The Functional Significance of Primate Mandibular Form WILLIAM L. HYLANDER Departments of Anatomy and Anthropology, Duke University, Durham, North Carolina 27710

ABSTRACT

A stress analysis of the primate mandible suggests that vertically deep jaws in the molar region are usually an adaptation to counter increased sagittal bending stress about the balancing-side mandibular corpus during unilateral mastication. This increased bending stress about the balancing side is caused by an increase in the amount of balancing-side muscle force. Furthermore, this increased muscle force will also cause an increase in dorsoventral shear stress along the mandibular symphysis. Since increased symphyseal stress can be countered by symphyseal fusion and as increased bending stress can be countered by a deeper jaw, deep jaws and symphyseal fusion are often part of the same functional pattern. In some primates (e.g., Cercocebus albigena),deep jaws are an adaptation to counter bending in the sagittal plane during powerful incisor biting, rather than during unilateral mastication. The stress analysis of the primate mandible also suggests that jaws which are transversely thick in the molar region are an adaptation to counter increased torsion about the long axis of the working-side mandibular corpus during unilateral mastication. Increased torsion of the mandibular corpus can be caused by an increase in masticatory muscle force, an increase in the transverse component of the postcanine bite force and/or an increase in premolar use during mastication. Patterns of masticatory muscle force were estimated for galagos and macaques, demonstrating that the ratio of working-side muscle force t o balancingside muscle force is approximately 1.5:1 in macaques and 3.5:1 in galagos during unilateral isometric molar biting. These data support the hypothesis that mandibular symphyseal fusion is an adaptative response to maximize unilateral molar bite force by utilizing a greater percentage of balancing-side muscle force.

Patterns of in vivo bone strain in the mandibular corpus were recently determined in both Galago crassicaudatus and Macaca fascicularis (Hylander, '79). The strain patterns observed in these experiments were used to infer probable forces acting along the mandible and the patterns of internal stress in the galago and macaque mandible during the power and opening strokes of mastication and ingestion, as well as during isometric biting on molars and incisors. Although inferred patterns of stress varied during these behaviors, only stress patterns associated with the power stroke of mastication and ingestion will be summarized here. During the power stroke of mastication, the balancing side of the mandibular corpus is primarily bent in the sagittal plane. This bending results in compressive J. MORPH. (1979)160: 223-240.

bending stress along the lower border of the corpus and tensile bending stress along the alveolar process. On the working side, the corpus is primarily twisted about its long axis. The masticatory muscle force on the working side twists the corpus so that its lower border everts and the alveolar process inverts. This twisting is partially countered by the resultant masticatory bite force which tends to twist the working-side corpus in the opposite direction, i.e., this force will invert the lower border and evert the alveolar process. Mandibular twisting is also countered in the symphyI This investigation was supported by NIH Research Career De velopment Award DE 00027, NIH Research Grant DE 4531 and NSF Research Grant BNS76 11924 2Bone strain was determined along the lateral surface of the mandibular corpus between the Pm, and M, in galagos and the Pm, and M, in macaques

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WILLIAM L. HYLANDER

tends to evert the lower border of the corpus and invert the alveolar process. The above stress patterns are illustrated in figure 1. In this paper, a functional analysis of primate mandibular morphology is presented on the basis of the results of the above summarized experiments. In particular the following specific morphological problems will be considered: (1) What is the general relationship between mandibular corpus morphology and patterns of stress? (2) Why do anthropoids generally tend to have deeper mandibles than extant prosimians? (3) What is the functional significance of the fused mandibular symphysis in primates? (4) Why do colobines have deeper mandibles than cercopithecines? (5) What is the functional significance of the cercopithecine mandibular fossa? (6) Why do robust australopithecines have vertically deep and transversely thick mandibular corpora?

Fig. 1 Stress patterns in the primate mandible during unilateral mastication. F, and F, are t h e condylar reaction and the resultant muscle forces on the balancing side, respectively. Fbal is t h e force transmitted through the symphysis from the balancing to the working side. T and C indicate the location of tensile stress and compressive stress, respectively. During the power stroke, t h e mandibular corpus on the balancing side (above) is primarily bent (also slightly twisted) in the sagittal plane, resulting in tensile stress along the alveolar process and compressive stress along the lower border of the mandible. On the working side (below), the corpus is primarily twisted about its long axis (also experiences direct shear and is slightly bent). The muscle force on this side tends to evert the lower border of the mandible and invert t h e alveolar process (see curved arrow labeled MI. The twisting moment associated with the bite force has t h e opposite effect (see curved arrow labeled B). That portion of t h e corpus between these two twisting moments experiences maximal twisting stress (see Hylander, '79 for details).

seal region, resulting in tensile stress along the lower border of the symphysis and compressive stress along its upper border. During the power stroke of ingestion, the mandibular corpus on each side is both bent in the sagittal plane and twisted about its long axis. The sagittal bending results in compressive stress along its lower border and tensile stress along the postcanine alveolar process. The twisting

Mandibular corpus morphology and stress patterns Coronal sections of the primate mandible through the region of the second mandibular molar (MJ demonstrate that the mandibular corpus consists of a thick layer of compact bone surrounding a large marrow space (fig. 2). These mandibular sections are somewhat oval-shaped and their vertical dimensions are larger t h a n their transverse dimensions. Within the marrow space run fine and delicate strands of trabecular bone. In addition, the inferior alveolar vessels and nerve lie within the marrow space and are often surrounded by trabecular bone. If the primate mandibular corpus were simply exposed to axial loads and/or simple direct shear stress, the ability of the mandibular corpus to effectively counter these loads would be a function of its bony cross-sectional area. The shape of t h e corpus, i.e., i t s geometric configuration, would have little mechanical significance. However, since the corpus is both bent and twisted, in addition to being directly sheared (Hylander, '791, its shape becomes crucial if the imposed loads are to be countered with a minimum amount of bone tissue. During twisting and bending, the amount of stress in a section of a member is inversely proportional to the polar moment (GI and sec-

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shaped mandibular corpus with its maximum diameter in the vertical direction. As seen in figure 2, sections of the mandibular corpus in both galagos and macaques are roughly oval-shaped and are deeper than they are wide. This, as previously mentioned, is an efficient design for a member that is both twisted about its long axis and bent much more in the sagittal plane than in the transverse plane. Furthermore, this analysis suggests that vertically deep mandibular corpora are able to resist relatively large bending moments in the sagittal plane. In addition, it suggests that mandibular corpora which are both transversely thick and vertically deep are able to resist relatively large twisting moments about their long axes and relatively large bending moments in the sagittal plane. Moreover, mandibular corpora which are thick relative to their vertical depth are able to resist relatively large twisting moments about their long axes. Functional implications of these various mandibular morphologies will be considered in greater detail below. Symphyseal fusion and patterns of masticatory muscle force in Galago crassicaudatus and Macaca fascicularis Fig. 2 Coronal sections through the mandibular corpus in the M1 region of Galago crassicaudatus (left) and It has recently been shown that the most Macaca rnulatta (right). The lingual surface faces to the striking difference in the patterns of mandibleft in each section. Indicated scale is 5 mm. ular bone strain between macaques and galagos is that galagos have much more workond moment (I) of inertia, respectively. If the ing-side bone strain relative to balancing-side primate mandibular corpus were solid bone, bone strain during the power stroke of mastivalues of G and I could be increased without cation and unilateral transducer biting. These adding any additional bone tissue by simply data suggest that compared to macaques, removing bone from the low-stress region a t galagos employ a larger amount of workingthe center of the sections and redepositing side muscle force relative to balancing-side bone along the high stress peripheral areas.3 muscle force during unilateral biting and "he mandible is, in fact, built like this, utiliz- mastication. Furthermore, since galagos have ing bone much more economically than would an unfused symphysis and macaques have a fused symphysis, these data support the hya solid rod of similar strength. In general, the mechanical attributes of the pothesis that a fused symphysis among primandible will vary with its shape. For exam- mates is an adaptation t o maximize molar bite ple, a round hollow mandibular corpus is ideal force by allowing larger amounts of balancingfor countering pure torsion. It is also efficient side muscle force to be recruited during unifor resisting equal amounts of bending in the lateral biting and mastication (Hylander, sagittal and transverse planes. However, since '75a; Beecher, '77a). However, there is no transverse bending loads during mastication satisfactory explanation as to why some priand ingestion are small relative to sagittal mates maintain an unfused mandibular s y m bending loads (Hylander, '791, a more efficient physis. Perhaps the retention of an unfused design to withstand simultaneous torsion and symphysis is somehow importantly related to sagittal bending during the power stroke as 3There are mechanical limits, however, as to how thin the outer well as lesser amounts of transverse bending cortical bone may become before buckling becomes a problem (Wainduring the opening stroke is a hollow oval- wright et al., '76).

