bite forces, canine strength and skull allometry in carnivores

J. Zool., Lond. (2005) 266, 133151 C 2005 The Zoological Society of London Printed in the United Kingdom doi:10.1017/S0952836905006643

Bite forces, canine strength and skull allometry in carnivores(Mammalia, Carnivora)

Per Christiansen* and Jan S. Adolfssen

Zoological Museum, Department of Vertebrates, Universitetsparken 15, 2100 Copenhagen O, Denmark

(Accepted 5 October 2004)

AbstractSkull variables were analysed for allometry patterns in 56 species of extant carnivores. As previously reported,many skull variables scale near isometrically with either skull length or lower jaw length. The maximal gapeangle scales insignificantly (P< 0.05) with skull size, but the clearance between the canines shows a significantrelationship with skull size and scales near isometrically. Maximal bite forces were estimated from geometricalcross-sectional areas of dried skulls, and the bending strength of the canines was computed by modelling the caninesas a cantilevered beam of solid, homogeneous material with an elliptical cross section. Previous hypotheses of largetaxon differences in canine bending strengths, so that felids have stronger canines than canids, are corroboratedwhen actual bite forces at the upper canine are ignored. Incorporation of bite force values, however, nullifies thedifferences in canine bending strength among felids and canids, and ursids seem to have stronger canines thanfelids. This is probably because of the significantly longer canines of felids compared to canids and ursids, and thegenerally high bite forces of felids.

Key words: bite forces, canine strength, skull allometry, Carnivora

INTRODUCTION

The Carnivora includes a variety of extant species fromvirtually herbivorous ursids to nearly strictly carnivorousfelids and certain canids. Studies have been carried outon the skull proportions of carnivores over the years, toelucidate patterns of proportional allometry and functionalanatomy (e.g. Emerson & Radinsky, 1980; Radinsky,1981a,b; Biknevicius, Van Valkenburgh & Walker, 1996;Gittleman & Van Valkenburgh, 1997), but one aspect oftheir anatomy has been wanting, namely estimated biteforces. Bite force is a crucial part of predaceous behaviour,and thus it is of some interest to provide an assessment ofthese factors, along with skull proportions and the bendingstrength of the teeth used for killing, mainly the canines.

Van Valkenburgh & Ruff (1987), in a pioneering study,addressed the issue of canine bending strength and killingbehaviour in extant carnivores, with an emphasis on felidsand canids. They reported that felid canines were, onaverage, stronger in bending than in canids at any givensize, particularly about the anteroposterior axis. Hyaenidsgrouped with felids in this respect. This was to be expectedas felids, particularly the large pantherines, usually use astrong throat or muzzle bite to subdue their prey, whichis often very large (Kruuk & Turner, 1967; Eaton, 1970;

*All correspondence to: P. Christiansen.E-mail: [email protected]

Sunquist & Sunquist, 2002), whereas many canids usuallykill proportionately smaller prey by bites to the body(Sheldon, 1992). Large, hypercarnivorous (sensu VanValkenburgh, 1991) pack-hunting canids such as Lycaon,Cuon and Canis lupus bring down larger prey, often byusing repeated slashing and tearing bites to various partsof the body, in addition to repeated bite-and-shake attacks,and there is no specialized killing bite as in felids (Estes &Goddard, 1967; Kruuk & Turner, 1967; Ewer, 1973;Sheldon, 1992; see also Palomares & Caro, 1999 forcarnivorecarnivore killings).

Hyaenids were reported as having a dental strengthcomparable to felids, but only Crocuta seems to huntlarge vertebrate prey regularly (Kruuk, 1972; Cooper,Holecamp & Smale, 1999; Silvestre, Novelle & Bogliani,2000), whereasHyaena hyaena, while occasionally killinglarge prey, usually feeds on smaller prey or carrion(Kruuk, 1976), as doesH. brunnea (Mills, 1978; Owens &Owens, 1978). This may not explain the necessity ofhaving strong canines, but as bones are usually dispatchedwith the premolars, Van Valkenburgh & Ruff (1987) sug-gested that the large canines of hyaenids, which are roundin cross-section, may indicate the tendency of hyaenidsto scavenge bones, as they occasionally crack bones withtheir anterior teeth as well (B. Van Valkenburgh, pers.comm.). Ursids were unfortunately not included in theanalysis of Van Valkenburgh & Ruff (1987).

The findings of Van Valkenburg & Ruff (1987) werealso in agreement with a previous study by Radinsky

134 P. CHRISTIANSEN AND J. S. ADOLFSSEN

(1981a), who stated that mustelids and felids had thestrongest bites relative to body size of extant carnivores,and canids the weakest, mainly influenced by the differen-ces in their skull proportions, such as relative snout lengthsand inlever moment arms for the main jaw adductors.It is, however, not enough to simply compare computedcanine bending resistance to either body mass or skulllength, as in Van Valkenburgh & Ruff (1987). A significantrelationship does exist between body mass and bite force(Meers, 2002), as the true mechanical strength of thecanines relative to bite force will depend on the actualforce that is put on them by the action of the jaw adduc-tors. Such values were, however, not available at the time(Van Valkenburgh & Ruff, 1987: 383).

Thomason (1991), however, proposed a simple modelto compute bite forces in carnivores, which is used in thepresent study. Estimated bite forces can then be used tocompare the bending strength of the canines in variouscarnivores. Additionally, comparative studies of skull pro-portions in several carnivores can elucidate the proportionof total force produced at the back of the skull by the jawadductors, compared to the amount of force applied atboth the canine or carnassial. Automatically, one wouldassume that this proportion would be less in canids (andursids) than in felids or mustelids, in accordance with theabove, owing to the apparently longer snouts compared tooverall skull length in these taxa. This question was alsoaddressed in the present study.

MATERIALS AND METHODS

The skulls of 56 species of carnivores were analysed forthe purpose of this study (Table 1), with emphasis on theUrsidae, Canidae and Felidae, which includes all the large,extant carnivore species. All the material is housed inthe mammal collections of the Zoological Museum inCopenhagen. All were adult specimens and no distinctionwas made between male and female specimens, as theskulls included were chosen primarily for dental complete-ness and ontogentic stage, and several specimens did notinclude data on sex. The canines of adult carnivores areoften worn or even broken through feeding contact withbone (see also Van Valkenburgh, 1988). Not distinguish-ing between sexes could, however, introduce a slight bias insome of the data, since previous studies have demonstratedsexual dimorphism in several of the variables includedin this study, such as canine morphology and inferredmoments arms of the masseter (MAM) and temporalis(MAT) muscles from lower jaw morphology (Gittleman &Van Valkenburgh, 1997; see also Dayan et al., 1989, 1990,1992). No systematic bias should be introduced, however,since males and females can be inferred to be representedin the data sample.

Data gathering

Sixteen measurements were taken on each skull with digi-tal callipers (all measurements < 155.2 mm) and normalcallipers (measurements > 155.2 mm), consisting of

8 measurements for the cranium and mandible, respec-tively. Measurements were chosen for their relevance tobite force estimation.

Measurements on the skull include (Table 1, Fig. 1):total skull length; basicranial length and snout length;distance from upper jaw joint cotyle to centre of carnas-sial and centre of canine; dorsoventral height and antero-posterior (AP) and lateromedial (LM) diameters of thecanine at the gum line. Basicranial (occiput to orbit) lengthwas measured as the horizontal distance from the occipitalcondyles to the anteriormost extant of the orbital fenestra,as in Biknevicius et al. (1996). In contrast, Radinsky(1984) and Gittleman & Van Vakenburgh (1997) used thehorizontal distance from the midventral border of the fora-men magnum to the basisphenoidpresphenoid suture.This measurement is less satisfactory from a mechanicalpoint of view, as it terminates anterior to the main jawadductors. Additionally, basicranial length, as used in thisanalysis, focuses on the area in front of the orbit, where theskull constricts into the snout. As Greaves (1982) pointedout, the muscle force resultant of the jaw adductors hasto be posterior to the last molar so as not to introducesubstantial tensile forces in the jaw rami.

Lower jaw measurements were (Table 1, Fig. 1): overalllength from dentary tip to jaw condyle; moment arm ofthe masseter (MAM) and temporalis (MAT) (see alsoEmerson & Radinsky, 1980); jaw joint to centre of carnas-sial and canine; lower canine height and AP and LMdiameters. Upper and lower canine height is here definedas total canine height from the jaw line, as in Emerson &Radinsky (1980), unlike Van Valkenburgh & Ruff (1987),who used the dentineenamel junction. From a mechanicalpoint of view, however, the former measurement is moresatisfactory, as the tooth can thus be viewed as a beamanchored at one end (see Alexander, 1983, 1989).

