Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
zoolugical Journal o f t h e Linnean Society (1985), 85: 267-274. With 3 figures The generalized carnivore jaw W. S. GREAVES Department of Oral Anatomy, The Universib of Illinois at Chicago, 801 South Paulina Street, Box 6998, Chicago, Illinois 60680, U.S.A. Received June 1984, accepted f o r publication March 1985 A model is presented of the jaw mechanism that relies on the geometrical similarities among mammalian carnivores with carnassial teeth. These similarities, together with estimates of the location of the resultant force of the jaw muscles, allow the model to predict that the mechanical advantage of the jaw lever system is the same in all carnivores with carnassials and, therefore, that the magnitude of the bite force is mainly determined by the absolute amount ofjaw musculature. KEY WORDS:--Carnivora -jaw geometry -jaw lever system - model. CONTENTS Introduction . . . . Methods and assumptions . Analysis . . . . . . . . . Discussion. Conclusion . . . . . . Acknowledgements . . . . References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 268 268 270 274 274 274 INTRODUCTION The forces exerted on the lower jaw by the muscles on both sides of the head can be resolved into a single resultant force for purposes of analysis. During strong biting, the mediolateral location of this resultant force, judging from electromyographic studies, is near the midline of the jaw (cf. Leibman & Kussick, 1965; Gorniak & Gans, 1980). The exact anteroposterior location of the resultant force is difficult to determine and has not yet been measured. Nevertheless, estimates based on muscle attachment sites on wet specimens place it approximately one-third of the way aiong the lower jaw, measured from the jaw joint. These estimates agree with the predictions of two recent models of the jaw mechanism. The first model predicted that this one-third position of the resultant force of the jaw muscles in most mammals would preclude the generation of large torsional forces around the long axis of the jaw ramus (Greaves, 1982). An independent model has demonstrated that in carnivores the largest bite force possible is realized a t the carnassial tooth when the muscle 0024-4082/85/ 110267 + 08 $03.00/0 267 0 1985 ‘The Linnean Society of London 268 W. S. GREAVES resultant force acts one-third of the way along the jaw (Greaves, 1983). This latter model did not determine whether the location of the carnassial or the location of the muscle resultant was of primary importance, only that there was a relationship between the two. However, if the one-third location of the resultant force precludes torsional forces on the horizontal part of the jaw, it is possible that the location of the carnassial tooth is dependent upon the location of the muscle resultant. Nevertheless, different locations for the carnassial tooth are possible for a given position of the resultant force. The purpose of this note is to introduce a geometrical analysis based on the above models that clarifies the relationship between the positions of the tooth and the resultant force. METHODS AND ASSUMPTIONS Recent work suggests that the jaw lever in mammals extends from the working tooth to a point near the jaw joint on the opposite side of the head (e.g. Greaves, 1978; Weijs, 1981; Weijs & Dantuma, 1981). Using monkeys, Hylander (1979) and Hylander & Bays (1979) confirmed the prediction of Greaves (1978: 284) that: “. . . forces at the joint on the working side will be relatively small while the balancing side joint supports most of the system’s reaction forces. . .”. (Statements to the contrary in these papers are apparently due to a misinterpretation of the analysis of a n idealized model as opposed to predictions about real animals from this model.) T h e carnassial tooth in carnivores is an extremely important element of the dentition and the bite force at this tooth will be stressed in this analysis, without suggesting that other teeth are unimportant. This account of the jaw mechanism is highly idealized and merely approximates the situation in any real animal because only an estimate of the anteroposterior location of the muscle resultant force is utilized and only vertical components of muscle force are considered. T h e importance of horizontal components of muscle force is not denied. Small deviations from this generalized description of the jaw mechanism will have little effect on the basic concept. The following analysis assumes that the resultant force of the jaw muscles acts one-third of the way along the jaw and that it acts at this location in most carnivores. The major prediction of the model is that the jaw lever systems in all carnivores with carnassials have essentially the same mechanical advantage. ANALYSIS Figure 1A is a dorsal view of the lower jaw of a cat, representing a generalized carnivore; Fig. 1A and B are separated for clarity. Line AD represents the midline and is