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WILLIAM L. HYLANDER TABLE 1

Approximate aoerage muscle and reaction force values in the vertical direction for galagos and macaques during 5 kg unilateral bite ~

Experiment

Macaque 2 Experiment 10 M , work-M, bal Macaque 3 Experiment 6 M, work-M, bal Macaque 3 Experiment 11 M, work-M, bal Galago I Pm,-M, work Pm,-MI bal Galago 4 M, work-M, bal PM2 work-PM, bal Galago 5 M, work-MIbal

~~

Force transmitted through symphysis from balancing to working side

Resultant balancingside muscle force

Balancingside TMJ reaction force

Resultant working side muscle force

Workingside TMJ reaction force

Ratio of working to balancing-side muscle force (probable range p < 0.051

1.5

3.9

2.4

5.1

1.6

1.3 (1.2-1.4)

1.3

3.4

2.1

5.2

1.5

1.6 (1.3-1.9)

1.4

3.7

2.3

4.9

1.3

1.3 (1.2-1.4)

0.7

2.0

1.3

7.1

2.8

3.6 (3.5-3.7)

0.7 1.2

1.9 3.3

1.2 2.1

6.7 8.1

2.4 4.3

3.5 (3.2-3.8) 2.5 (2.3-2.7)

0.8

1.9

1.1

6.7

2.5

3.5 (3.2-3.8)

Note All values are in kilograms. See footnote 4.

allowing certain types of occlusal contacts which would be impossible with a rigidly fused symphysis. Although bone strain data suggest that the ratio of working-side muscle force to balancing-side muscle force differs between macaques and galagos (Hylander, ’791,these data do not directly indicate the ratio of the values. However, first-approximation of these ratios can be calculated since some of the above data were derived from single-element strain gages which were aligned and positioned adjacent to and parallel to the lower border of the mandible. In the experiments in question, mandibular bone strain was recorded from both the working and balancing sides in galagos and macaques during unilateral transducer biting. These gages primarily sensed strain due to sagittal bending of the jaws, since both transverse bending and simple axial loading of the mandibular corpus are probably minimal during unilateral biting (Hylander, ’77a). Strain associated with both torsion about the long axis of the corpus and simple shear perpendicular to its long axis would not be sensed by these gages because of their alignment. Using data derived from the regression analysis of the bone strain and bite force values (table 7 in Hylander, ’791, the relative muscle (and condylar reaction) forces were estimated (see APPENDIX I for details.)

The results of this analysis are presented in table 1.These data demonstrate that the ratio of the estimated average working-side muscle force relative t o the estimated average balancing-side muscle force during isometric molar biting is about 1.5:l in macaques and about 3.5:1 in gala go^.^ There is no overlap in probable ratio values between macaques and galagos a t the 95% confidence interval. This analysis supports the conclusion that galagos probably use a larger amount of working-side muscle force relative to balancing-side muscle during unilateral biting than do macaques (Hylander, ’77a, ’79). This analysis is also supported by patterns of in vivo bone strain in the zygomatic arch of Macaca fascicularis, which suggest t h a t the ratio of working-side masseter force to balancing-side masseter force is between 1 . O : l to 1.5:l during isometric biting (Hylander, unpublished data). The data in table 1 also demonstrate that ‘ A wooden model of t h e mandible was constructed and known amounts of simulated muscle force were applied. Simulated condylar and bite reaction forces were then measured. In addition, a single-element strain gage was attached along the lower border of t h e wooden mandible and bending strain was recorded during loading. Using t h e procedure outlined in APPENDIX I, the ratio of t h e working-side “muscle” force to the balancing-aide “muscle” force was determined from t h e geometry of the model and the recorded strain and bite force data. The following results were obtained: (1) Actual workinghalancing ratio, 6: 1; calculated ratio, 7.7:l; (21 Actual 4 : l ; calculated 4.3:l; (3) Actual 3:l; calculated 3.0:l; (4) Actual 2 : l ; calculated 1.S:l; (51 Actual 1.5:l; calculated 1.3:l; and ( 6 ) Actual 1 : l : calculated 0.9:l.

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the ratio of working-side condylar reaction force relative to balancing-side condylar reaction force during unilateral biting differs between galagos and macaques. In the lateral projection, galagos are estimated to have more condylar reaction force on the working side, while macaques have more condylar reaction force on the balancing side. This analysis is supported by in vivo subcondylar bone strain patterns in Macaca fascicularis and Macaca mulatta which demonstrate that macaques do have more condylar reaction force on the balancing side than on the working side during mastication and unilateral isometric biting (Hylander and Bays, '79).

Anthropoid and prosimian mandibular morphology In addition to differences in symphyseal morphology, anthropoid and extant prosimians differ in the vertical dimensions of the mandibular corpus (fig. 3). Relative to jaw length, anthropoids have a deeper jaw than extant prosimians, although certain extinct prosimians are similar to anthropoids in that they have deep jaws and fused symphyses (e.g., see Simons, '72; Tattersall, '73; Gingerich, '75). On the basis of the results of the previously summarized stress analysis (Hylander, '79) and judging from the patterns of mandibular bone strain and jaw muscle activity in macaques and galagos, the relatively deep anthropoid jaw probably serves to counter increased sagittal bending moments during the power stroke of mastication and/or incisal biting. If a primate mandible is subjected to large bending moments that cause it to bend in the sagittal plane, these moments can be countered by increasing either the transverse thickness or vertical depth of the body of the mandible. Either dimensional expansion would increase its second moment of inertia (I), assuming that there has not been a reduction in the original amount of cortical bone. The value of I for a mandible that is being bent in the sagittal plane is directly proportional to a b , where a is the vertical depth of the jaw, and b is its transverse thickness. Since the amount of maximal bending stress in an oval beam is inversely proportional to a% (the section modulus; Alexander, '681,it would be more economical to counter mandibular bending in the sagittal plane by increasing the vertical dimensions ( a ) , rather than

Fig. 3 Lateral view of the mandible of Galago crassicaudatus (above) and Sairniri sciureus (below). Indicated scale is 5 mm.

the transverse dimensions ( b ) (Hylander, '72, '77b). Both fusion of the symphysis and increments in the vertical dimensions of the jaws among anthropoids might be adaptations to counter internal stresses in the mandible due to increasing amounts of balancing-side muscle force during powerful unilateral biting or mastication. The relationship between symphyseal morphology, patterns of stress, and muscle activity has already been discussed and need not be repeated here (Hylander, '75a, '77b, '79; Beecher, '77a). Bone strain data also support the hypothesis that the body of the mandible is bent (and twisted) during incisor biting (Hylander, '791, as well as during mastication. Among most living prosimians (with the exception of Daubentonia and the indriids), it is inferred that the mandibular corpus is probably not powerfully bent during biting along the anterior dentition since their anterior teeth, which are either absent or are quite gracile and not firmly rooted, are poorly adapted to withstand powerful axial and bending stresses (Kay and Hylander, '78). On the other hand, certain anthropoids have stout firmly-rooted, large crowned incisors (Hylander, '75b) that are often used to tear open large tough fruits. Therefore, possibly the increased jaw depth of some anthropoids might be an adaptation to