Finally, as much has historically been written about thegape in extant vs extinct carnivores, mainly sabre toothedcats (sensu lato), an estimate of the gape angle and theclearance between the tips of the upper and lower caninesis given for the included carnivores. This was achievedby the junior author taking a photograph of a skull indirect lateral view, with the senior author holding thelower jaw at the highest estimated gape, as indicated bythe fit of the craniomandibular jaw joint, as in Kurten(1954) and Emerson & Radinsky (1980). If the condyleseemed to slip away from the cotyle, so that a space wascreated between them, or the condyle articulating facetwas evaluated as extending too far beyond the cotyle, thejaw was deemed as having been opened too far and theprocedure was repeated. For estimation of gape angles andjaw clearance, horizontal lines were drawn on the digitalimages in Photoshop from the temporomandibular jointand following the approximate outline of the gums on thecranium and mandible (see also Emerson & Radinsky1980: fig. 4). The angle between the lines was thenmeasured digitally and the clearance between the upperand lower canines was computed from the ratio of the sizeof the digital image to the size of the actual specimen.Since this procedure is somewhat tentative, but similar toothers used previously (e.g. Akersten, 1985), the clearance

Bite forces, canine strength and skull allometry in carnivores 135

Table 1. Skull measurements of the 56 species of included carnivores. All measurements are in mm, except one of the gape dimensions,which is in degrees. Abbreviations: AP, anteroposterior diameter; Bsl, basicranial length; Can, canine; Carn, carnassial; L, length; LM,lateromedial diameter; MAM; moment arm of masseter muscle; MAT, moment arm of temporalis muscle; mm, clearance between upperand lower canine in mm at maximum gape; Sl, snout length

Skull proportions Jaw joint to Upper canine Lower jaw Jaw joint to Lower canine Gape

L Bsl Sl Carn Can L AP LM L MAT MAM Carn Can L AP LM mm Specimen

104.6 70.8 33.8 45.7 68.1 10.9 6.6 4.2 81.0 29.2 24.3 50.5 73.3 9.5 6.4 4.6 34.8 38.7 Ailurus fulgens CN5701140.0 90.9 49.1 55.4 76.7 17.0 9.6 6.9 94.5 24.4 12.9 55.6 80.7 15.9 9.8 6.9 57.0 61.5 Meles meles CN5419126.9 89.0 38.0 47.0 69.7 18.7 8.5 6.7 88.6 23.2 16.4 44.1 77.8 18.5 8.8 6.8 56.6 59.2 Taxidea taxus CN5437137.2 93.5 43.8 49.6 79.7 21.1 9.4 7.9 94.4 30.5 13.3 47.4 84.7 18.4 9.5 8.6 44.2 39.9 Gulo gulo CN668107.4 61.2 46.2 41.4 67.7 8.2 4.2 2.5 78.3 13.1 9.0 47.1 71.6 8.9 4.5 2.9 46.8 44.3 Nasua nasua CN1799127.6 84.0 43.6 52.7 77.9 14.2 6.3 5.2 94.8 25.9 14.2 56.4 83.3 14.8 7.6 5.0 60.2 68.1 Procyon cancrivorus CN1408110.0 72.1 37.9 45.9 67.8 15.9 6.3 4.7 80.5 19.3 13.6 51.5 72.8 13.5 5.9 4.3 54.8 49.3 Procyon lotor CN5618215.0 160.0 55.0 105.5 135.3 19.3 11.9 139.6 36.5 28.2 88.0 125.1 14.1 8.8 Tremarctos ornatus CN927228.4 164.2 78.6 101.4 129.2 41.8 23.4 18.1 163.7 47.3 29.9 115.2 139.4 39.7 25.0 16.6 60.4 129.4 Ursus malayanus CN5683262.6 179.3 83.3 119.1 153.4 32.9 19.6 13.2 190.4 42.1 29.7 115.6 173.2 29.7 17.8 12.3 54.7 117.7 Ursus ursinus CN1300266.0 187.1 78.9 116.1 156.7 29.2 17.1 10.4 181.0 46.7 34.0 111.8 169.6 26.7 11.9 9.7 58.0 125.7 Ursus americanus CN5436288.1 196.0 92.0 128.4 173.3 36.3 18.3 11.6 206.0 47.2 30.5 120.1 189.8 36.7 20.3 13.7 60.6 158.4 Ursus thibetanus CN607306.1 201.8 104.2 138.4 183.6 38.6 24.2 14.6 225.1 49.3 40.5 130.0 204.2 37.4 23.2 15.2 54.7 146.4 Ursus arctos CN577367.9 236.7 131.3 155.6 216.2 45.4 24.8 17.0 244.8 65.2 41.9 148.0 228.2 40.2 23.1 14.8 64.7 201.2 Ursus maritimus CN587112.9 69.4 43.6 49.5 72.1 12.2 5.3 3.5 86.4 16.3 31.8 43.8 74.7 10.5 4.9 3.7 57.2 55.8 Nyctereutes procynoides CN5702104.1 63.6 40.5 45.6 66.5 8.7 4.5 2.7 74.2 12.0 28.0 41.3 68.8 8.7 4.6 2.6 60.7 72.8 Otocyon megalotis CN5403

83.2 54.2 28.9 29.8 51.2 8.9 3.2 2.2 60.1 10.7 8.5 28.9 54.8 7.6 3.0 2.3 62.4 46.0 Fennecus zerda CN4236114.7 65.0 49.7 42.9 72.7 14.5 5.8 3.5 86.9 18.1 16.5 39.1 78.0 14.2 6.2 3.7 64.9 66.9 Alopex lagopus CN2834146.0 81.7 64.3 54.6 95.6 18.0 7.5 4.5 112.3 21.2 17.1 51.0 101.9 17.2 7.9 4.8 60.3 79.2 Vulpes vulpes CN5233198.2 116.1 82.1 83.5 129.6 24.5 11.7 7.6 152.1 32.8 32.5 75.9 140.2 22.8 10.5 8.0 59.4 101.7 Lycaon pictus CN3678125.0 81.1 43.8 47.5 75.9 17.6 7.3 5.2 91.9 20.3 18.1 43.9 80.3 18.6 7.8 5.7 64.2 67.8 Speothos venaticus CN285235.1 131.3 103.8 96.2 160.2 29.1 12.0 7.2 182.9 35.1 30.8 94.4 176.7 27.1 11.1 7.4 60.7 140.8 Chrysocyon brachyurus CN832161.7 96.3 65.4 65.2 104.3 20.0 9.5 5.7 124.7 27.8 26.6 63.4 114.3 18.9 10.0 6.6 64.2 107.7 Cuon alpinus CN3048255.3 139.9 115.4 98.9 168.0 31.9 14.3 10.0 197.6 4.6 38.4 96.1 184.4 29.6 14.7 9.7 65.0 163.5 Canis lupus CN6060133.8 77.2 56.6 55.8 90.0 13.0 6.1 3.7 103.0 18.1 23.2 51.6 94.0 11.7 5.6 4.1 60.1 86.7 Cerdocyon thous CN1488133.9 77.9 56.1 50.2 85.9 17.1 6.7 4.0 102.9 18.6 16.7 49.9 91.3 15.4 6.1 4.4 60.5 79.6 Dusicyon gymnocerus CN935105.8 66.3 39.5 45.8 69.6 13.5 4.8 3.1 81.3 15.6 13.0 43.1 75.8 11.6 5.0 3.5 64.9 62.2 Lycalopex vetulus CN249

76.9 52.1 24.9 32.2 45.8 8.4 2.9 2.5 54.4 12.3 9.3 30.1 48.5 7.2 3.2 2.1 58.6 32.5 Nandinia binotata CN3003151.8 103.9 47.9 67.3 93.5 19.1 9.2 5.2 112.6 27.6 21.1 65.1 101.2 14.9 8.4 4.8 48.4 74.7 Arctictis binturong CN1109

87.0 60.9 26.1 30.1 53.2 9.3 3.5 2.6 60.6 12.6 11.2 27.4 55.6 9.4 3.9 2.5 57.7 43.0 Genetta genetta CN6810117.3 75.4 41.9 49.2 69.7 9.7 4.9 3.3 86.1 17.4 13.1 47.6 77.0 9.2 4.2 3.2 63.5 42.5 Civettictis civetta CN4289

88.2 62.5 25.7 30.5 52.5 10.2 4.1 2.8 60.2 12.8 9.0 27.8 53.8 9.7 4.2 3.0 60.6 34.4 Viverricula indica CN155251.0 158.8 92.2 84.8 154.0 28.1 14.8 10.4 183.0 46.7 35.8 79.0 172.8 28.1 13.7 10.8 57.5 151.0 Crocuta crocuta CN138217.0 137.8 79.2 74.8 135.0 27.8 12.8 9.6 167.1 39.8 31.2 70.4 149.0 32.0 16.1 11.6 59.0 99.9 Hyaena hyaena CN127218.9 139.6 79.4 72.7 135.4 27.0 16.5 11.4 168.0 41.8 30.4 72.8 151.7 29.5 16.5 11.6 59.2 79.8 Hyaena brunnea CN134168.9 119.4 49.5 59.3 103.3 42.3 14.2 10.2 124.2 31.5 23.2 62.2 113.2 31.2 12.4 8.6 71.4 79.0 Neofelis nebulosa CN35175.6 124.0 51.6 68.3 108.0 31.6 13.5 11.3 129.6 32.6 23.2 62.9 116.7 29.2 13.3 10.2 70.8 89.1 Panthera uncia CN4321188.2 132.1 56.1 69.2 113.2 33.1 13.1 10.8 137.3 35.5 23.2 66.6 124.2 27.3 13.3 9.5 63.8 91.6 Panthera pardus CN5661359.7 224.4 135.3 146.0 230.8 60.0 28.2 19.5 274.1 69.7 57.1 143.7 259.8 46.0 26.5 17.2 60.2 95.1 Panthera leo CN7241302.3 203.2 99.1 114.9 186.0 61.0 28.0 19.3 226.2 63.7 51.8 109.2 204.5 50.9 25.9 16.9 62.3 70.8 Panthera tigris CN5668219.8 151.1 68.7 80.8 132.3 38.4 18.6 14.2 164.7 40.5 29.7 76.4 143.8 33.4 18.1 12.6 66.6 70.1 Panthera onca CN5659113.8 83.6 30.2 40.4 63.0 15.1 6.5 5.0 76.7 18.5 13.3 39.7 70.4 13.2 6.9 4.8 56.5 37.7 Leopardus pardalis CN1114

