus are equally sampled
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Only individuals with complete M1-M3 or P4-M2 series were analyzed. Specimens with
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occlusal wear that masked the identification of individual cusps, or with interproximal wear that
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affected >20% of the occlusal margin, were not included in the extant sample. For teeth with
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moderate interstitial wear, the worn margin was reconstructed by approximating the curvature of
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the margin from overall crown shape (Wood and Uytterschaut, 1987; Bailey and Lynch, 2005).
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Specimens were photographed using a Canon Digital Rebel XT camera fitted with a 60
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mm macro lens. A scale was set and leveled in the occlusal plane of the teeth, and levels on the
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camera and photography stand were used to make sure that the occlusal plane was parallel to the
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lens of the camera. Maximum mesiodistal and buccolingual diameters for each postcanine tooth
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were obtained via scaled measurements in TPSDig (Figure S1; Rohlf, 2009), and occlusal areas
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were computed by multiplying these diameters (Kavanagh et al., 2007; Polly, 2007; Wilson et
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al., 2012; Halliday and Goswami, 2013). Mesiodistal and buccolingual diameters for all extant
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primate and fossil hominin specimens are available at
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http://dx.doi.org/10.6084/m9.figshare.1181983.
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To investigate intra-observer error, 45 individuals (i.e., c. 20 % of the extant sample)
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were drawn from among all of the extant taxa in the study and re-measured two months after the
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initial set of measurements. Intra-observer error for linear measurements was ±0.4 mm.
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3. Analysis
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Two different postcanine cascades, the standard M1-M3 and the P4-M2, were tested
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against the murine inhibitory cascade model. We used two inter-tooth ratios for each analysis,
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M2:M1 and M3:M1 for the molar cascade and M1:P4 and M2:P4 for the premolar-molar cascade.
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Reduced major axis regression (RMA) was used to examine the nature of any
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correlations between relative occlusal areas. There are reservations about the use of RMAs for
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anything other than the ratios of the standard deviations of y on x (Smith, 2009), but RMA is
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used in the inhibitory cascade model because a single line defines the ratio between x and y (i.e.,
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the relationship of the data is symmetrical). Data were considered to falsify the predictions of the
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inhibitory cascade model when the 95% confidence interval of the slope does not include 2.00.
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Because RMA regressions have the tendency to drive small sample sizes toward a slope of 1, the
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use of the RMA makes it more likely that the prediction that groups will fall within the
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boundaries of the inhibitory cascade model will be falsified.
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RMA regressions were performed in software developed in the C programming language
with standard linear regression error estimates (Bohonak, 2004). Data were bootstrapped 1000
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times and the resulting regression compared to the predictions of the murine inhibitory cascade.
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Even when the significance values for r2 were low, regressions with confidence intervals that
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included the 2.0 slope and -1.0 intercept predicted by the inhibitory cascade model were
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determined “validated” as is prior practice (Renvoise et al., 2009; Wilson et al., 2012; Halliday
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and Goswami, 2013).
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Means and standard deviations of the occlusal areas of each postcanine tooth, P4-M3, are
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reported for the extant genera in Table S2. The individual measurements from each fossil tooth
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are given in Table S3. Results of a MANOVA conducted in R indicated that the ratios of
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occlusal areas for all taxa are significantly distinct from one another (Table S4). A Pillai trace
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was applied to protect against Type I errors for small samples. Small samples were of a
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particular concern for the interpretation of the slopes of P. boisei and P. robustus, and Student’s
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t-test was employed to test whether the slopes of the regression lines for the relative molar sizes
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of P. boisei and P. robustus were statistically different (Table S5).
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Results
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1. RMA regressions
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In most extant primates, RMA regressions of the molar ratios at both the species and
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genus levels have 95% confidence intervals that include the slope and intercept predicted by the
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murine inhibitory cascade (Table 1). Thus, based on the results of this analysis, the inhibitory
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cascade model can be generally applied to the extant primates included in this study. The
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exceptions among extant primates include Cercopithecus, which is not validated by the model at
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either the species or genus level, and Papio ursinus, which unlike its congeners does not fit the
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model. All other extant congeners share similar fits to the inhibitory cascade.
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Among the fossil hominin genera, the molar ratios of Australopithecus and Homo
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conform to the predictions of the murine inhibitory cascade model at the species level. At the
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genus level, the relationship between the occlusal areas of the molars of Homo can be described
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by the intercept of the inhibitory cascade but not by its slope. The maximum confidence interval
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of the slope of Homo in this study is 1.96 as opposed to the 2.00 dictated by the parameters of the
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inhibitory cascade, which may relate to the variation observed in the relative occlusal areas of H.