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WILLIAM L. HYLANDER

counter large bending moments during incisal biting. In general, however, primates with the relatively deepest jaws (colobines, howlers, geladas, siamangs, etc.) tend to be more folivorous, suggesting that deep jaws are usually related t o powerful unilateral mastication. In summary, anthropoids have relatively deep jaws and a fused symphysis, while living prosimians have shallow jaws and an unfused symphysis. Deep jaws and a fused symphysis are probably part of the same functional pattern. Both of these features are probably adaptations to counter internal stress in the mandible due to increased use of balancing-side musculature during unilateral biting. The notion that the deep anthropoid mandible is related to the fact that mthropoids have larger teeth and a more efficient grinding apparatus than prosimians (Avis, '61) is not convincing. Although deep jaws among some primates may also be adaptations to counter sagittal bending during incisal biting, fusion of the symphysis is probably not related to incisal biting (as suggested by Hiiemae and Kay ('73) and Hiiemae ('76)) since most rodents Dau bentonia, Propithecus, and certain phalangeroid marsupials (Petaurus, Dactylopsila and Dactylonax), all of which gnaw with their incisors, retain an unfused mandibular symphysis.

30

I

I

75

dr:

LOG,MZII LENGTH (nml

Fig. 4 A plot of mean values of vertical height dimensions of the mandibular corpus in the M 2 region versus t h e midsagittal distance between a line fitted to the distal contact points of the left and right M2 and the most anterior point on the I , for all female cercopithecoids examined. Colobines (solid circles) generally have relatively large mandibular height dimensions (deep jaws). Three large cercopithecines (open circles) also have relatively deep jaws; i.e., they fall above the regression line. In order of increasing size of the M21, length, they are the following: Cercocebus albigena, Cercocebus torquatus, and Theropithecus gelada. Thirty-one species were examined and each species is represented by from four t o eight individuals.

ing moments in the sagittal plane. Since colobines apparently do not engage in frequent incisal preparation of large tough foods (Hylander, '75b), it seems doubtful that their enlarged mandibular corpus dimensions repColobine and cercopithecine mandibles resent an adaptation to resist powerful bendThere is considerable morphological diver- ing moments during incisal biting. Instead, sity of the mandibular corpus among cer- because colobines are essentially leaf eaters, copithecoids. In this section, the functional their jaws are probably especially designed t o significance of variability in vertical dimen- withstand bending moments during leaf-massions of the mandibular corpus and of the tication. Specifically, the enlarged vertical dimandibular fossa among cercopithecids is con- mensions in colobines are an adaptation t o counter sagittal bending along the balancing sidered. side of the mandible during unilateral mastiDepth of the mandibular corpus cation of leaves. As seen in figure 4, in contrast to most cerLeaf-chewing probably requires larger avercopithecines, colobines have deeper jaws in age biting force than the chewing of most the molar region relative to the length of the fruits (Hylander, "79); however, this gendental arch. The usual "explanation" for these eralization must have numerous exceptions morphological differences is that colobine jaw since there must be considerable variation in morphology is somehow better adapted for the mechanical attributes of fruits and leaves. powerful chewing. If one assumes (1) that the The hypothesis that leaf-chewing generally shape and size of the mandibular corpus in pri- requires larger masticatory muscle force is mates is related primarily to its ability to supported by morphological evidence, which counter masticatory stress and (2) that bones suggests that among primates with unfused in general are designed to incorporate the mandibular symphyses the symphyseal tisminimum amount of structural materials, sues of more folivorous forms are better then it follows that the deep colobine mandi- adapted t o transmit force from the balancing ble is probably an adaptation to counter bend- side of the mandible than are the symphyseal

PRIMATE MANDIBULAR FORM

tissues of more frugivorous forms (Beecher, ’77b). Presumably, the stronger symphysis allows a greater utilization of the balancingside muscle force in order to maximize the amount of the molar bite force. Colobine mandibles, however, probably do not experience excessively large magnitudes of masticatory stress. There is no evidence to suggest that colobines have masticatory muscles that are significantly larger (and by inference more powerful) than the muscles of a comparable-sized cer~opithecine,~ although there is reason to believe that for a given amount of masticatory muscle force, more of t h a t force is converted into usable bite force in colobines. This greater conversion of muscle force into bite force is due to the fact t h a t the resultant masticatory muscle force in colobines is positioned closer to the bite point than it is in cercopithecines. (For example, among colobines the resultant force of the masseter muscle is positioned closer to the tooth row than it is among cercopithecines since the anterior root of the zygoma, from which t h e superficial masseter originates, is positioned above the MI in colobines, rather than above the M2 or M3 as in cercopithecines.) Colobines apparently have optimized bite-force magnitudes a t the expense of a reduction in jaw gape in order to masticate leaves more efficiently. An increase in jaw gape is a n attribute that is advantageous to more frugivorous and/or terrestrial primates since they eat large food objects, which require extensive incisal preparation, and/or because of canine display or canine slashing. Although relative bite-force values may be larger in colobines than in cercopithecines, moment arms associated with masticatory bending moments about the colobine mandibular corpus are smaller since colobine jaws are shorter. Therefore, bending moments along the mandibular corpus of colobines are probably not unusually large relative to cercopithecines. Thus, although the colobine mandible appears to be well designed to resist bending moments in the sagittal plane, there is no convincing evidence t h a t colobine jaws are subjected to excessively large bending moments during mastication. However, there is one factor that is probably of great importance in t h e design of jaws, and this relates to the fatigue strength of bone. Compared to the more frugivorous cercopithecines, colobines probably spend a greater amount of time chewing food. Walker and

229

Murray (’75) found t h a t per unit weight, lettuce was chewed more than apples, and by inference leaves must generally require more chewing cycles than fruits. Although there are no data indicating how many times colobines or other folivorous primates chew each day, Stobbs and Cowper (‘72) determined that dairy cows engaged in as many as 51,000 “bites” per day during grazing and rumination. Since colobines, like dairy cows, must consume many leaves each day in order to satisfy energy demands, they also must load their mandibles an enormous number of times each day. Structural materials like bone fail far below their maximal strength limits when exposed to repetitive cyclical loading (Evans and Lebow, ’57; Lafferty et al., ’77). For example, after human and rhesus cortical bone has been loaded from 100,000 to 200,000 times, it will fail a t stress levels of about 25-30%of its maximal strength (Lafferty et al., ’77). The importance of repetitive cyclical loading for studies of bone morphology is evinced by the in VIVO fatigue fractures which are frequently seen in humans. Among army recruits, foot bones often become fractured (“stress fractures”) simply because of prolonged marching (Morris and Blickenstaff, ’671, demonstrating that bones will fail structurally when exposed to repetitive cyclical loading a t stress magnitudes well within normal or ordinary physiological limits. It seems likely, therefore, that the increased depth of the colobine jaw probably represents an adaptation to counter repetitive bending loads, and is not simply an adaptation to counter powerful bending moments. In addition t o increasing t h e bending strength of the jaw by deepening it, another adaptive response to repetitious bending loads is to remove and replace fatigued bone before structural failure occurs (Enlow, ’77). This mechanism of adaptive remodeling allows an organism to repair constantly its supporting structures throughout life, rather than having initially to build up extremely large bones in order to prevent fatigue failure. There are, of course, finite limits to how fast fatigued bone can be resorbed and replaced with secondary Haversian bone (as indicated by fa5Perhaps there nre important differences in the percentage of vanous muscle fiber types between colobines and cercopithecines For example, since colobines presumably engage in more prolonged penods of mastication than most cercopithecmes, perhaps colobines have a greater percentage or number of fatigue reslstant fibers