81.5 60.9 20.7 29.5 45.2 11.3 4.4 3.2 53.4 11.8 11.0 27.8 48.9 10.0 4.5 3.3 59.7 24.0 Leopardus wiedii CNL4483.0 62.2 20.7 29.0 44.2 10.0 4.0 3.2 53.7 12.5 10.6 28.5 48.7 9.5 4.1 3.0 66.7 34.2 Leopardus tigrinus CNL4593.7 68.6 25.1 35.6 54.5 13.5 5.1 3.7 63.3 17.0 11.5 34.1 57.9 11.5 4.8 3.6 65.8 24.6 Leopardus geoffroyi CN1366

133.4 99.5 33.9 51.1 81.2 23.0 9.0 7.1 100.4 25.7 17.6 49.7 92.0 20.1 8.9 6.6 61.2 47.3 Lynx lynx CN2542171.7 107.1 64.6 74.7 109.1 28.2 12.9 10.2 129.5 37.3 26.9 74.4 119.6 20.8 10.5 7.6 61.0 66.8 Acinonyx jubatus CN5607161.1 107.7 53.4 62.7 97.2 25.0 10.8 8.9 117.6 33.8 25.2 60.9 106.4 23.1 10.2 8.1 69.1 82.2 Puma concolor CN1198

94.5 72.2 22.3 31.3 49.6 11.2 4.8 3.5 59.9 18.4 14.2 31.7 55.3 9.7 4.5 3.3 54.5 25.0 Herpailurus yagouaroundi CN110890.2 63.3 26.9 34.7 54.5 14.1 6.3 4.8 66.5 17.7 12.0 33.2 59.5 13.0 6.7 4.2 63.3 21.0 Pardofelis marmorata CN1391

102.2 72.1 22.3 38.9 62.5 15.0 5.2 4.4 73.9 18.9 12.6 37.8 67.2 12.3 4.8 3.8 61.3 31.1 Felis chaus CN103496.8 71.2 25.6 36.2 58.7 14.3 5.6 4.2 66.9 14.6 11.2 35.2 61.7 14.5 5.4 4.0 61.3 31.6 Ictailurus planiceps CN212683.4 61.1 22.3 30.0 48.0 11.2 4.2 3.1 56.6 15.9 11.2 29.3 51.6 9.2 4.3 2.9 64.0 32.3 Prionailurus bengalensis CN1696

106.5 79.5 27.1 43.5 64.1 12.4 5.4 4.3 76.3 19.7 15.6 39.7 68.5 12.0 5.1 4.1 66.4 53.3 Leptailurus serval CN2452118.4 81.4 36.9 46.5 69.5 18.4 8.2 6.5 88.5 21.8 20.9 45.3 78.4 17.0 7.5 5.6 66.0 52.5 Caracal caracal CN112117.9 83.7 34.2 47.3 71.9 15.8 6.8 5.2 84.1 24.0 16.7 44.1 78.2 13.0 6.2 4.6 63.4 43.2 Profelis aurata CN4441

used in the analyses are in cm, not mm, so that thereliability of the data is not overstated.

Statistical analysis

Traditionally, proportions of the carnivore skull havebeen analysed with traditional regression statistics (e.g.Emerson & Radinsky, 1980; Radinsky, 1981a,b, 1984; VanValkenburgh & Ruff, 1987). Taxa are not statistically in-dependent data points (Felsenstein, 1985), however, but in-variably linked through evolutionary processes, expressed

in the hierarchical nature of a cladogram. Accordingly,traditional regression analyses confuse true adaptation(i.e. convergence) and plesiomorphy, and nearly alwaysresuling in a higher correlation than when taking thephylogeny of the included species into account (e.g.Christiansen, 2002a,b). Gittleman & Van Valkenburgh(1997), however, applied a phylogenetic autoregressivemethod to their craniodental characters, and in the presentstudy the data variables were analysed with both tra-ditional regression analyses and independent-contrastsregression analyses (Garland, Harvey & Ives, 1992;


Bcl Sl

Ujca

SklM

AT

Ujc

Ljl

LjcLjca

Uch

Lch

MAM

Fig. 1. Skull of male Malayan sunbear Ursus malayanus, illustrating measurements. Bcl, basicranial length; Ljc, lower jaw joint to canine;Ljca, lower jaw joint to carnassial; Lch, lower canine height; Ljl, lower jaw length; MAM, moment arm of masseter; MAT, moment armof temporalis; Skl, skull length; Sl, snout length; Ujc, upper jaw joint to canine; Ujca, upper jaw joint to carnassial; Uch, upper canineheight.

Garland, Midford & Ives, 1999; Garland & Ives, 2000),which incorporates the hierarchical phylogeny of theincluded species.

It is possible to use a variety of values for the branchlengths, but preferred values for this type of study areinferred split ages for all taxa (Garland, Dickerman et al.,1993; see also Purvis, 1995; Harris & Steudel, 1997), bothterminal taxa and larger taxon units. The phylogenetic treeand estimated split ages used in this analysis (Fig. 2) weremainly derived from the comprehensive study by Bininda-Emonds, Gittleman & Purvis (1999). The topology of theCanidae was arranged according to Wayne et al. (1997),however, a study not included in the former analysis. Thetopology of the Felidae was largely arranged according toMattern & McLennan (2000), although the higher cladeage of 16.2 Mya for the Felidae was used (see also Bininda-Emonds et al., 1999; Christiansen, 2002a,b) instead of8.2 Mya, implied in the tree of Mattern & McLennan(2000: fig. 1). The topology of the Felidae, as presented inMattern & McLennan (2000) diverges in several respectsfrom traditional views, notably the placement of Acinonyx(for a discussion of discrepancies between morphometricsand traditional felid systematics, see Werdelin, 1983).

For traditional regression analysis, the data werelogarithmically transformed and regression lines werefitted to the data using a model I (least-squares) regressionanalysis. Confidence intervals (95% CI) were computedfor both the slope and least-squares intercepts, along withthe correlation coefficient, the standard error and theF-statistic and resultant significance level for each equa-tion. Independent contrasts analyses produces a regressionthrough the origin, and, thus, no intercept. Confidenceintervals were fitted to the slope (b) and the regressionequation statistics were computed as for the traditionalregression analyses.

Before independent contrast analysis, however, the datacontrasts must be standardized, so that their common vari-ance is independent (at P 0.05) of the branch lengths.This can be evaluated by generating a plot of standardizedcontrasts to their standard deviations (Garland, Huey &Bennett, 1991; Garland, Harvey et al., 1992; Garland,Midford et al., 1999). Such plots can be analysed visuallyand should show no discernible structure, or, preferably,the correlation coefficient of the plots can be computed.If above 0.05 the contrasts are deemed as not properlystandardized, and the branch lengths can then be


Ailurus fulgensMeles melesTaxidea taxusGulo guloNasua nasuaProcyon cancrivorusProcyon lotorTremarctos omatusUrsus malayanusUrsus ursinusUrsus americanusUrsus thibetanusUrsus arctosUrsus maritimusNyctereutes procynoidesOtocyon megalotisFennecus zerdaAlopex lagopusVulpes vulpesLycaon pictusSpeothos venaticusChrysocyon brachyurusCuon alpinusCanis lupusCerdocyon thousDusicyon gymnocerusLycalopex vetulusNandinia binotataArctictis binturongGenetta genettaCivettictis civettaViverricula indicaCrocuta crocuta

Hyaena brunneaHyaena hyaena

Neofells nebulosaPanthera unciaPanthera pardusPanthera leoPanthera oncaPanthera tigrisLeopardus pardalisLeopardus wiedii

Profelis aurataCaracal caracalLeptailurus servalPrionailurus bengalensisIctailurus planicepsFelis chausPardofelis marmorataHerpailurus yagouaroundiPuma concolorAcinonyx jubatusLynx lynxLeopardus geoffroyiLeopardus tigrinus

2.8

4.63.9

2.56.0

8.53.2

6.38.2

3.2

2.7

9.1

3.4

18.8

25.016.2

10.44.5 22.7

26.8

5.17.6

4.82.7

2.84.8

4.86.88.49.3

32.2

15.5

10.2

3.4

2.0

4.26.04.6

5.4

9.3

29.310.6

7.76.7

5.5

12.3

22.3

20.810.2

6.55.3

14.57.5

5.73.32.8

6.021.5

1

Fig. 2. Tree topology and inferred split ages (in Mya) of the included specimens of carnivores.

transformed using a variety of methods, log, square root,cube root, Nee, Pagel and Grafen (see also Garland, 1994;Garland, Harvey et al., 1992).