perpendicular to the line BDC. These lines have undetermined lengths because the diagram is meant to represent jaws of all lengths and widths. The jaw joints are located near B and C; choosing a specific location for point C determines the location of point B because jaw joints are equidistant from the midline. Lines AB and AC, representing the horizontal rami of the jaw, are not included because they will change with the changing positions of points A, B and C; Fig. 1C is an example of a completed diagram. Point E, which represents the location of the carnassial tooth, will likewise change although it will always lie at approximately the midpoint of the jaw ramus (Gaunt, 1959; Radinsky, T H E GENERALIZED CARNIVORE JAW A B 269 C A E B D C Figure I . Dorsal view ofthe lowerjaw ofa cat, representing a generalized carnivore, see text for details. 1981). Point G is one-third of the way along line AD, and represents the estimated position of the muscle resultant force. For a maximum output force, the jaw joint ( C ) , the carnassial tooth (E), and the muscle resultant force (G) must all lie on the same line. This line (EGC) is the idealized lever of the jaw (Greaves, 1978, 1983). Because the two sides of the jaw are equal, an isosceles triangle can be drawn to represent any carnivore jaw regardless of its length and width. A line can also be drawn from C to E in any of these triangles. Since the carnassial tooth lies at the midpoint of the jaw ramus, the line connecting this tooth to the jaw joint on the opposite side of the head is a median. A median is a line extending from an angle of a triangle to the midpoint of the opposite side. Clearly the midline of the jaw is also a median. One can prove that in any isosceles triangle, the medians intersect each other at a single point and divide each other in the ratio of 1 : 2 (Fig. 1C). Therefore, if the resultant force of the jaw muscles acts at the midline and lies on the jaw lever, it will also be located one-third of the way along line DA. More significantly, the resultant force acting at point G will divide the jaw lever (EC) in the ratio of 1 : 2. The actual location of the carnassial tooth can be observed and the position of the resultant muscle force can be estimated. The major point of this analysis is that it suggests that the mechanical advantage of the jaw lever system (with reference to the carnassial teeth) is the same in all carnivores. T h a t is, the input lever CG is two units in length and the output lever CE is three units long regardless of jaw length or width because this idealized jaw lever is a median (Fig. 1C). The absolute mass of jaw musculature differs among carnivores, and since the mechanical advantage of the jaw mechanism is the same, the absolute amount of musculature is the principal variable determining bite force; changing jaw width or jaw length has no effect because the median, representing the jaw lever, is divided in the ratio of 1 : 2 in all cases (Fig. 1C and inset in Fig. 2). If the influence of muscle architecture is ignored and the absolute amount of jaw musculature is the same, longer jaws have greater potential gape, but maximum bite force remains the same because the mechanical advantage does not change. Equivalent bite points at any position along the jaw (e.g. canine teeth) in any carnivore will also have the same mechanical advantage. 13 W. S. GREAVES 270 s 6ol 80 40 20 - I A+.” ’ I I I I I I I I I , I I , l I / I 1 1 1 1 1 1 1 1 / , 1 1 1 , 1 1 1 1 1 1 I , I 1 1 ) I Greaves ( 1983) demonstrated a relationship between the carnassial tooth and the resultant force of the jaw muscles. However, for any given anteroposterior location of the muscle resultant there are many possible locations for the carnassial tooth as long as this tooth lies on the line that passes through both the resultant position (G) and the balancing joint (C). Extending this line to intersect with the only structural element capable of supporting the tooth, the jaw ramus, uniquely defines the position of the tooth if the position of the muscle resultant force is given. This analysis has therefore clarified the relationship between the carnassial and the resultant but still relies on the idea that the location of the tooth depends upon the muscle resultant position. An earlier analysis also predicted that the output force would act at the midpoint of the jaw where the carnassial is located (Greaves, 1982). Coincidence of an important bite point (the carnassial tooth) and the location of the output force is expected since that insures that the greatest force will act at the location of the tooth. DISCUSSION Since the carnassial teeth are located at the approximate midpoints of the jaw (Radinsky, 1981; cf. Gaunt, 1959), carnivores with the same jaw length (as measured along the midline) have jaw joints, carnassial teeth and canine teeth at the same places along the jaw. This prompts one to ask how the various T H E GENERALIZED CARNIVORE JAW 27 1 