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habilis sensu lato. Within the genus Paranthropus, the congeners P. robustus and P. boisei differ
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notably. While the relative occlusal areas of P. robustus are well described by the inhibitory
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cascade, neither the intercept nor slope of P. boisei fit the model.
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There is no evidence of a consistent pattern for the premolar-molar cascade among extant
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or fossil genera (Table 2). Among the extant primates, the molarized premolars of Cercocebus fit
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the proposed premolar-molar cascade, but the proposed premolar-molar cascade also fits some
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taxa with no evidence of molarization (e.g., Cercopithecus mitis and Hylobates albibarbis).
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Within Paranthropus, both P. robustus and P. boisei are considered to have molarized
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premolars, but only P. robustus fits the proposed premolar-molar cascade.
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2. Regression plots
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The results of the RMA are summarized in linear regression plots of the molar cascade
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and the proposed premolar-molar cascade. The proportions of the molar occlusal areas of extant
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primates are weakly correlated (r2 = 0.55). The cercopithecoids in the extant sample conform to
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the slope of murine inhibitory cascade model more closely than the hominoids (Figure 2).
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Hominoids, including fossil hominins, have similarly-sized M2s and M3s compared to
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cercopithecoids (Figure 3). That is, most hominoids are described by the occlusal relative size
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order, M1<M2≈M3.
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The regression of molar sizes in P. boisei differs from that of its congener P. robustus
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(Figure 4). Whereas P. robustus shares the M1<M2<M3 pattern seen in the majority of primates
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in this study, P. boisei is unusual because of the relative sizes of its M2s and M3s, which are
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much larger than predicted from the occlusal area of M1. The area of the M2 is especially large
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given the size of the M1.
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If we accept a working hypothesis that P4 development influences the size of the M1 and
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M2, we can report a few patterns from an examination of premolar-molar ratios. The premolar-
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molar ratios of extant primates are very weakly correlated (r2 = 0.27). Catarrhine primates have a
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P4-M2 relative size sequence (P4<M1<M2) that resembles that for M1-M3. At the level of the
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superfamily, cercopithecoids tend to have premolar-molar proportions above the trajectory
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predicted on the basis of the molars (Figure 5), whereas extant hominoids consistently fall below
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this trajectory. This is because, when P4 crown size is normalized, cercopithecoids tend to have
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larger M2s than hominoids. Among the fossil hominins, although Au. africanus, H. habilis s.l., H.
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erectus s.l., and P. robustus resemble extant hominoids (Figures 6 and 7), most P. boisei
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specimens tend to follow the cercopithecoid pattern.
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Discussion
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1. Molar cascade
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The murine inhibitory cascade predicts the relative occlusal areas of extant primate
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molars, and we suggest that it is the plesiomorphic condition for catarrhine primates. The
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catarrhines are broadly described by a molar row in which the relative occlusal areas increase in
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size. Hominoids tend to have more similarly-sized M2s and M3s than cercopithecoids. Based on
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the murine experiments, this suggest that hominoids have a derived developmental pathway in
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which there is less activation on the posterior molars, more inhibition on the posterior molars, or
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some combination of these effects. The M1<M2≈M3 pattern may relate to the timing of the
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emergence of the M1, which occurs later in Pan than in cercopithecoids (Kelley and Smith,
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2003). Late emergence of the M1 may delay the initiation of posterior molars and subsequently
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affect the final size of posterior molars. If late emergence of the M1 is the plesiomorphic
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condition of hominoids, this would account for the reduced M3s described in several hominoid
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lineages (Nanda, 1954; Garn, 1962, 1963; Garn et al., 1964; Frisch, 1967, 1973; Lavelle, 1970;
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Lavelle and Moore, 1973; Mahler, 1973; Kinzey, 1984; Plavcan and Gomez, 1993; Smith, 1994;
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Swindler, 1998; Dean and Lucas, 2009). This condition may also be the precursor to the much
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delayed emergence of the M1 in H. erectus s.l. and later Homo (Dean et al., 2001).
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Our null hypothesis, which is that closely-related taxa will share the same inhibitory
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cascade, is supported by the observation that in all but one extant primate genera, congeners
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share the same inhibitory cascade. The exception, Papio, has a complex evolutionary history
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featuring substantial introgression (Keller et al., 2010; Jolly et al., 2011) and paraphyletic species
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(Zinner et al., 2009). Rather than divisions along traditionally recognized species lines,
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mitochondrial DNA studies have detected a major division between Papio groups in East and
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southern Africa (Newman et al., 2004; Zinner et al., 2009). This division is also found in this
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study, with specimens of Papio from East Africa (Papio anubis and Papio cynocephalus) sharing
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the same inhibitory cascade, while the southern African group (Papio ursinus) did not.