Bite force estimation

To analyse and compare the canine strength of theincluded carnivores, the estimated bite force at the caninewas computed for the 56 included species of carnivores(Fig. 3), following Thomason (1991). Initially the cross-sectional areas of the temporalis and massetermedialpterygoid complex were computed based on picturestaken of all 56 carnivores in posterodorsal, direct lateraland direct ventral views (Fig. 3). The resulting area was

multiplied by the estimated maximal isometric force gen-erated by mammalian muscle, as discussed below. As inThomason (1991), it was assumed that the resultant forcevectors about the temporomandibular joint (T for thetemporalis and M for the masseter, respectively) actedthrough their respective centroids perpendicular to theplane of the muscle cross-sectional area, as indicated inFig. 3. Then the inlever moments arms for the temporalis(I t) and masseter (Im) about the temporomandibular jointwere computed from the photographs. Thus, the bite force(Bf ) can be estimated as

B f = (T It + M Im)/Io (1)where Io is the outlever moment arm to the centre ofthe upper carnassial and upper canine, as appropriate. All


(a)

(c)

(b)

T

M

Im

lt

T

Fig. 3. Skull of the Falkland Island wolf Dusicyon gymnocerus illustrating temporalis and masseterpterygoideus cross-sectional areasand their respective inlever moment arms for the purpose of estimating bite force. (a) Posterodorsal view, showing the resultant forcevector of the temporalis (T) acting through the centroid (white circle); (b) ventral view, showing resultant force vector of the masseterpterygoideus (M) acting through the centroid (white circle) with an inlever moment arm of Im about the temporomandibular joint;(c) lateral view, showing the inlever moment arm (I t) of the temporalis about the temporomandibular joint. Shaded areas: reconstructedmuscle cross-sectional areas in: (a) the temporalis; (b) the masseterpterygoid group.

measurements are in SI units, which returns the bite forcevalue in Newtons (N). In contrast to Thomason (1991), itwas decided not to double the value to arrive at a total biteforce. Instead, equation (1) was used to compute the biteforce at each jaw ramus and, thus, at each carnassial orcanine. Accordingly, the section modulus of the canine for

bending in the AP and LM plane may be directly comparedto the force acting upon the tooth.

Thomason (1991) used the traditional value of 300 KPa(misprinted as 300 MPa, in Thomason, 1991: 2329) formaximal isometric contractile force of vertebrate striatedmuscle (e.g. Alexander, 1981, 1983; Sinclair & Alexander,


Table 2. Overview of the main masticatory muscles in carnivores, their origins and insertion and function, following Reighard & Jennings(1951) and Turnbull (1970). Inf, infratemporal

Origin Insertion Function

Jaw adductorsMasseter groupm. masseter pars profunda Ventral part of the Lower, lateral border of Adduction, some anterior

zygomatic arch mandibular ramus actionpars superficialis Zygomatic process of Mandibular ramus (masseteric Adduction, some anterior

maxilla (malar) crista to medial surface actionof angular process)

m. zygomandibularis Medial surface of Mandibular Adduction, some anteriorzygomatic arch ramus (masseteric fossa) action

Pterygoideus groupm. pterygoideus pars internus Palatine, lower border of Bottom of ascending

inf. fossa pterygoid fossa ramus to posterior edgeof angular process. Adduction,some anterior action

Temporalis groupm. temporalis pars profunda Sagittal crest, lambdoidal Inner surface of coronoid, Adduction, some posterior

crest and most of temporal planum tendineum temporalis actionpars superficialis Frontal and temporal Anterior edge of coronoid Adduction, some posterior

process actionpars zygomatica Dorsal edge of posterior Lateral surface of coronoid Adduction, some posterior

buttress of zygomatic arch process action

Jaw abductorsDigastricus groupm. digastricus Ventral edge of Ventral to the foramen Abduction

ascending ramus rotundum

1987), although some studies have used a lower value of250 KPa (Cleuren, Aerts & de Vree, 1995; Herzog, 1995).This resulted in lower than actual values, however, whencompared with muscle dissections on Didelphis skulls(Thomason, 1991), probably owing to the actual maximalcontractile force of a muscle having to be computed fromthe physiological cross-sectional area (Weijs & Hillen,1984a,b, 1985; Sinclair & Alexander, 1987; Koolstraet al., 1988; Cleuren et al., 1995) and not from an simpleestimate of a cross-sectional area, as in the present analysisand Thomason (1991). Also, the present model doesnot include other, smaller jaw adductors, such as thezygomaticomandibularis (see also Table 2). Accordingly,a slightly higher value of 370 KPa (see Weijs & Hillen,1985; Koolstra et al., 1988) was used in the present study.Similarly, Johnston & Gleeson (1984) found maximalisometric forces of around 330 KPa in lizard muscle.

The bending strength of the canines was computed asin Van Valkenburgh & Ruff (1987). The canines weremodelled as cantilevers, solid beams of homogenousmaterial properties with elliptical cross sections that werefixed at one end. The model makes the assumption ofmodelling the canines as straight beams, but in fact,most canines are recurved, and it further assumes thatthe material properties among species are identical. Themaximum stress in a cross-section of such a beam is

max = My/I (2)where M is the bending moment at distance y from theneutral axis of the section to the exterior edge and I is thesecond moment of area. The bending moment is equal to

applied force times the distance from force application tothe section in question, and thus, the bending momentwill be highest around the tooth base, since force isassumed to be applied at the tip, e.g. during the killing bite.Application of force perpendicular to the longitudinal axisof the canine thus implies that the bending moment will beequal to force times canine height. The second momentsof area for bending about the anteroposteror (AP) andlateromedial (LM) axes may be computed as:

IAP = (xy3)/4 (3)ILM = (yx3)/4 (4)

where x is the anteroposterior radius and y is the latero-medial radius of the canine, measured at the gumline. Peakbending strength is estimated as the inverse of peak stressso the bending strength (S) of the canines can be computedas

SAP = IAP/hy (5)SLM = ILM/hx (6)

where h is crown height. One may also directly incorporatethe bite force at the canine tips into the above computationsby multiplying hx and hy by the applied force. In thisstudy, the neutral bending strength was computed, as inVan Valkenburgh & Ruff (1987), assuming equal forceapplication in all species, and subsequently each valuewas divided by the applied force. This procedure allowsa comparison of the differences in canine bendingstrength among various carnivores when assuming equal


0.1 (a)

(d)

0.080.060.040.02

Ab

solu

te v

alue

of

stan

dard

ized

cont

rast

0.020.015

0.010.005

010 15 20 25 30 35

03 3.5 4 4.5 5 5.5

0.1 (b)0.080.060.040.02

03 3.5 4 4.5 5 5.5

0.1 (c)0.080.060.040.02

03 3.5 4 4.5 5 5.5

0.1 (f)0.080.060.040.02

03 3.5 4 4.5 5 5.5

0.1 (e)0.080.060.040.02

03 3.5

Standard deviation of contrast4 4.5 5 5.5

Fig. 4. Plots of standardized contrasts and their standard deviations: (a) lower jaw length to skull length; (b) snout length to skull length;(c) gape angle to skull length; (d) MAM to lower jaw length; (e) MAT to lower jaw length; (f ) distance from jaw joint to canine to lowerjaw length.

Table 3. Branch length transformation of data samples beforestatistical analysis. The method that yielded the lowest correlationwas used for statistical analysis

Sample

Variable All Canidae Felidae

Skull length tobasicranial length Nee Log Neesnout length Log Log Logjaw joint to carnassial Log Log Logjaw joint to canine Log Log Loggape angle () 3

Nee Log

clearance Log Nee Logcanine height 3

Log Log

canine strength (AP) 3

Log Logcanine strength (LM) 3

Log Log

lower jaw length Log Log Log

Lower jaw length toMAT Log Log LogMAM 3

Nee Nee

jaw joint to carnassial Log Log Logjaw joint to canine Log Log Logcanine height 3

Log 3

canine strength (AP) 3

3 Logcanine strength (LM) 3

Nee Log

bite forces and its implications for those preliminaryconclusions when the actual bite forces are applied.

RESULTS

Branch length transformation for the purpose of the inde-pendent contrasts regression analyses are shown in Table 3(see also Fig. 4af). Ideally, the standardization of thebranch lengths should yield a non-significant relationshipbetween the absolute values of the standardized contrastsand their corresponding standard deviations (i.e.P< 0.05). As can be seen from Table 3, however, no suchrelationship could be demonstrated for the unmodifiedbranch lengths, and in order to bring the contrasts to acommon variance, the branch lengths were transformed,

and the analyses run again. The transformations thatresulted in the lowest correlations were used for statisticalanalysis (Table 3).

Variable allometry

As expected, skull length to lower jaw length was highlycorrelated (Table 4, Fig. 5), and the distance between thejaw joint to the canine in both the skull and lower jaw wasalso highly correlated. The distance between the jaw jointand the carnassials was also highly correlated with skulllength and lower jaw length in all carnivores, as indicatedby the high correlation coefficients (Table 4).