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tigue fractures). Therefore, bones must also be designed t o prevent fatigue failure. In summary, it is suggested that the vertically deep colobine jaw is an adaptation to counter bending moments on the balancing side of the jaw during leaf-mastication. This adaptive response IS not necessarily to counter excessively large bending moments. Instead, it is primarily a response to prevent mandibular bone fatigue due to cyclical repetitious bending loads. Geladas and mangabeys also have relatively deep jaws (fig. 4) Gelada jaws are probably not especially adapted to resist bending moments during incisal biting because the diet of geladas consists almost entirely of grasses (Dunbar and Dunbar, '74) which require little incisal preparation before masticating (Jolly, '70). Since these primates eat large amounts of grass, they also presumably load their mandibles more often per unit time than more frugivorous cercopithecines. The enlarged vertical dimensions of geladas' mandibular corpora are, like those of colobines, an adaptation to counter bending moments on the balancingside corpus during mastication. In both cases, this adaptation is primarily a response to prevent fatigue failure of the mandibular bone due t o repeated cyclical bending stress. Unlike colobines and geladas, mangabeys are highly frugivorous (Waser, '77). Field observations show that mangabeys (at least C. albigena) habitually eat large, extremely hard, tough fruits that require extensive amounts of incisal preparation. The skin of these fruits is so hard and tough that other primates ordinarily do not eat them (Haddow, '52; Chalmers, '68) unless they have been opened previously and then discarded by an adult C. albigena (Waser, '77). Mandibular morphology in C. albigena is unusual. The corpus is vertically deep, and there frequently is an unusually deep concavity (the mandibular fossa) along the lateral aspect of the mandibular corpus between the first mandibular premolar (PmJ and the third mandibular molar (MJ. Moreover, the bone at the base of this concavity is often paper-thin (fig. 5). The behavioral data demonstrate that C. albigena engages in vigorous incisor biting and these primates have very large incisors (Hylander, '75b). Furthermore, we can infer that C. albigena rarely engages in powerful mastication since their postcanine teeth are quite small and because most of the

fruits they eat probably require little masticatory preparation before swallowing. The relatively deep jaws of mangabeys are also probably adapted to counter sagittal bending, although these bending moments are generated during incisor biting, rather than during mastication. Since mangabeys bite into food objects which are often quite hard and because the incisal biting forces have relatively long moment arms about the mandibular corpus, the mangabey mandible is probably stressed frequently by very large bending moments. Experimental evidence, however, suggests that the macaque mandible is twisted, as well as bent, during incisal biting (Hylander, '79). This twisting is largely due to the position of the resultant masticatory muscle force along each side of the jaw. Since this force is positioned lateral t o the long axis of each mandibular corpus among macaques, there is a tendency for the lower border of the macaque mandible t o be everted, while the alveolar process is inverted during incisal biting (and during unilateral mastication). However, it seems doubtful that powerful twisting occurs in the mangabey mandible during incisal biting since their mandibular fossa is often unusually deep and extensive, and their mandibular corpus is transversely narrow throughout its length. If there is less twisting of the mangabey jaw during incisal biting, this is probably because the proportions of the masticatory muscles of mangabeys differ from those found in macaques and most other cercopithecines. In most cercopithecines, the temporalis muscle is ordinarily about four to five times larger than the masseter muscle, and the masseter is about twice as large as the medial pterygoid muscle (Schumacher, '61; Cachel, '76). In contrast, the temporalis muscle in mangabeys is only about twice as large as the masseter (Tappan, '67). In addition, the medial pterygoid muscle in mangabeys is relatively large; the belly of this muscle is even thicker and more fleshly than the masseter muscle (Hill, '74). Thus, among mangabeys the temporalis muscle is relatively small and the medial pterygoid muscle is relatively large. These data suggest that the resultant masticatory muscle force during the power stroke of mastication and ingestion among mangabeys is not positioned as far laterally from the long axis of the mandibular corpus as it is in most other

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and the extent of the mandibular fossa are not closely correlated, contrary to Freedman's statement. In addition, Murray ('73) noted that the pouch itself is not located opposite t h e mandibular fossa in Papio or Theropithecus. In addition, the presence of a well developed mandibular fossa in cercopithecines does not correlate with the presence of a large cheek pouch. For example, macaques and guenons have relatively larger cheek pouches than do baboons or geladas (Murray, '751, yet they do not have mandibular fossae. Furthermore, although geladas have well developed mandibular fossae, their cheek pouches are small and very poorly developed. In a t least one instance, the mandible of a n adult gelada had well developed fossae but its cheek pouches were absent (Murray, personal communication). In summary, comparative anatomical data do not demonstrate a close correlation between size and extent of t h e mandibular fossa and buccal cheek pouches among cercopithecines. These data, therefore, do not support the hypothesis that the cercopithecine mandibular fossa is funcThe cercopithecine mandibular fossa tionally related to buccal cheek pouches. The presence, depth and extent of mandibuIf cercopithecine mandibular fossae are not lar fossae are variable among cercopithecines functionally related to buccal cheek pouches, (fig. 5). Although mandibular fossae are ab- then what is the functional significance of sent or barely detectable (slight depression) these fossae? In vivo bone strain data demonamong species of Macaca, Cercopithecus, Mio- strate that the area of the macaque mandible, pithecus, Allenopithecus and Erythrocebus, which is homologous to the location of the they are well developed among species of Cer- baboon's mandibular fossa, is strained (and cocebus (particularly some specimens of C. therefore stressed) very little relative to other albigena), Theropithecus, Papio and Mandril- regions of the macaque mandibular corpus lus. Freedman ('57), i n a discussion of mandib- (Hylander, '79). On morphological grounds, ular morphology in baboons, noted that the t h e same region must also be stressed mandibular fossa is located opposite the minimally in Papio, Theropithecus and Cerorifice of the baboon's buccal cheek pouch, and cocebus. It is possible that the mandibular suggested that the mandibular fossa accom- fossa represents an adaptive response to modates t h e cheek pouch when it is distended reduce the amount of bone in an area of dewith food, and that the fossa aids the transfer creased mandibular stress. Decreased stress in of food through the pouch orifice. this area may be due to two factors. First, this There are problems with the notion that the area is not subjected to much bending stress mandibular fossa is functionally related to the because (a) it is located close to the bending cheek pouch orifice or to cheek pouches in gen- axis of neutrality and (b) bending moments eral. Murray ('73, '751, following a detailed about this area are relatively small. Second, dissection of buccal cheek pouch musculature unlike the more posterior portions of the manin cercopithecines, noted that the cheek pouch dibular corpus, this area resists very little tororifice ordinarily extends from the Pm,-M, re- sional stress or direct shear stress during the gion to the M2-M3region. Since the mandibular fossa is usually confined to the region be6 A comparison of the power stroke bone-strain values demontween the Pm, and M, (except in some Cer- strates that the portion of the macaque mandibular corpus which closely corresponds to the location of the baboon and gelada mandibcocebus where it is often much more exten- ular fossa is stressed minimally during mastication and ingestion of sive), the location of the cheek pouch orifice apples (table 8 and fig. 13 in Hylander, '79).

cercopithecines. If so, the mangabey mandibular corpus would be twisted very little about its long axis during the power stroke of ingestion. In conclusion, the extremely deep mandibular fossa and transversely thin mandibular corpus of at least some Cercocebus albigena indicate t h a t the mangabey mandible cannot be subjected to large twisting moments during incisor biting or mastication. It is inferred that the jaws of C. albigena are especially adapted to resist bending in the sagittal plane during powerful incisor biting. Bending moments during incisal biting are countered by the reinforced bar of bone along the inferior border of the mandible and by the thick bone of the alveolar process. The paper-thin bone lining the base of the concavity in the corpus is probably located in a low stress area, and therefore this area need not be filled with bone as i t is in many other Old World monkeys (particularly colobines). It is tempting to view this morphological configuration as a close approximation to the engineer's I-beam.

