Download The generalized carnivore jaw

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.