Radinsky (1981a) showed that MAT and MAM dis-played a higher variability with skull size and this iscorroborated by the present analysis. MAT and MAMhave lower correlation coefficients with lower jaw lengththan most other variables, except lower canine proportions(Table 4, Fig. 6). Most variables are nearly isometric witheither skull length or lower jaw length (Table 4, Figs 5 & 6),as also found by Radinsky (1981a), but basicranial lengthand snout length are marked negatively and positivelyallometric, respectively, to skull length. Canine bendingstrengths varied substantially with either skull length orlower jaw length, as indicated by the lower correlationcoefficients.

As expected, gape angle showed virtually no correlationwith skull size, whereas gape clearance correlated fairlywell with skull size, and thus, body size, since skullsize is highly correlated with body size (Janis, 1990;Van Valkenburgh, 1990; see also Christiansen, 1999).The gape angle of most of the included carnivores wasc. 5565 (Table 1), regardless of body size, and, thus, anycorrelation with size will inevitably be extremely low. Theupper exceptions are Panthera uncia and Neofelis, whichboth reached values of > 70. Neofelis has proportionallythe longest canines of any extant carnivore and, thus,would be expected to have the largest gape angle. At theopposite end of the observed range, Ailurus, Nasua andGulo displayed markedly low values for gape angle. Thelow values are, however, among the most reliable, as the


Table 4. Regression coefficients and confidence intervals for the sample of all carnivorans. Equations are given as Log Y = Log a + b LogX, and X is either skull length, lower jaw length or bite force, as appropriate. All osteological measurements are in mm, except clearancebetween upper and lower canines at maximum gape, which is given in cm

Traditional regression analysis Independent contrasts analysis

n a 95% CI b 95% CI r SE F P b 95% CI r SE F PSkull length toBasicranial 56 0.057 0.117 0.944 0.054 0.979 0.037 1242.159 0.000 0.878 0.049 0.980 0.024 1291.018 0.000

lengthSnout length 56 0.760 0.222 1.129 0.102 0.949 0.070 492.729 0.000 1.227 0.102 0.956 0.051 578.530 0.000Jaw joint to 56 0.547 0.121 1.065 0.055 0.982 0.038 1471.521 0.000 1.078 0.071 0.972 0.035 929.005 0.000

carnassialJaw joint to 56 0.281 0.076 1.030 0.034 0.992 0.024 3556.789 0.000 1.071 0.038 0.992 0.019 3203.966 0.000

canineGape angle ()a 55 1.739 0.163 0.018 0.075 0.065 0.051 0.224 0.638 0.007 0.092 0.021 0.046 0.024 0.848Clearance (cm)a 55 1.611 0.384 1.117 0.177 0.867 0.120 160.712 0.000 1.105 0.210 0.824 0.105 111.692 0.000Canine heighta 55 1.187 0.290 1.141 0.134 0.920 0.091 292.269 0.000 1.067 0.170 0.865 0.085 158.107 0.000Canine strength 55 5.830 0.696 2.790 0.321 0.923 0.218 303.748 0.000 2.500 0.371 0.881 0.185 182.866 0.000

(AP)a

Canine strength 55 5.817 0.599 2.853 0.276 0.943 0.188 428.375 0.000 2.556 0.343 0.899 0.171 223.010 0.000(LM)a

Lower jaw 55 0.226 0.068 1.040 0.031 0.994 0.021 4440.422 0.000 1.060 0.041 0.990 0.021 2673.657 0.000lengtha

Lower jaw length toMAT 56 0.716 0.206 1.045 0.101 0.942 0.072 427.517 0.000 1.033 0.123 0.917 0.061 285.373 0.000MAM 56 0.709 0.259 0.990 0.128 0.904 0.091 242.285 0.000 0.934 0.181 0.815 0.090 107.099 0.000MAMb 54 0.795 0.203 1.027 0.100 0.944 0.071 426.863 0.000 0.985 0.143 0.886 0.071 190.586 0.000Jaw joint to 56 0.311 0.134 1.015 0.067 0.973 0.047 944.003 0.000 1.016 0.067 0.972 0.033 924.733 0.000


canineCanine heighta 55 0.956 0.240 1.086 0.119 0.930 0.084 339.879 0.000 0.955 0.157 0.858 0.078 148.402 0.000Canine strength 55 4.964 0.609 2.559 0.300 0.920 0.213 292.622 0.000 2.143 0.334 0.870 0.167 165.289 0.000

(AP)a

Canine strength 55 4.864 0.586 2.585 0.289 0.927 0.205 322.191 0.000 2.179 0.343 0.868 0.171 162.491 0.000(LM)a

a Excluding Tremarctos.b Excluding outliers Nyctereutes and Otocyon.

0.5 (a)

(d)

(b)

(e)

(c)

(f)

0.4

Cont

rast

2

0.30.20.1

0

0 0.1 0.2 0.3 0.4-0.1

0.120.1

0.080.060.040.02

0

0 0.02 0.04 0.06 0.08 0.1-0.02

0.10.080.060.040.02

0

0

0 0.02 0.04 0.06 0.08 0.1

0.02 0.04 0.06 0.08 0.1-0.02

0.10.080.060.040.02

0-0.02

0.20.15

0.10.05

0-0.05-0.1

0 0.02 0.04 0.06 0.08 0.1

0.0080.0060.0040.002

0-0.002-0.004-0.006

0 0.005 0.01 0.015Contrast 1 (skull length)

Fig. 5. Independent contrasts least squares regression plots of six different log-transformed skull variables to log skull length:(a) basicranial length; (b) snout length; (c) lower jaw length; (d) gape angle; (e) clearance between canines; (f ) upper jaw joint tocarnassial.

jaw joints of Ailurus and Gulo (and Meles and Taxidea)are highly constrained with a deep, subcircular cotyle inthe skull, so much so that the lower jaw could barely bedislocated from the skull when taking photographs.

Canidae (Table 5) and Felidae (Table 6) showed thesame trends as the overall sample, where most variablesscaled isometrically to skull and lower jaw length, and withslightly higher independent contrasts regression slopes in


0.10 (a) (b) (c)

(f)(e)(d)

0.080.060.040.02

0-0.02-0.04

0.030.020.01

0-0.01-0.02-0.03

0.100.080.060.040.02

0-0.02

0.060.040.02

0

0

0 0.02 0.04 0.06 0.08 0.10

0.005 0.01 0.015 0.02

-0.02-0.04

0.060.040.02

0-0.02-0.04

0 0.005 0.01 0.015Contrast 1 (lower jaw length)

0.02

0

Cont

rast

2

0.02 0.04 0.06 0.08 0.1 0 0.005 0.01 0.015 0.02

0 0.02 0.04 0.06 0.08 0.1

0.120.100.080.060.040.02

0

Fig. 6. Independent contrasts least-squares regression plots of six different log-transformed lower jaw variables to log lower jaw length:(a) MAT; (b) MAM; (c) jaw joint to carnassial; (d) upper jaw joint to canine; (e) canine AP bending strength; (f ) canine LM bendingstrength.

Table 5. Regression coefficients and confidence intervals for the Canidae. Equations are given as Log Y = Log a + b Log X, and X iseither skull length, lower jaw length or bite force, as appropriate. All osteological measurements are in mm, except clearance betweenupper and lower canines at maximum gape, which is given in cm



lengthSnout length 13 0.795 0.298 1.187 0.120 0.989 0.027 474.898 0.000 1.303 0.100 0.993 0.045 826.878 0.000Jaw joint to 13 0.426 0.298 1.013 0.138 0.979 0.031 259.972 0.000 1.011 0.157 0.974 0.072 199.736 0.000


canineGape angle (o) 13 1.786 0.177 0.002 0.083 0.019 0.019 0.004 0.951 0.051 0.088 0.357 0.040 1.604 0.431Clearance cm 13 1.316 0.442 1.039 0.206 0.958 0.047 123.409 0.000 1.039 0.199 0.961 0.091 131.577 0.000Canine height 13 1.260 0.552 1.153 0.257 0.948 0.058 97.546 0.000 1.011 0.281 0.922 0.128 62.663 0.000Canine strength 13 5.834 1.117 2.679 0.520 0.960 0.117 128.779 0.000 2.160 0.601 0.922 0.272 62.636 0.000

(AP)Canine strength 12 5.967 0.890 2.731 0.413 0.978 0.092 216.986 0.000 2.585 0.550 0.957 0.247 109.772 0.000

(AP)a

Canine strength 13 5.658 1.016 2.688 0.472 0.967 0.107 156.560 0.000 2.240 0.565 0.935 0.257 76.166 0.000(LM)