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power stroke of both mastication and ingestion (Hylander, '79). This explanation does not, however, indicate why the mandibular fossa is absent or only barely detectable in colobines and species of Cercopithecus or Macaca. The absence or weak development of the mandibular fossae in colobines may be related to increased mechanical demands of leaf-mastication, e.g., increased emphasis on premolar use during mastication. An increase in premolar use during mastication might be associ-

ated with an increase in premolar bite force which would increase both twisting moments about the long axis of the corpus and direct shear stress about the premolar portion of the mandibular corpus. The increased stresses could be effectively countered by a transversely thicker mandible in the premolar region, resulting in the absence of a well developed mandibular fossa. However, there is no evidence to suggest that the premolar crowns of colobines are larger than those of cercopithe-

Fig. 5 Photographs of the lateral view of the mandible: (A) Cercocebus albigena, male (USNM#452500),

(B) Cercopithecus mitis, male (AMNH#36386), (C)Theropithecus gelada, male (AMNH#60568), (D) Colobus angolensis, female (AMNH#52169), (E) Papio cynocephalus, male (AMNH#27702), and (F) Presbytis johni, male (AMNH#54760). A well developed mandibular fossa is present in A, C, and E. A weakly developed fossa is present in F and the fossa is absent in B and D. Indicated scale is 10 mm.

PRIMATE MANDIBULAR FORM

cines. Therefore, the wear potential of these teeth is not greater, implying that colobines are not necessarily engaging in greater use of the premolar tooth during mastication. Colobine molar size, however, is also not greater than the molar size among cercopithecines (Goldstein et al., '78; Hylander, unpublished data), implying that an increase in wear potential is not always associated with increased mastication. One fact which suggests that larger forces are acting on the colobine premolars is that their premolar roots are relatively larger than the premolar roots of cercopithecines. Therefore, perhaps colobine premolars are better adapted to resist increased biting forces. Ward ('78 and personal communication) has noted that the premolar roots of colobines are about the same length as are their molar roots, whereas among cercopithecines the premolar roots are shorter than the molar roots. The longer premolar root of colobines presumably has both (1) a larger number of periodontal fibers to anchor the tooth more firmly during mastication, and (2) an increased mechanical advantage to counter larger tipping forces which are applied to the teeth during mastication. The absence of a mandibular fossa in colobines might also be related (at least partially) to their smaller vertical jaw dimensions in the premolar region. Although colobines have a deep mandibular corpus in the M2 region (fig. 51, the depth of their mandibular corpus usually decreases rostrally towards the premolar region. Conversely, cercopithecine jaws usually increase in depth from the M Zregion rostrally. These differences are related to symphyseal morphology. Whereas colobines have a rather gracile mandibular symphysis, cercopithecines have a deep robust mandibular symphysis. Perhaps, colobines lack a mandibular fossa primarily because the more rostral portion of their mandibular corpus is shallow and therefore there is not a large unstressed central portion of the mandibular corpus below the premolars. Without a large relatively unstressed region in the colobine mandible, it is unlikely that a fossa would develop. This does not explain, however, why some cercopithecines do not have a mandibular fossa, particularly some of the larger species of macaques. Available anatomical facts do not indicate t h a t the central portion of the mandibular corpus below the premolars is stressed (i.e., twisted or directly sheared) more in macaques than it is in baboons.

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Robust australopithecine morphology

Compared to most other primates, robust australopithecine teeth and jaws are unique in having (1) relatively small, vertically implanted incisors and canines, (2) large molars and premolars with both thick enamel and flattened occlusal surfaces (Robinson, '561, and (3) a mandibular corpus that is both unusually deep and transversely thick in the postcanine region (Howell, '69). These features suggest that the chewing apparatus of these early hominids was especially designed to generate and dissipate large forces during powerful postcanine biting and/or mastication (Robinson, '56; Leakey, '59; Tobias, '67; Crompton and Hiiemae, '69; Jolly, '70; Pilbeam, '72; Wolpoff, '73; Simons, '77; and DuBrul, '77). The purpose of this section is to discuss the functional significance of these enlarged mandibular-corpus dimensions. The following discussion is based on two assumptions. First, the mandible of robust australopithecines was primarily adapted to resist stress generated during the power stroke of unilateral mastication. It is unlikely that the robust australopithecine mandible was adapted to resist stress generated during incisor or canine biting since these teeth are greatly reduced in size, and therefore in functional importance (Jolly, "70). The second assumption is that the australopithecine mandible during the power stroke of mastication was stressed like the mandibles of other primates, i.e., the mandibular corpus on the balancing side was primarily bent in the sagittal plane, while on the working side it was primarily twisted about its long axis and directly sheared perpendicular to i t s long axis (Hylander, '79). As previously discussed, the most efficient response to counter internal stress in the mandibular corpus due to an increase in sagittal bending loads is to deepen the corpus in the vertical direction. The most efficient response to counter an increase in twisting loads about the long axis of the mandibular corpus is to increase its transverse thickness. In order to withstand increased direct shearing loads, the cross-sectional area of mandibular corpus cortical bone need only be increased. Based on the above, i t follows that the robust australopithecine mandibular corpus was well able to withstand the above bending, twisting and shearing stress. In a previous section, i t was argued that the

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WILLIAM L. HYLANDER

deep mandibular corpus of colobines serves to counter bending moments acting on the balancing side of the jaw during unilateral mastication. However, unlike robust australopithecines, the colobine mandibular corpus does not have unusually large transverse dimensions, indicating that the colobine jaw is not especially designed to resist powerful twistingmoments. Why then should deep jaws among colobines and both deep and thick jaws among robust australopithecines both be adaptations to withstand increased stress due to vigorous unilateral mastication? Or, put another way, why would only the australopithecine mandibular corpus be subjected to increased twisting moments during unilateral mastication? There are a t least three possible reasons why the working side of the australopithecine mandible might have been subjected to unusually large twisting moments. These reasons are related to (1) differential activity, position, or enlargement of the muscles of mastication, (2) a large transverse component to the direction of the postcanine bite force, and (3) increased emphasis on premolar mastication. Whereas the masseter and temporalis muscles have a tendency to evert the lower border of the mandibular corpus and invert the alveolar process during mastication, the medial pterygoid muscles have the opposite effect. Therefore, if robust australopithecines had a masseter muscle (or an anterior temporalis muscle) which was more active than their medial pterygoid muscle during mastication (relative to the condition among other primates), twisting of the mandibular corpus would have been increased. This possibility is both unlikely and untestable. Robust australopithecines may have had unusually large twisting moments about their mandibular corpus due to the position and the increased relative size of their temporalis and masseter muscles; however, it is difficult to estimate, solely on the basis of the skull, whether their masseter muscles were unusually large relative to their medial pterygoid muscles, although robust australopithecines did apparently have an unusually large anterior temporalis muscle (Tobias, '67). Moreover, their large temporalis muscle caused the zygomatic arch to flare laterally, thereby displacing the masseter muscle laterally and thus possibly increasing the twisting moments about t h e mandibular corpus.