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The results from the analysis of extant primates provide a comparative context for
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interpreting the relationships between fossil hominins. Paranthropus robustus shares the
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plesiomorphic condition of extant primates, in which M3 is predictably the largest tooth in the
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molar series. Conversely, P. boisei has much larger M2s than predicted by the occlusal areas of
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the M1 and, as a taxon, has the absolutely and relatively largest M2:M1 ratio in this study. A
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distinct M1<M2>M3 molar size sequence is rare among mammals, requiring both low inhibition
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levels and a premature stop to M3 development (Kavanagh et al., 2007; Polly, 2007; Labonne et
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al., 2012); such genetic constraints may be one of the determinants of the relative size of the M2
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in P. boisei.
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2. Premolar-molar cascade
There was no consistent evidence of a premolar-molar cascade among the primate genera
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and species examined here, even within taxa described by molarized premolars. However, when
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the data are considered at the superfamily level, there is a difference in the P4-M2 relative size
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relationships between cercopithecoids and hominoids. Cercopithecoid taxa tend to fall above the
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predictions of this model, whereas the hominoid taxa tend to fall below this prediction. That is to
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say, for similar M1:P4 occlusal area ratios, cercopithecoids tend to have larger M2s than
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hominoids. This is consistent with the results of the molar cascade, which suggests that
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hominoids have reduced M3s compared to cercopithecoids. Rather than assume that the
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principles of the molar cascade can be applied to premolars and molars without any
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modification, experimental work using mouse mutants with artificially induced premolars
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(Peterkova et al., 2005; Klein et al., 2006; D’Souza et al., 2007) could help develop a model
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specific to the P4-M2 sequence. This would also help researchers better understand the factors
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that contribute to premolar molarization.
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6. CONCLUSION
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This study is an example of how models derived from the principles of evolutionary
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development can help improve our understanding of macroevolutionary trends. By determining
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how postcanine crown area may be influenced by an inhibitory cascade, it is possible to evaluate
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dependent relationships between dental morphologies that may otherwise appear as independent
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traits. Thus, on the basis of the inhibitory cascade, the taxa within the fossil hominin genus
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Paranthropus do not share the same molar size relationships. Relative molar size is not
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consistent with the hypothesis of Paranthropus monophyly. This study adds to other
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morphological differences seen in the megadont postcanine dentitions of P. boisei and P.
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robustus (Wood, 1988; Suwa et al., 1994, McCollum, 1999) and suggests that it may no longer
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be prudent to assume that postcanine megadontia is a synapomorphy of Paranthropus. If the
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results of the analyses conducted here are confirmed, they affect our understanding of the
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evolutionary significance of postcanine megadontia and premolar molarization. Developmental
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biology continues to illuminate the details of the complex relationships between genotype and
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phenotype, and by doing so it improves our ability to generate more reliable hypotheses about
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early hominin taxonomy and phylogeny.
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7. ACKNOWLEDGEMENTS
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The manuscript was greatly improved by comments from Drs. Patricia Hernandez, Aida Gomez-
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Robles, and Mark Grabowski (George Washington University), Matthew Skinner (University
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College London), Paul Constantino (Marshall University), and two anonymous reviewers. Brian
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Richmond provided comments on an early version of the manuscript. This study was conceived
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while under the supervision of Dr. Jukka Jernvall (University of Helsinki) and benefited from his
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comments. Dr. Peter Ungar (University of Arkansas) provided access to many fossil casts.
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Access to extant species was made possible through Linda Gordon, Darrin Lunde, and Dr.
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Matthew Tocheri (NMNH), Eileen Westwig (AMNH), and Roberto Portela Miguez (BMNH).
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Kristen Ramirez (CUNY) and Christine Foltz assisted with photography. David Otten
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(University of Arkansas), Michael Frick, Teresa Girolamo, and David Cobey provided
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hospitality during museum visits. Funding for this research was provided by the NSF-IGERT
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DGE-0801634, an NSF-GRF to KS, a Cosmos Club Scholars Award to KS, and a special gift
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from the Council of Scientific Society Presidents to KS. The authors declare no conflict of
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interest.
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Author contributions: KS conceived of the application of the inhibitory cascade to fossil
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hominins, and BW encouraged the application of the model to reinterpreting the relationships
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among Paranthropus taxa. BW assisted with arranging visits to extant and fossil collections. All
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measurements and analyses were performed by KS. The initial manuscript was drafted by KS
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with critical revisions by both authors.
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8. REFERENCES
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9. SUPPLEMENTARY MATERIAL
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There is no supplementary material for this manuscript.
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10. TABLES
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25
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548
549
550
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552
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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