Lower jaw length 13 0.238 0.091 1.055 0.042 0.998 0.010 2997.890 0.000 1.065 0.043 0.998 0.020 2909.058 0.000Lower jaw length toMAT 13 1.045 0.338 1.166 0.167 0.978 0.040 237.710 0.000 1.005 0.185 0.964 0.084 142.994 0.000MAM 13 0.452 1.162 0.881 0.573 0.714 0.137 11.458 0.006 0.851 0.544 0.720 0.247 11.858 0.005Jaw joint to 13 0.292 0.224 0.994 0.111 0.986 0.026 392.808 0.000 0.983 0.119 0.984 0.054 332.538 0.000


canineCanine height 13 1.097 0.576 1.125 0.284 0.935 0.068 75.949 0.000 0.924 0.299 0.899 0.626 46.247 0.000Canine strength 13 4.866 1.137 2.398 0.560 0.943 0.134 88.798 0.000 1.791 0.621 0.886 0.282 40.327 0.000


(AP)a

Canine strength 13 4.715 1.129 2.406 0.557 0.944 0.133 90.602 0.000 1.830 0.625 0.889 0.284 41.498 0.000(LM)

a Excluding outlier Speothos.

the Felidae compared to the Canidae, with the exception ofthe negatively allometric basicranial length (especially incanids) and positively allometric snout length. Jaw joint

to the canine was slightly positively allometric in boththe Canidae and the Felidae, as in the overall sample.Lower jaw length to skull length, however, scaled with


Table 6. Regression coefficients and confidence intervals for the Felidae. Equations are given as log Y = log a + b log X , and X is eitherskull length, lower jaw length or bite force, as appropriate. All osteological measurements in mm, except clearance between upper andlower canines at maximum gape, which is given in cm



lengthSnout length 21 1.024 0.201 1.228 0.094 0.987 0.037 742.204 0.000 1.364 0.164 0.970 0.078 302.858 0.000Snout lengtha 20 0.995 0.172 1.213 0.081 0.991 0.032 987.507 0.000 1.306 0.149 0.975 0.071 339.968 0.000Jaw joint to 21 0.531 0.140 1.051 0.065 0.992 0.026 1126.499 0.000 1.164 0.096 0.985 0.046 639.021 0.000


canineGape angle (o) 21 1.750 0.161 0.025 0.075 0.156 0.030 0.471 0.501 0.024 0.134 0.085 0.064 0.137 0.673Clearance 21 1.452 0.622 1.000 0.292 0.854 0.115 51.373 0.000 1.095 0.507 0.720 0.242 20.445 0.001Canine height 21 1.432 0.328 1.292 0.154 0.971 0.061 309.407 0.000 1.239 0.255 0.919 0.098 103.737 0.000Canine heightb 20 1.378 0.241 1.262 0.113 0.984 0.044 548.904 0.000 1.219 0.207 0.946 0.098 153.568 0.000Canine strength 21 5.812 0.619 2.849 0.291 0.978 0.115 421.236 0.000 2.740 0.541 0.940 0.259 112.321 0.000


(LM)Lower jaw length 21 0.346 0.044 1.094 0.044 0.997 0.017 2727.414 0.000 1.129 0.063 0.993 0.030 1387.673 0.000Lower jaw length toMAT 21 0.651 0.177 1.033 0.089 0.984 0.039 587.386 0.000 1.020 0.146 0.958 0.070 213.568 0.000MAM 21 0.767 0.220 1.028 0.112 0.976 0.048 374.434 0.000 1.008 0.186 0.933 0.090 128.397 0.000Jaw joint to 21 0.214 0.087 0.962 0.044 0.996 0.019 2134.104 0.000 1.037 0.063 0.992 0.030 1177.512 0.000


canineCanine height 21 0.927 0.258 1.100 0.130 0.971 0.056 313.324 0.000 0.989 0.211 0.914 0.101 96.495 0.000Canine strength 21 4.731 0.433 2.492 0.219 0.984 0.095 570.865 0.000 2.251 0.338 0.955 0.161 194.754 0.000


(LM)

a Excluding outlier Acinonyx.b Excluding outlier Neofelis.

significantly more positive allometry in the Felidae thanin the Canidae (independent contrasts values; 95% CI incanids exclude the slope of felids and vice versa). Theoutliers in this respect seem to be felids, because the slopefor lower jaw length to skull length of the total sample wasnot different from that of canids (within the 95% CI), butthe 95% CI of felids excluded the independent contrastsslope of the total sample (Tables 46).

The clearance between upper and lower canines showeda rather poor correlation with skull length in the Felidae(Table 6) compared to both the overall sample (Table 4)and the Canidae (Table 5). MAM to lower jaw lengthshowed a much higher correlation in the Felidae (Table 6)than in both the overall sample (Table 4) and the Canidae(Table 5). Overall, regression slopes in felids differ morefrom the total sample than in canids, in accordance withtheir derived crania. Upper jaw joint to canine scales witha significantly higher slope (1.139) in felids (Table 6)than in the overall sample (1.071), as the 95% CI of theformer value excludes the latter value. Upper jaw joint tocarnassial in felids also scale with a higher slope in felidscompared to the overall sample, but not significantly so.

Bite forces

The estimated force produced by both the temporalis andmasseterpterygoid complex, along with estimated biteforces produced at the carnassial and canine, respectively,are listed in Table 7. The highest bite forces at boththe carnassial and the canine are present in the largepantherines, followed by the big ursid species Ursusarctos and U. maritimus. Both Tremarctos and the largemale specimen of the small species U. malayanus hadsurprisingly high bite forces, owing to their proportionallyrather abbreviated snouts compared to other ursids and thelarge size of the zygomatic arches in the latter species.

The hyaenids seem not to have a markedly strongerbite than the big hypercarnivorous canids (see VanValkenburgh, 1991), such as Canis lupus and Lycaon,although Crocuta has the highest carnassial and caninebite forces of any species of comparable size, and is onlysurpassed by much larger ursids and the lion and the tiger.The other two hypercarnivorous species Speothos andCuon have considerably lower bite forces thanC. lupus andLycaon, owing to their smaller size. Hyaena sp. usually


Table 7. Muscle cross sectional areas of the main jaw adductors and bite force estimation for the included carnivores. All cross-sectionalareas are given as mm2, and all bite force values as Newtons. All areas and forces are for one side of the skull only

M. masseter M. temporalis Bite force at

Specimen Area Force Area Force Carnassial Canine

Ailurus fulgens 1038.1 384.1 1375.2 508.8 335.9 225.7

MustelidaeMeles meles 973.2 360.1 2521.0 932.8 255.2 184.2Taxidea taxus 1129.4 417.9 1592.9 589.4 322.8 217.9Gulo gulo 1106.8 409.5 2100.6 777.7 408.3 254.3ProcyonidaeNasua nasua 481.6 178.2 882.3 326.4 87.1 53.2Procyon cancrivorus 1022.4 378.3 2129.3 787.9 267.5 180.8Procyon lotor 797.8 295.2 881.2 326.1 176.4 119.5

UrsidaeTremarctos ornatus 3588.5 1327.8 7187.3 2659.3 1536.8 1197.2Ursus malayanus 4995.1 1848.2 8116.1 3003.0 1441.7 1131.5Ursus ursinus 3168.1 1172.2 5632.8 2084.1 708.9 550.4Ursus americanus 3858.6 1427.7 9684.7 3583.3 1174.1 869.9Ursus thibetanus 3534.3 1307.7 8192.4 3031.2 819.8 607.4Ursus arctos 4974.3 1840.5 12164.1 4500.7 1417.6 1068.6Ursus maritimus 7558.4 2796.6 16859.9 6238.2 2403.9 1730.1

CanidaeNyctereutes procynoides 564.3 208.8 880.4 325.8 108.9 74.8Otocyon megalotis 492.1 182.1 2478.1 176.9 86.6 59.4Fennecus zerda 257.3 95.2 226.2 83.7 55.8 32.5Alopex lagopus 707.1 261.6 1102.9 408.1 203.7 120.1Vulpes vulpes 957.9 354.4 1535.3 568.0 298.4 170.3Lycaon pictus 2297.2 850.0 4905.9 1815.2 854.0 550.5Speothos venaticus 847.4 313.5 1035.2 383.0 272.0 170.1Chrysocyon brachyurus 2817.5 1042.5 3977.7 1471.8 725.3 435.6Cuon alpinus 1209.2 447.4 2735.6 1012.2 379.0 237.0Canis lupus 3940.6 1458.0 5097.2 1886.0 1262.3 743.0Cerdocyon thous 834.7 308.8 1109.0 410.3 182.7 113.3Dusicyon gymnocerus 695.0 257.2 1269.2 469.6 205.4 120.1Lycalopex vetulus 539.7 199.7 916.6 339.1 130.5 86.0

ViverridaeNandinia binotata 215.9 79.9 400.9 148.3 54.1 38.0Arctictis binturong 1492.9 552.4 2181.7 807.2 356.7 256.7Genetta genetta 310.4 114.8 617.6 228.5 88.4 50.0Civettictis civetta 511.4 189.2 1059.6 392.1 148.4 104.7Viverricula indica 293.4 108.5 435.5 161.1 75.5 44.0

HyaenidaeCrocuta crocuta 3735.0 1381.9 8183.4 3027.9 1421.6 782.7Hyaena hyaena 2745.4 1015.8 5890.0 2179.3 1041.5 576.5Hyaena brunnea 2743.9 1015.2 7167.6 2652.0 1222.8 656.2