Fig. 6 Section through t h e anthropoid mandibular corpus in the M,-M, region. The point labeled 0 represents the twisting axis of neutrality of the mandibular corpus along the biting side (the exact position of this point is unknown). F, and F2 are two differently directed bite forces. As the bite force becomes more laterally directed (FJ, there is a greater tendency for twisting of the mandibular corpus since t h e twisting moment is increased. The twisting moment equals t h e magnitude of the bite force multiplied by the perpendicular distance between the bite force and the twisting axis of neutrality. This twisting, which in this section results in eversion of the alveolar process and inversion of the lower border of t h e mandible, is countered primarily by a n oppositely directed twisting moment associated with the resultant muscle force. This latter twisting moment causes the lower border of the mandible to evert and the alveolar process t o invert.

The direction of the bite force can also influence twisting of the mandible. For example, if the direction of the postcanine bite force passes through the long axis of the mandibular corpus, this force will not cause the corpus to be twisted about its long axis. On the other hand, if the mandibular bite force passes lateral to the long axis of the mandibular corpus, this force will have a tendency to twist the corpus by everting its alveolar process and inverting its lower border. As seen in figure 6, the larger the transverse component of the bite force, the greater the twisting moment about the mandibular corpus. Among primates, the direction of the bite force during mastication has not been characterized, except for some preliminary data on humans (Graf, '75). A consideration of primate jaw movement data and tooth morphology suggests that there must be a t least a small laterally-directed component of force along the mandibular teeth during puncture-crush-

PRIMATE MANDIBULAR FORM

ingand Phase I1 (Hylander,’79). Although the working-side mandibular teeth are also moved medially during Phase I, as they are during puncture-crushing and Phase I1 (Kay and Hiiemae, ’741, it cannot be routinely assumed that the mandibular bite force has a laterallydirected component during Phase I. This is because the morphology of the postcanine teeth of most primates ordinarily will cause medial movement of the working-side teeth, even if the bite force is wholly vertical. The only exception to this is found among those primates which have flat occlusal surfaces along all their postcanine teeth (such as robust australopithecines). If it is assumed that t h e working-side mandibular teeth also were moved medially during Phase I among robust australopithecines, then there must have been an associated laterally-directed component of force along the mandibular teeth, since the shape of the teeth would not automatically cause t h e jaw to move medially during closure. Thus, the reaction force exerted against the mandibular teeth of robust australopithecines during both puncture-crushing and tooth-tooth contact probably had a substantial lateral component. The larger the lateral component of this force, the greater the tendency to twist the mandibular corpus. In addition to having thick enamel and flat occlusal surfaces, the molars and premolars of robust australopithecines exhibit occlusal morphology and wear facets which suggest that Phase I and Phase I1 movements were nearly continuous and that there was a pronounced accentuation of Phase I1 movements (Kay, personal communication). Moreover, since Phase I1 movements of the mandibular teeth have a large transverse and anterior component (Kay and Hiiemae, ’741, canine reduction in hominids may have been an adaptive response to increase Phase I1 movements because the canines, which extend beyond the occlusal plane, would interfere with an extensive Phase I1 excursion, particularly along the balancing side of the mandible. Reduced canines also would allow a more extensive Phase I transverse excursion to take place, although in this instance it is t h e interference of the working-side canine which would be eliminated. Among australopithecines, the flat biting surfaces of the postcanine teeth and the reduced height of the canines indicate a large potential for medial and anterior movements of the working-side mandibular teeth during

235

tooth-tooth contact. Large transverse and antero-posterior components of the bite force were probably associated with these movements. Due to the large transverse component of the bite force, the mandibular corpus of r o b u s t a u s t r a l o p i t h e c i n e s probably was twisted powerfully. This is in contrast to the condition of most primates, such as colobines, where there is much less potential for such transverse and anterior mandibular movements during tooth-tooth contact because of trenchant steep-cusped cheek teeth andlor elongated canines which extend beyond the occlusal plane. Relatively small transverse components of the bite force and therefore relatively small twisting moments about the mandibular corpus are probably, although not necessarily associated with these lesser horizontal movements. Some of these conclusions have been advanced by Simons (‘77). While pointing out that the lower jaw in the molar region ofAustralopithecus and Ramapithecus is relatively thick compared to living apes, Simons suggests that . . . “Where chewing by chopping and biting mainly exerts vertical forces, grinding includes some nearly horizontal forces” (page 32). Since the dentition of Ramapithecus and Australopithecus clearly emphasized crushing and grinding, Simons suggests that thick jaws in these early hominids were an adaptation to horizontal biting forces. This is essentially in agreement with the analysis presented here, i.e., the transverse component of the bite force increases twisting of the working-side mandibular corpus and the transversely thick jaws are an adaptation to counter this twisting. The premolars of robust australopithecines are both molarized and heavily worn, indicating that there was an increased functional emphasis on the premolar teeth during mastication. The accentuation of the importance of the premolars during mastication also probably resulted in increased twisting of the robust australopithecine mandibular corpus. This is because in contrast to the molars, the premolars of australopithecines (and most other anthropoids) are positioned more lateral relative to the long axis of the mandibular corpus, and therefore there is a larger twisting moment arm associated with the premolar bite force. In summary, the morphology of the robust australopithecine mandible indicates that it was well designed to resist increased bending,

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twisting, and direct shearing loads during unilat era1 mastication. The increased depth of the mandible probably was an adaptive response to counter increased sagittal bending along the balancing side. The large cross-sectional area of the mandibular corpus might have been an adaptive response to counter increased direct shear stress along the working side. More importantly, the thick mandibular corpus was well designed to counter increased twisting along the working side during unilateral mastication. These increased twisting moments were probably due to a large transverse component of the postcanine bite force and increased emphasis of premolar use during powerful mastication. In contrast, although colobines have deep jaws which are also especially designed to resist sagittal bending moments, their jaws are not usually thick. Because the bite force in colobines is more vertically directed (as inferred from their elongated canines and elevated postcanine tooth cusps), the working side of the colobine mandible is not twisted powerfully during unilateral mastication. The precise contribution of the masticatory muscles to increased mandibular twisting among australopithecines is unclear, although these muscles must have contributed a t least partially to increased twisting since a large transverse component of the bite force can be produced only by differential muscle contraction. Differences between colobines and robust australopithecines in the direction of the postcanine bite force are probably directly a t tributable to the physical properties of their diets. Leaves are more easily reduced in size by shearing than by crushing and grinding because of their two-dimensional n a t u r e (Walker and Murray, '75). Particle size reduction among colobines is achieved by emphasizing the amount of vertical shear (Walker and Murray, '751, which presumably necessitates an increase in the vertical component of the bite force. On the other hand, the morphology of the robust australopithecine dentition suggests that i t was designed especially to reduce food particle size by crushing and grinding, rather than vertical shear. For powerful crushing, the vertical component to the bite force would be emphasized. For powerful grinding, both the vertical and horizontal components would be emphasized. The role of fatigue failure, i.e., whether the australopithecine mandible was subjected to an unusually large number of stress cycles per day cannot

be determined accurately as the feeding behavior of these early hominids is unknown. Jolly ('701, however, has argued convincingly that these early hominids were well adapted to chewing small hard food objects which required little incisal preparation; seeds, roots, and bones are all possible items eaten routinely by these hominids (Jolly, '70; Mann, '72; Coursey, '73; Wolpoff, '73). Regardless of the precise nature of the robust australopithecine diet, large postcanine teeth, extensive tooth wear, massive facial buttresses, and enormous masticatory muscles indicate that these hominids must have subjected their jaws to powerful repetitious loads. Therefore, mandibular morphology among these hominids probably reflects a n adaptation to counter large repetitious bending, twisting, and shearing loads during unilateral mastication. ACKNOWLEDGMENTS