taxonomic groups compare with each other in this regard. Figure 2 is a plot of jaw length against jaw width for a sample of carnivore families that possess carnassial teeth. Jaw length and jaw width were measured on the lower jaws or skulls of a sample of recent and fossil carnivores from the Division of Mammals and the Division of Geology, Field Museum of Natural History, and the Department of Oral Anatomy, University of Illinois a t Chicago (Table 1). The specimens included represent all the carnivore families with carnassials. Jaw length was measured along the midline, from the level of the tips of the canine teeth to the level of the joints; jaw width was taken as the distance between the approximate midpoints of the jaw joint surfaces. This plot is meant to demonstrate that (1) there is variation within the carnivores and (2) that the members of the various taxa cluster together. Felids have wider, and canids narrower, jaws for equal jaw lengths. Mustelids (weasels, skunks, otters), viverrids (civets, mongooses), hyaenids and procyonids (Bassariscus astutus, the ring-tailed cat) are the other carnivore families with members which have carnassial teeth. With the exception of the hyaenas, animals in these families are generally small. The reader must clearly understand that these data do not speak to the truth or falsity of the hypothesis presented here. They only present the length-width relationships of carnivore jaws for discussion. Carnivore jaws may be compared by examining animals with equal jaw widths but differing jaw lengths or, conversely, by comparing animals with equal jaw lengths and varying jaw widths (inset, Fig. 2 and Fig. 3 ) . The former comparison is the more common, and illustrates that cats have short jaws relative to those of dogs. Animals with the same jaw width (e.g. bobcat and medium-sized dog) are similar in body size and in the comparable volume of jaw musculature. As the mechanical advantage of the jaw lever system is the same for all carnivores, animals of the same jaw width (and similar absolute muscle masses) can exert similar bite forces. A longer jaw in the dog, providing a greater number of smaller teeth and a potentially larger gape, may be important to canids and of less importance to felids but the maximum bite force is comparable if muscle architecture is ignored. Alternatively, animals with the same jaw lengths may be compared (e.g. medium-sized dog and mountain lion); in this case, the variable jaw widths will reflect differences in the absolute amount of muscle mass. Relative to canids, cats can exert larger bite forces by virtue of a wider jaw and therefore a greater absolute mass of musculature. A cat with the same jaw length as a dog has larger teeth in addition to a larger bite force. Cats have fewer teeth than dogs because large teeth take up more room along a jaw of the same length. Assumed differences in bite force between animals with the same jaw length are based on the absolute amounts of jaw musculature (medium-sized dog compared with mountain lion) because the mechanical advantage of each system is the same. Radinsky (1981) studied the functional aspects of carnivore skulls and jaws in a different way and, to the extent that our studies overlap, his conclusions are in general agreement with the above analysis (i.e. felids and mustelids have the most powerful bites). Radinsky also studied the cross-sectional areas of carnivore jaws and concluded that felid jaws are abIe to resist greater bending and torsional forces than those of canids. This result is consistent with the model and is exactly what one would predict. Considering jaws of equal length, the felid 13* W. S. GREAVES 272 Table 1. Species measured Viverridae Ciuetticus ciuetta Cynictis penicillata Eupleres goudotii Galidea elesans Genetta sp. Herpestes ichneumon Herpestes fuscus Nandinia binotata Prionodon linsang Prionodon pardicolor Viuerra civetta Viuerra tangalunga Viuerra zibetha Viuerricula indica Eusmilus sicarius Felis concolor Felis leo Felis libyca Felis manul Felis marginata Felis onca Felis pardalis Felis pardus Felis rubiginosa Felis syluestris Felis tigris Lynx rufus Smilodon califrnicus Smilodon neogaeus Procyonidae Bassariscus astutus Canidae Aenocyon dirus Alopex lagopus A t e l o p u s microtis Canis adustus Canis aureus Canis latrans Canis lupus Canis mesomelas Canis rufus Canis simensis Cerdocyon thous Chrysoyon brachyurus Cuon alpanus Fennecus Zerda Hesparocyon gregarius Lycalopex uetulus Lycaon rerda Nyctereutes procyonides Speothos uenaticus Urocyon cinereoargenieus Vulpesfulua Vulpes uulpes Mustelidae Aelurocyon breuijacies Aonyx lutra Arctoryx collaris Conepatus rex Eirn barbara Galictis uittata Culo gulo Gulo luscus Ictonyx kalharicus Lutra canadensis Lutra felina Lutra incarum Martes americana Meles mediterraneus Meles meles Melliuora capensis Melliuora sagulata Melogale moschata Mephitis mephitis Mustela frenata Mydaus jauanensis Oligobunis crassivultus Oligobunis