FelidaeNeofelis nebulosa 1628.0 602.4 3362.0 1244.0 587.8 337.3Panthera uncia 2071.1 766.3 6957.1 2574.1 884.8 559.2Panthera pardus 2528.0 935.4 7917.3 2929.4 1376.8 841.5Panthera leo 12137.2 4490.8 13833.2 5118.3 3405.4 2152.3Panthera tigris 7968.1 2948.2 16345.5 6047.8 3007.2 1859.3Panthera onca 2521.3 932.9 8909.0 3296.3 1253.6 765.9Leopardus pardalis 824.2 305.0 2142.5 792.7 256.9 164.8Leopardus wiedii 447.8 165.7 977.4 361.6 112.6 73.5Leopardus tigrinus 333.3 123.3 573.3 212.1 110.4 72.4Leopardus geoffroyi 584.6 216.3 1151.4 426.0 180.8 118.3Lynx lynx 1274.7 471.6 2623.9 970.9 454.9 286.4Acinonyx jubatus 2584.4 956.2 3858.2 1427.5 635.1 434.6Puma concolor 2073.4 767.1 5450.7 2016.8 905.6 584.3Herpailurus yagouaroundi 449.7 166.4 700.4 259.2 104.6 66.1Pardofelis marmorata 558.5 206.6 802.3 296.9 151.4 96.5Felis chaus 703.2 260.2 2149.0 795.1 294.6 183.4Ictailurus planiceps 543.9 201.3 1045.5 386.8 172.4 106.2Prionailurus bengalensis 412.7 152.7 951.6 352.1 93.7 58.5Leptailurus serval 704.7 260.7 1822.3 674.2 223.2 151.4Caracal caracal 853.0 315.6 2338.0 865.1 203.8 136.4Profelis aurata 1052.5 389.4 2158.9 798.8 281.5 185.2


1

0.8

0.6

Ursids Canids FelidsHyaenid

s

Ursids Canids FelidsHyaenid

s

0.4

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t len

gth/

sk

ull l

engt

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l len

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engt

h

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0.1

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1 5 9 13 17 21 25 29 33 37 41

1 5 9 13 17 21 25 29 33 37 41

Fig. 7. Plots of the ratios of basicranial length to skull length and snout length to skull length in ursids, canids, hyaenids and felids.

feeds on carrion or smaller vertebrate prey, and usuallyhunts singly in small numbers (Kruuk, 1976; Mills, 1978),whereas Crocuta hunts both in packs and subdues largeprey, as well as feeding on carrion (Cooper et al., 1999;Silvestre et al., 2000), crushing even large bones with theirpremolars. Apparently, the main distinction from largewolves is not the jaw adductor power for doing so, butthe massive premolars (Van Valkenburgh & Ruff, 1987).Chrysocyon had a surprisingly high estimated bite force,given its main diet of small vertebrates, invertebrates andeggs (Nowak, 1991; Sheldon, 1992).

On average, the felids have stronger bites at any givenbody size than canids and ursids, and the mustelids, especi-allyGulo, also seem to have a proportionally powerful bite,as previously suggested by Radinsky (1981a). The largestpantherines Panthera leo and P. tigris seem to have verypowerful carnassial and canine bites, despite not feedingon bone to the same extent as Crocuta, which is alsoevident from dental wear (Van Valkenburgh, 1988).

Bite forces and skull proportions

Ursids and canids visually have distinctly longer snoutscompared to overall skull length than felids (Radinsky,1981b, 1984). Conversely, the basicranial length of the

latter should constitute a larger proportion of total skulllength than in the former. Tables 46 show that basicraniallength scales with negative allometry and snout lengthwith positive allometry to skull length. As ursids arethe largest extant carnivores and the present data sampleincludes many small felids (Table 1), this could be takenas indicative of just such proportional differences.

Indeed, comparing the ratio of basicranial length toskull length (Fig. 7) reveals that when comparing the felidsample (average 0.7087) to the sample of canids (0.5949)and ursids, the three samples are significantly different(F = 40.5707, 0.05 > P > 0.01). Surprisingly, the ursidsample average (0.6905) is very similar to the felidaverage. Conversely, the ratio of snout length to total skulllength (Fig. 7) in felids (average 0.2913), canids (0.4057)and ursids (0.3185) are also significantly different(F = 39.895, 0.05 >P> 0.01). From the above it may beconcluded, that canids, but not ursids and felids are long-snouted compared to overall skull length. Felids do,however, seem to have shorter skulls compared tobody size than other carnivores (Radinsky, 1981a; VanValkenburgh & Ruff, 1987).

When comparing the total force produced by thetemporalis and masseterpterygoid group at the backof the skull to the force at the carnassials and canines(Table 7, Fig. 8), the above differences are not maintained,


0.5

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Ursids Canids Felids

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enid

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Ursids Canids Felids

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enid

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Bite

forc

e a

t can

ine/

to

tal b

ite fo

rce

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forc

e a

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ial/

to

tal b

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rce

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0.25

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1 5 9 13 17 21 25 29 33 37 41

1 5 9 13 17 21 25 29 33 37 41

Fig. 8. Plots of the ratios of total force produced by the temporalis and masseterpterygoid complex muscles and the bite force at thecarnassial and the canine in ursids, canids, hyaenids and felids.

however. The ratios of total force at the back of the skullto force at the carnassial in felids (average 0.2782), canids(0.2923) and ursids (0.2590) are not significantly different(F = 0.8421, P> 0.05). The ratios of total force to forceat the canine in felids (average 0.1767), canids (0.1801)and ursids (0.1966) are also not significantly different(F = 0.8592,P> 0.05). Thus, the seemingly longer snoutsof canids do not lead to a proportional loss of bite force ateither the carnassial or the canine, compared to the totalforce produced by the jaw adductors at the back of theskull.

Bite forces and canine bending strengths

Van Valkenburgh & Ruff (1987) reported that canids onaverage had weaker canines, especially in bending aboutthe AP axis, than felids and hyaenids. This was based onthe assumption that force at the canines was equal, in theabsence of bite force data. Their results are corroboratedhere, where the bending strength of canid teeth appearsconsistently below the corresponding values for felids atany given body size (Fig. 9). Indeed, when comparing theratios of canine bending strength about the AP axis to skulllength in ursids (average 0.0414), canids (0.007), hyaenids

1.5

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endi

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th of u

pper

can

ine

Log

LM b

endi

ng s

treng

th of u

pper

can

ine

2.52Log skull length

3

Fig. 9. Plot of upper canine bending strengths to skull length. Opentriangles, felids; open squares: hyaenids; closed triangles, canids;closed squares, ursids.


1.5

1

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-0.5

-1

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2

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endi

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ine

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endi

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ine

0.5

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-0.5

-1

1 1.5 2 2.5 3 3.5

1 1.5 2Log biteforce at canine (N)

2.5 3 3.5

Fig. 10. Plot of upper canine bending strengths to estimated biteforces. Open triangles, felids; open squares: hyaenids; closed tri-angles, canids; closed squares, ursids.

(0.0256) and felids (0.0180) the samples are significantlydifferent (F = 27.0992, 0.05 >P> 0.01). The results forbending strength about the LM axis are similar (ursids0.0611; canids 0.0108; hyaenids 0.0361; felids 0.0238;F = 28.6401, 0.05 >P> 0.01), and in both cases canidshave distinctly weaker canines than felids at any givenskull length, whereas ursids seem to have even strongercanines than felids, although much of this is clearlyallometric and owing to the large body size of most ursids(Fig. 9).

Incorporation of estimated bite force at the canine(Table 7), however, challenges the conclusions of theabove. If the ratios of canine bending strength to forceproduced at the canine are compared in felids, canids andursids (Fig. 10), it becomes evident that the strength ofbending about the AP axis to bite force in felids (average0.008), hyaenids (0.009), canids (0.005) and ursids (0.012)are significantly different (F = 124.5767, P< 0.01).However, in this case the felid and canid averages arerather similar, as can also be seen from Fig. 10. Thehyaenid average is nearly identical to that of felids, where-as ursids again appear to have the strongest canines. Theratio of canine bending strength about the LM axis tobite force is similar (felids 0.010; hyaenids 0.0123; canids0.008; ursids 0.018; F = 137.1555, P < 0.01). Again thefelid and canid averages are similar, and again the bendingstrength of ursid canines seems distinctly higher. As above,however, this is heavily biased by the large size of theursids and the presence of many small species in the felidand canid samples.

DISCUSSION

The results of variable allometry in this study broadlyagree with previous analyses, although there are severaldifferences. It is hardly surprising that lower jaw lengthis highly correlated to skull length, as also found byEmerson & Radinsky (1980), but it is not perfect sincecranial proportions can and do vary intra- and interspeci-fically. Accordingly, in a large sample of 233 red foxesVulpes vulpes the correlation between lower jaw length andskull length was 0.961 (P. Christiansen, pers. obs.), indi-cating that interspecific variation can exceed intraspecificvariation (Tables 46). This also indicates that some of thevery high interspecific correlations may be allometric.