I would like to thank Doctors Robert Beecher, Matt Cartmill, Ken Glander, Karen Hiiemae, Richard Kay, Peter Murray, Tim Strickler, and Ms Marianne Bouvier for their help andlor suggestions throughout various phases of this investigation. I would also like to thank the staff of the following institutions for their assistance: The American Museum of Natural History, The Cleveland Museum of Natural History, The Field Museum of Natural History, The U.S. Museum of Natural History, The Duke University Vivarium and The Duke University Center for the Study of Primate Biology and History. LITERATURE CITED Alexander, R. M. 1968 Animal Mechanics. University of Washington Press, Seattle. Avis, V. 1961 The significance of the angle of the mandible: An experimental and comparative study. Am. J. Phys. Anthrop., 19: 55-61. Beecher, R. M. 1977a Function and fusion at the mandibular symphysis. Am. J. Phys. Anthrop., 47: 325-333. 1977h Functional Significance of the Mandihular Symphysis. Ph.D. Thesis, Duke University. Cachel, S . 1976 The Origins of the Anthropoid Grade. Ph.D. Thesis, The University of Chicago. Chalmers, N. R. 1968 Group composition, ecology and daily activities of free living mangaheys in Uganda. Folia primatol., 8: 247-262. Coursey, D. G. 1973 Hominid evolution and hypogeous 8: 634-635. plant foods. Man (NS), Crompton, A. W., and K. M. Hiiemae 1969 How mammalian molar teeth work. Discovery, Yale Peahody Museum, 5: 23-34. DuBrul, E. L. 1977 Early hominid feeding mechanisms. Am. J. Phys. Anthrop., 47: 305-320. Dunbar, R . I. M., and E. P. Dunbar 1974 Ecological relations and niche separation between sympatric terrestrial primates in Ethiopia. Folia primatol., 21: 36-60.

PRIMATE MANDIBULAR FORM Enlow, D. H. 1977 The remodeling of hone. Yearbook of Physical Anthropology 1976, 20: 19-34. Evans, F. G., and M. Lebow 1957 Strength of human compact bone under repetitive loading. J. Appl. Physiol., 10: 127-130. Freedman, L. 1957 The fossil Cercopithecoidea of South Africa. Ann. Transvaal Mus., 23: 121-262. Gingerich, P. D. 1975 A new genus of Adapidae (Mammalia, Primates) from the Late Eocene of Southern France, and its significance for the origin of higher primates. Contrib. Mus. Paleontol. Univ. Mich., 24: 163-170. Goldstein, S., D. Post and D. Melnick 1978 Analysis of Cercopithecoid odontometrics. I. The scaling of the maxillary dentition. Am. J. Phys. Anthrop., 49: 517-532. Graf, H. 1975 Occlusal forces during function. In: Occlusion: Research in Form and Function. N. H. Rowe, ed. The University of Michigan School of Dentistry and the Dental Research Institute, pp. 90-109. Gysi, A. 1921 Studies on t he leverage problem of t he mandible. Dent. Digest, 27: 74-84, 184-190, 203-208. Haddow, A. J. 1952 Field and laboratory studies on an African monkey, Cercopithecus ascani us schmidti Matshie. Proc. Zool. Lond., 122: 297-394. Hiiemae, K. M. 1976 Masticatory movements in primitive mammals. In: Clinical and Physiological Aspects of Mastication. D. J. Anderson and B. Matthews, eds. John Wright and Sons, Ltd., Bristol, England, pp. 105-118. Hiiemae, K. M., and R. F. Kay 1973 Evolutionary trends in the dynamics of primate mastication. In: Symp. Fourth Int. Cong. Primatology, 3. Karger Basel, pp. 28-64. Hill, W. C. 1974 Primates: Comparative Anatomy and Taxonomy, VII, Cynopithecinae. John Wiley and Sons, New York. Howell, F. C. 1969 Remains of Hominidae from Pliocene/ Pleistocene formations in the Lower Om0 Basin, Ethiopia. Nature, 223: 1234-1239. Hylander, W. L. 1972 The Adaptive Significance of Eskimo Craniofacial Morphology. Ph.D. Thesis, University of Chicago. 1975a The human mandible: Lever or link? Am. J. Phys. Anthrop., 43: 227-242. 1975b Incisor size and diet in anthropoids with special reference to Cercopithecidae. Science, 189: 1095-1098. 1977a In vivo bone strain in t he mandible of Galago crassicaudatus. Am. J. Phys. Anthrop., 46: 309-326. 1977b The adaptive significance of Eskimo craniofacial morphology. In: Orofacial Growth and Development. A. A. Dahlberg and T. Graber, eds. Mouton, The Hague, pp. 129-169. 1979 Mandibular function in Galago crasszcaudatus and Macaca fascicularis : An in vivo approach to stress analysis of t h e mandible. J. Morph., 159: 253-296. Hylander, W. L., and R. Bays 1979 An in uiuo strain gauge analysis of temporomandibular joint reaction force during mastication and incision in Macaca mulatta and Macaca fascicularis. Arch. oral Bio., in press. Hylander, W. L., and H. Sicher 1979 Functional anatomy of the temporomandibular joint. In: The Temporomandibular Joint: A Biologic Basis for Clinical Practice. Third ed. B. G . Sarnat and D. Laskin, eds. Charles C Thomas, Springfield, Ill., in press. Jolly, C. J. 1970 The seed-eaters: A new model of hominid differentiation based on a baboon analogy. Man (NS), 5: 5-26. 1973 Changing views of hominid origins. Yearbook of Physical Anthropology 1972,16: 1-17. Kay, R. F., and K. M. Hiiemae 1974 Jaw movement and

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tooth use in Recent and fossil primates. Am. J. Phys. Anthrop., 40: 227-256. Kay, R. F., and W. L. Hylander 1978 The dental structure of mammalian folivores with special reference to primates and phalangeroids (Marsupialia). In: Arboreal Folivores. G. G. Montgomery and J. Eisenberg, eds. Smithsonian Press, Washington, D. C. Lafferty, J. F., W. G. Winter and S. A. Gambaro 1977 Fatigue characteristics of posterior elements of vertebrae. J. Bone Joint Surg., 59A: 154-158. Leakey, L. S. B. 1959 A new fossil skull from Olduvai. Nature, 184: 491-493. Mann, A. 1972 Hominid and cultural origins. Man (NS), 7: 379-386. Morris, J. M., and L. D. Blickenstaff 1967 Fatigue Fractures: A Clinical Study. Charles C Thomas, Springfield, Illinois. Murray, P. 1973 The Anatomy and Adaptive Significance of Cheek Pouches (Bursae Buccales) in Cercopithecinae, Cercopithecoidea. Ph.D. Thesis, University of Chicago. 1975 The role of cheek pouches in cercopithecine monkey adaptive strategy. In: Primate Functional Morphology and Evolution. R. H. Tuttle, ed. Mouton Publishers, The Hague, Paris, pp. 151-194. Pilbeam, D. 1972 The Ascent of Man: An Introduction to Human Evolution. Macmillan Series in Physical Anthropology. The Macmillan Company, New York. Robinson, J. T. 1956 The dentition of the Australopithecinae. Transv. Mus. Mem., No. 9, Transvaal Museum, Pretoria. Schumacher, G. H. 1961 Funktionelle Morphologie der Kaumuskulatur. Gustav Fisher Verlag, Jena. Simons, E. L. 1972 Primate Evolution: An Introduction to Man’s Place in Nature. The Macmillan Series in Physical Anthropology. The Macmillan Company, New York. 1977 Ramapithecus. Scientific American, 236: 28-35. Stobbs, T. H., and L. J. Cowper 1972 Automatic measurement of the jaw movements of dairy cows during grazing and rumination. Trop. Grasslands, 6: 107-112. Tappan, N. 1967 Some relationships between split-line patterns and underlying structure in primate skeletons. In: Progress in Primatology. D. Starck, R. Schneider and H. J. Kuhn, eds. Gustav Fischer Verlag, Stuttgart, pp. 80-89. Tattersall, I. 1973 Cranial anatomy of Archeolemurinae (Lemuroidea, Primates). Anthropol. Pap. Am. Mus. Natl. Hist., 52: 1.110. Tobias, P. V. 1967 Olduvai Gorge. Vol. 2. University Press, Cambridge. Wainwright, S. A., W. D. Biggs, J. D. Currey and J. M. Gosline 1976 Mechanical Design in Organisms. John Wiley and Sons, New York. Walker, P., and P. Murray 1975 An assessment of masticatory efficiency in a series of anthropoid primates with special reference to the Colobinae and Cercopithecinae. In: Primate Functional Morphology and Evolution. R. H. Tuttle, ed. Mouton Publishers, The Hague, Paris, pp. 135-150. Ward, S. 1978 Mandibular alveolar process proportions and dental root angulation in cercopithecoid primates. Am. J. Phys. Anthrop., 48: 446. Waser, P. 1977 Feeding, ranging and group size in the mangabey. In: Primate Ecology. T. H. Clutton-Brock, ed. Academic Press, London, New York and San Francisco, pp. 183-222. Wolpoff, M. H. 1973 Posterior tooth size, bodv size. and diet in South African gracile australopithecines. Am. J. Phys. Anthrop., 39: 373-394.