darbyi Poecilictis libyca Poecilogale albinucha I’romartes lepidus Pteronura sp. Spilogale putorius Taxidea taxus Vormela peregusna Felidae Acinoryx jubatus Dinictis sp. Dinobastis serus Hyaenodontidae Hyaenodon crucians Hyaenodon horridus Hyaenodon mustelinus Hyaenidae Crocuta crocuta Hyaena brunnea Hyaena hyaena T H E GENERALIZED CARNIVORE JAW 273 I Figurc 3. Dorsal views of the skulls and jaws of: A, the gray fox (Urogon cznereoargenteus); B, the bobcat (Lynx rufus); C, a domestic dog (Canisfamiliaris); and D, the mountain lion (Felis concolor). The jaws of the fox and bobcat are of equal length but the bobcat’s jaws are wider. T h e jaws of the dog and mountain lion are of equal length but the lion’s jaws are wider. The dog and the bobcat have jaws of equal width but the dog’s jaws are longer. jaw must resist larger forces than that of the canid because a greater mass of musculature in the felid exerts larger forces on the jaw. I n some mustelids, the skull posterior to the level of the jaw joint appears to be elongated. However, by comparing mustelids with other carnivores having the same jaw length (e.g. otter with bobcat), this difference is less apparent. The skull appears longer in many mustelids because the skull of a cat or a dog with the same jaw length has a greater height. Speculating in an evolutionary sense, a dog, for example, could increase its bite force in two independent ways. First, by becoming larger, with a concomitant increase in jaw length, the bite force would increase because the absolute amount of jaw musculature would increase. Secondly, the addition of extra jaw musculature alone would increase bite force. However, musculature would have to be added at a limited anteroposterior region, requiring greater skull and jaw width. The dog’s head then would approach the same jaw 274 W. S. GREAVES proportions as a cat with the same jaw length (cf. Rosenzweig, 1966). Presumably, simply becoming larger, in a n evolutionary sense, is more likely than changing skull and jaw width. This may explain in part, the vertical distribution of the various families of carnivores in Fig. 2. CONCLUSION I have presented the hypothesis that the jaw lever systems of carnivores with carnassial teeth are equivalent in that the muscles have the same mechanical advantage regardless ofjaw size or shape; the lengths of input and output levers may vary but the proportions are the same. Therefore, differences in bite force between carnivores are mainly due to the absolute mass of jaw musculature. The location of the carnassial teeth, approximately at the midpoint of jaw length, is dependent upon the geometry of the jaws as well as the location of the resultant of the jaw muscle force. Comparative studies must allow that certain features of the jaw mechanism are equivalent among the carnivores. ACKNOWLEDGEMENTS I thank H. Barghusen, D. Dessem, R. Druzinsky, M . Greaves, K. Gordon, S. Herring, W. H. Meyer and R. Scapino, for comments, suggestions and assistance. The Division of Mammals and the Department of Geology, Field Museum of Natural History kindly made available specimens in their charge. M. L. Greaves drafted the figures. REFERENCES GAUNT, W. A., 1959. The development of the deciduous cheek teeth of the cat. Acta Anatomica, 38: 187-212. GORNIAK, G . C. & GANS, C., 1980. Quantitative assay of electromyograms during mastication i n domestic cats (Felis catus). Journal of Morphology, 163: 253-28 I . GREAVES, W. S., 1978. The jaw lever system in ungulates: a new model. Journal of .Soology, London, 184: 271-285. GREAVES, W. S., 1982. A mechanical limitation on the position of the jaw muscles of mammals: the onethird rule. Journal of Mammalogy, 63: 261-266. GREAVES, W. S., 1983. A functional analysis of carnassial biting. Biological Journal o f t h e Linnean Society, 20: 353-363. HYLANDER, W. L., 1979. An experimental analysis of temporomandibular joint reaction force in macaques. American Journal of Physical Anthropology, 51: 433-456. HYLANDER, W. L. & BAYS, R., 1979. An in uiuo strain-gauge analysis of the squamosal-dentary joint reaction force during mastication and incisal biting in Macaca mulatta and Macaca,fascicularis. Archives of Oral Biology, 24: 689-697. LEIBMAN, F. M . & KUSSICK, L., 1965. An electromyographic analysis of masticatory muscle imbalance with relation to skeletal growth in dogs. Journal o f Dental Research, 44: 768-774. RADINSKY, L. B., 1981. Evolution of skull shape in carnivores. 1. Representative modern carnivores. Bioloeical.7ournal of the Linnean Society, 15: 369-388. ROSEN?W<IG, M: L., 1966. Community structure in sympatric carnivora. Journal o j Mammalogy, 47: 602-612. WEIJS, W. A,, 1981. Mechanical loading of the human jaw joint during unilateral biting. Acta Morphologzcu ~eerlando-Scandinauica,19: 261-262. WEIJS, W. A. & DANTUMA, R., 1981. Functional anatomy of the masticatory apparatus in the rabbit (Oryctolagus cuniculus L.). Netherlands Journal of .Soology, 31: 99-147.