The distances from the upper and lower jaw jointsto upper and lower carnassials were highly correlatedwith skull length and lower jaw length, respectively, aspreviously found by Radinsky (1981a,b). This supportsthe work of Greaves (1983, 1988), who showed thatmaximum masticatory and shearing efficiency would tendto position the carnassials in the same relative positionalong the jaws, regardless of overall size. Greaves (1983)suggested that in carnivores with carnassials the resultantforce of the jaw adductors will be positioned c. 60% ofthe distance from the jaw joint. In this study, the averagedistance of the carnassials from the upper jaw joint wasfound to be 0.394 ( 0.036 SD) of total skull length. Theposition of the muscles and their respective resultants asa function of skull length was, however, not addressed inthis study.

The traditional method of estimating gape angles bymanipulation of skulls and jaws was also used in thisanalysis. This method would seem to predict gape angleswith some conviction, albeit with a certain degree ofuncertainty, because it involves visual inspection of theproper fit of the jaw joint and the possible extremewhere this is maintained. There are anecdotes, however, tosuggest that this widely accepted method may sometimesunderestimate the true gape angles possible. Neofelis waspredicted to be able to attain a maximum gape angleof c. 71 (Table 1). Pictures of a yawning Neofelis,however, suggests a much higher angle (Scapino 1976:856), perhaps approaching 90, a value otherwise ascribedto machairodontine felids only (e.g. Kurten 1954;Emerson & Radinsky, 1980; Akersten, 1985). Thissuggests that some of the other values reported in thisstudy may also be conservative.

The bite force values reported here (Table 7) areuniformly higher than corresponding values for the samespecies (e.g. leopard, lion, wolf) reported in Thomason(1991) based on skull estimations only, probably owing toa higher isometric contractile value being used in thisstudy, but perhaps also owing to slight differences inthe skull sizes of the specimens included, which willremain tentative, since Thomason did not publish hisvalues. The values are, however, broadly similar to andfrequently below Thomasons (1991) corrected estimates,where values based on dry skulls were corrected based onmuscle dissections and inferred bite forces in Didelphis.As Thomason (1991) noted, the validity of extending such


a correction based solely on opossums to, for example,large pantherines, is tentative, and his corrected valuesshould thus be interpreted with caution.

It may seem surprising that the apparently massiveupper canines of felids are not proportionally stronger thanthe apparently more feeble canines of canids or ursids.Felid canines, however, often seem to be distinctly longerat any given size (compare values in Table 1 and notehigher felid slopes in Tables 5 & 6). Indeed, comparedto skull length, the height of the upper canine in felids(average 0.1564) is significantly different (F = 493.25,P< 0.01) from the canid (0.1183) and ursid (0.1322)samples. The lower canines are always smaller than theupper ones, and are not included in the computations.None the less, lower canine height to lower jaw lengthin felids (average 0.1882) is again significantly different(F = 754.52, P< 0.01) from the sample of canids(0.1453), whereas the ursids are more similar to felids(0.1756), mainly owing to the very large canines andabbreviated skull in Ursus malayanus whose canine ratio(0.243) is much higher than in the other ursids (0.1470.178), even the predaceous (DeMaster & Stirling, 1981)U. maritimus (0.164). Thus, the long canines of felidswould tend to compromise their bending strength, andcombined with the often very high bite forces compared toother, comparably sized carnivores (Table 7), this renderstheir canines no stronger relative to inferred bite forcesthan those of the other comparably sized carnivores.

The apparently very strong canines of ursids comparedto the total sample of felids are primarily an allometriceffect, owing to their very large body size. In all taxa,the bending strength of the teeth are lower percentages ofthe estimated bite forces at the canines in small vs largetaxa. The presence of many small felids in the sample thusintroduces a size bias. Comparably sized felids (lion andtiger) have equally strong, but not stronger, teeth comparedto large ursids, mainly owing to the very long crown heightof felid canines, compromising their bending resistance,and the very high bite forces estimated at the canines.Hyaenids also have stronger teeth than canids, even thoughtheir bite forces are also higher than in comparably sizedcanids.

It can also be questioned whether the specialized killingbite of felids really requires disproportionately strongupper canines compared to the high bite forces, as opposedto the slashing and tearing used by many canids and hya-enids when subduing prey, as noted above. Initially justthe reverse seems to be true, but actually there are nosignificant differences in canine bending strengths whencompared to bite forces. In contrast, the main differenceswould seem to be the stronger bite forces of felidscompared to canids and ursids at any given size.

Akersten (1985) suggested that serrated posteriorcanines seem to be characteristic of carnivorous carni-vores, and used this in his analysis on the feeding habits ofthe large machairodontine Smilodon. The validity of thischaracter, present in many theropod dinosaurs and sharks(Farlow et al., 1991), but conspicuously absent in mostextant carnivorans including the frequently omnivorousursids, is compromised by its frequent, though not

unanimous presence in specimens of U. malayanus withunworn canines (pers. obs.), although this species isknown to be primarily insectivorous and frugivorous,virtually never attacking larger vertebrates (Fitzgerald &Krausman, 2002).

Prediction of maximal bite forces using the currentmodel is a rough approximation. The inferred levers ofthe insertion on the lower jaw (MAT and MAM, for thetemporalis and masseter, respectively) were not incorpo-rated into the model. Instead, the model simply focusedon the cranium and not the actual fulcrum, the lower jaw.MAT and MAM are not uniform from one species to thenext and, as noted above, also seem to differ betweenlarge taxonomic units, such as the Felidae vs the Canidae.A further problem is the computation of force producedby the jaw adductors, since the resultant force is notdependent on a simple geometric cross-sectional area, butthe physiological cross-sectional area, as noted above. Theactual angle to the fulcrum for every fibre also has to betaken into account, which is also not addressed in thepresent model. Thus, the model could be further refinedby dissections of large numbers of carnivores.

Previously, attempts have been made to use the ratioof MAT and MAM (Van Valkenburgh & Ruff, 1987), orthe ratio of the distance from the temporalis insertion to thetemporomandibular joint and the distance from the tempo-ralis origin to the temporomandibular joint (Herring &Herring, 1974; Emerson & Radinsky, 1980) to give anoverview of relative bite forces in various carnivores,mainly feline and machairodontine felids. This is a usefulcomparative procedure, but will not itself result in anyabsolute bite force values.

Accordingly, despite its obvious shortcomings, thepresent model for computation of bite forces seems tobe superior to previous analyses. Although estimationvalues of bite force could be refined by using physiologicalcross-sectional areas and muscle fibre orientation, such arefined model would also be an approximation. This isbecause maximal generation of bite force in mammalsseems not to be a simple matter of muscle size. Analyseshave shown that various jaw adductors show maximalcontractile activity at different gape angles and not allfibres fire simultaneously (Thexton & Hiiemae, 1975;Weijs & Dantuma, 1975; Clark, Luschei & Hoffman,1978; Hiiemae, 1978; Herring, Grimm & Grimm, 1979;Gorniak & Gans, 1980; Dessem, 1989), which is also thecase in reptiles sensu lato (Gorniak, Rosenberg & Gans,1982; Cleuren et al., 1995).

Also, the present model does not ascertain the gapeangle at which maximal contractile force occurs. Indomestic cats, jaw adduction is initiated by the zygoman-dibularis (Gorniak & Gans, 1980), and maximal tensionseems to occur when the mouth is opened widely(Mackenna & Turker, 1978). Also, muscle activity pat-terns and chewing mechanics seem to vary with foodcomposition (Gorniak & Gans, 1980). As in other mam-mals (de Vree & Gans, 1976; Gorniak, 1977; Gans, deVree & Gorniak, 1978; Hiiemae, 1978), the masticatorymovements in cats are not a simple scissor-like action butmore three-dimensional (Gorniak & Gans, 1980). As in


other mammals (Herring & Scapino, 1973; Weijs, 1975;Weijs & Dantuma, 1975), cats chew food preferably withone side of the mouth at a time (Gorniak & Gans, 1980).Thus, masticatory movements and probably also biteforces, are more complex than estimations of muscle sizesand inlever and outlever moment arms would suggest. Forthis reason, an approximate model seems to be acceptable,and probably as good as any currently available model.

A potentially more reliable way of computing bite forceswould be to use specific types of structures whose tensilestrengths could subsequently be measured. Erickson et al.(1996) estimated the maximum bite force in the gianttheropod dinosaur Tyrannosaurus by computing howmuch force it would take to drive a replicate of aTyrannosaurus tooth a given distance into bone. This wasbased on discoveries of prey animals with numerous deeptooth marks, and depending on the position of the toothposition in the jaw, the procedure yielded bite forces of640013 400 N, far exceeding those of any extant animal(see also Meers, 2002). This should, at least in theory, alsobe possible with carnivore mammals. In fact, bite forces oforang-utans have been inferred using thick-shelled seeds,which the apes had cracked (Lucas, Peters & Arrandale,1994). Analyses showed that no less than 6000 N wasrequired to crack open the particularly hard Mazzettiaseeds, and this bite force far exceeds even the highestvalues estimated in this analysis for the largest ursidsand pantherines. For this reason alone the values reportedin the present analysis should probably be regarded asconservative.

Acknowledgements

We express our gratitude to Dr Jeff Thomason for helpfuldiscussions on carnivore bite strengths and to Dr BlaireVan Valkenburgh and an anonymous reviewer for muchvaluable criticism.

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