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APPENDIX I 'The relative muscle and condylar reaction forces in Macaca fascicularis and Galago crassicaudatus, which are presented in table 1, were estimated using previously published data (table 7 in Hylander, '79) in the following manner. The amount of bone strain on the balancing side of the jaw (€ball is equal to the bite force (Fl,ite)multiplied by the balancing-side regression slope value (Pbal) :

'bal = @bal) ( b i t e )

(1)

A similar relationship holds for bone strain on the working ;side of the jaw: (2)

'work

Therefore: (3) Or:

@work) (FBite)

('bal) -('work) -F ~ i =t ~ @ball @work)

('work) @ball = ('ball @work)

The amount of compressive bending strain (c) in the mandibular corpus during sagittal bending is directly proportional to the bending moment (MI and the distance between the portion of the mandible analyzed and the axis of neutrality (y). The amount of bending strain is inversely porportional to the second moment of inertia (I) and the modulus of elasticity (El (see Hylander, '79 for detail^),^ i.e.,

'

z=-

(M) (y) (I) (El

Substituting in equation (3) yields: (4)

(Y)'Pbal) (I) (E)

(Mwork)

=

(MbaI) (Y) @work)-

(I) (El

If it is assumed that the bending axis of neutrality is positioned in about the same place on both working and balancing sides during unilateral biting, then the distance between the axis of neutralit,y and the strain gage (y), the second moment of inertia (I), and the modulus of elasticity (El, do not differ significantly between working and balancing sides. Equation (41, therefore, reduces to (5)

(Mwork) @bal) = (Mbal) @work)

There is only one bending moment acting rostra1 to the gage site on the balancing side of the jaw (fig. 7). This moment (M ba l), which causes the strain gage site to experience compressive bending stress, is equal to the force being transmitted through the symphysis from the balancing side to the working side (Fbal) multiplied by &a], which is the distance between the strain gage and a point defined by the intersection of a line fittedto the long axis

Fig. 7 Lateral view of the working and balancing sides of a primate mandible (above and below, respectively). The large black dot represents the strain gage site. &ite and Xbal are defined in the text. Fc is the condylar reaction force; F, is the muscle force; Fbite is the bite force; Fbal is the internal reaction force that is associated with the transfer of force from the balancing to the working side of the mandible.

of the mandibular corpus and condyle with the midsagittal plane (Gysi, '21). (Mbal) = (Fbal) (Xbal)

There are two bending moments acting rostral to the gage site on the working side (fig. 7). The bending moment associated with the bite force causes the strain gage site to experience compressive bending stress. The bending moment associated with the symphyseal force, which is opposite in direction to the moment associated with the bite force, causes the strain gage site to be bent in the opposite direction (Hylander, '77a). The net bending moment about the gage site on the working 'It is assumed that bone along the gage site is experienclng uniaxial stress. Actually, only the outermost portion of a member experiences uniaxial stress during bending. Nevertheless, for firstlevel approximations of patterns of stress, engmeers often treat analogous situations as experienclng uniaxial stress

PRIMATE MANDIBULAR FORM

239

This method of analyzing working and balancing sides separately is outlined elsewhere (Hylander and Sicher, '79).* For this analysis, the position of the resultant muscle force in both galagos and maMwork = Mbite - Mbal caques was estimated on the basis of anatomiThe bending moment associated with the cal dissection, muscle weight data (Schubite force (Mblte) is equal to the bite force macher, '61; Cachel, '761, and t h e assumption (Fblte)multiplied by the perpendicular dis- that during unilateral isometric molar biting tance between the strain gage and the bite the mandibular elevator muscles on a given force (Xblte). side do not exhibit marked differential activiMbite = (Fhite) (Xbite) ty. It was also assumed that resultant muscle The bending moment associated with the sym- forces and reaction forces were approximately parallel in the lateral projection during uniphyseal force is equal to (Fbal) (&all. lateral molar biting. Resultant muscle force Therefore, and condylar reaction force estimates in table Mwork = (Fbite) (Xhite) - (Fhal) (Xbal) Equation (5) can now be rewritten as follows: 1 are not estimates of total masticatory muscle and total reaction forces. Instead, they are only rough estimates of those forces that cause the galago and macaque mandible to The linear distances Xbite and Xbal were bend in the sagittal plane. There are other measured directly from each individual forces which were not included in this analyradiograph (the rostra1 point for determining sis. For example, in galagos, and possibly also X b a l is approximately located a t the level of in macaques, twisting of the jaws also affects the tip of the lower incisors in macaques and condylar reaction forces (Hylander and Bays, galagos); the slope values P b a l and Pwork were '79). Cinefluorographic studies demonstrate previously determined in the regression anal- that the lower border of the galago mandible ysis (Hylander, "79). Given these values, Fbal everts while the coronoid and alveolar proccan be determined during a given amount of esses invert during the power stroke of mastibite force. For purposes of this analysis, the cation. These movements must cause the latbite force was fixed a t 5 kg for both macaques eral aspect of the galago mandibular condyle and galagos. to be pressed against its articular disc, while After Fhal was determined, moments were its medial aspect probably often lifts off the taken about the balancing-side mandibular articular disc. Furthermore, this condylar condyle in order to solve for the balancing-side reaction force is present even if an analysis of muscle force (fig. 7 ) . Moments were also taken forces acting on the mandible in the lateral about the balancing-side muscle force in order projection indicates that net temporomanto solve for the balancing-side condylar reac- dibular joint (TMJ) reaction forces are absent, tion force. As both the symphyseal and bite i.e., even if the resultant muscle force passes force moments were known, the working-side through the bite point. muscle force was determined by t a k i n g " A s the left and right side of the mandible are firmly united (at moments about the working-side mandibular least in macaques), the method outlined above is only a first-level condyle. In addition, condylar reaction force approximation because the system is actually statically indetermiSince the symphysis of galagos is quite mohile, this method on the working side was determined by taking nate. probably yields a slightly better approximation of mandibular force moments about the working-sidemuscle force. for galagos than for macaques. side (Mwork)is equal to the bending moment associated with the bite force (Mblte) minus the bending moment associated with the symphyseal force (Mbal).