Abstract

Observations on extant mammals suggest that large body mass is selectively advantageous for a terrestrial predator on large herbivores. Yet, throughout the Cenozoic, some lineages of terrestrial mammalian predators attained greater maximal body masses than others. In order to explain this evolutionary pattern, the following biomechanical constraint on body mass is hypothesized. The stress, set up in the humerus by the bending moment of the peak ground reaction force at maximal running speed, increased with increasing body mass within a given lineage of terrestrial mammalian predators, resulting in a decreasing safety factor for the bone, until a predator could no longer attain the maximal running speed of its smaller relatives. The selective disadvantage of reduced maximal running speed prevented further increase of body mass within the lineage.
This hypothesis is tested by examining the scaling of humeral dimensions and estimating maximal body masses in several lineages of terrestrial mammalian predators. Among lineages with otherwise similar postcranial skeletons, those with the more robust humeri at a given body mass attained the greater maximal body masses. Lineages with the longer deltoid ridges/deltopectoral crests of the humeri and/or the more distally located deltoid scars (suggesting the more distal insertions of the humeral flexors) at a given body mass also attained the greater maximal body masses. These results support the existence of the proposed biomechanical constraint, although paleoecological data suggest that some lineages of terrestrial mammalian predators failed to reach the limits, imposed by this constraint, because of the small size of available prey.

Keywords

  1. Body mass
  2. evolutionary constraint
  3. bone stress
  4. maximal running speed
  5. terrestrial mammalian predators
All extant terrestrial mammalian predators with an average adult body mass above 25 kg feed mostly on terrestrial herbivorous mammals with a body mass similar to their own (Carbone et al. 1999) or, in the case of social predators, – with a body mass similar to the combined mass of the social group members attacking the prey animal (Earle 1987). Observations on two such predators, the lion (Panthera leo) and the spotted hyena (Crocuta crocuta), in their natural habitat suggest that a large body mass is selectively advantageous for a terrestrial predator on large herbivores. The lion and the spotted hyena are in intense interspecific competition, hunting many of the same prey species and frequently confronting each other directly (Kruuk 1972; Schaller 1972). Despite the lack of retractile claws and the slender distal limb musculature, a single spotted hyena appears well matched with a single big cat of similar body mass, such as the leopard (Panthera pardus), both in direct confrontations (Kruuk 1972) and in the ability of a single individual to bring down large prey (Schaller 1972; Kingdon 1977). Yet, a pride of lions with a combined body mass equal to or less than that of a clan of spotted hyenas can bring down larger prey and take over or defend a carcass from the latter (Kruuk 1972; Schaller 1972; Joubert 1994).
Given the advantages of a large body mass, one would expect all lineages of terrestrial mammalian predators weighing more than 25 kg to have attained similar maximal body masses. But the fossil record indicates that, during the Cenozoic, some lineages of large terrestrial mammalian predators attained greater maximal body masses than others. For example, the lion‐sized Pachycrocuta brevirostris, the largest known member of the Hyaenidae (Turner & Antón 1996), was only half as massive as the American lion (Panthera atrox) and Smilodon populator, the largest known felids. In turn, Sarkastodon mongoliensis, the largest known member of the Oxyaeninae, a subfamily of cat‐like creodonts, attained a body mass nearly twice that of the largest American lion (Table 1).
Table 1. Maximal body mass estimates for the lineages of terrestrial mammalian predators considered in this paper.
LineageLargest known species of the lineageSkeletal dimension used to estimate body massSource for max. skeletal dimension of largest speciesExtant model for the largest known species of the lineageSource for max. skeletal dimension of extant modelSource for max. body mass of extant modelMax. body mass (kg) of the lineage
1Extrapolated to the maximal greatest radius length (Hawksley et al. 1973) from the humerus (measured by the author) and the radius (greatest length from Hawksley et al. 1973) of the Powder Mill Creek Cave individual.
2The Hemphillian species of Epicyon referred to as E. validus by Munthe (1989).
3The species is referred to the genus Plithocyon by Hunt (1998a).
4Viranta (1996) provides greatest femur length and body mass for a single large individual.
5Extrapolated to the maximal basal skull length of southern African male Panthera leo (Turner & Antón 1996) from the measurements of the skull and mandible of a male P. leo FMNH 35741 taken by the author.
6Extrapolated to the condylobasal skull length of Megistotherium osteothlastes M26173 (Savage 1973) from the measurements of the associated skull and left humerus of Hyaenodon horridus F: AM 75701 taken by the author.
7Extrapolated to the maximal condylobasal skull length of male Panthera tigris altaica (Stroganov 1969) from the measurements of the skull and humeri (part of a complete skeleton) of a male P. tigris altaica AMNH 85404 taken by the author.
‘Felinae’Panthera tigris altaicaStroganov 1969320
Panthera spelaea/atroxPanthera atroxBasal skull lengthMerriam & Stock 1932Southern African male Panthera leoTurner & Antón 1996Turner & Antón 1997420
SmilodonSmilodon populatorCondylobasal skull lengthKurtén & Werdelin 1990Male Panthera tigris altaicaStroganov 1969Stroganov 1969470
HomotheriumHomotherium serumGreatest femur lengthMeade 1961Crocuta crocutaKurtén 1956Nowak 1999190
HoplophoneusHoplophoneus occidentalisCondylobasal skull lengthMeasured by the authorPanthera oncaMerriam & Stock 1932Turner & Antón 1997160
HyaenidaePachycrocuta brevirostrisBasal skull lengthTurner & Antón 1996Crocuta crocutaKurtén 1956Nowak 1999190
CaninaeCanis dirus, MissouriInterarticular humerus lengthExtrapolated by the author1Canis lupusMunthe 1989Nowak 1999110
EpicyonEpicyon haydeni2Greatest humerus lengthMeasured by the authorCrocuta crocutaKurtén 1956Nowak 1999170
North American PlithocyonHemicyonursinus3Interarticular humerus lengthMeasured by the authorCanis lupusMunthe 1989Nowak 1999170
AmphicyoninaeAmphicyon ingensGreatest femur lengthMeasured by the authorMale Ursus arctos middendorffiViranta 19964Viranta 19964600
OxyaeninaeSarkastodon mongoliensisLower canine‐last molar lengthGranger 1938Southern African male Panthera leoExtrapolated by the author5Turner & Antón 1997800
HyaenodontinaeMegistotherium osteothlastesInterarticular humerus lengthExtrapolated by the author6Male Panthera tigris altaicaExtrapolated by the author7Stroganov 1969500
BorhyaenoideaProborhyaena giganteaLower canine‐last molar lengthPatterson & Marshall 1978Southern African male Panthera leoExtrapolated by the author5Turner & Antón 1997600
ThylacosmilusThylacosmilus atroxCondylobasal skull lengthRiggs 1934Panthera oncaMerriam & Stock 1932Turner & Antón 1997150
In this paper the author proposes the hypothesis that increasing stress, set up in the humerus by the bending moment (force*moment arm) of the peak ground reaction force generated at maximal running speed, imposed an upper limit on body mass in a given lineage (a morphologically uniform clade or a paraphyletic morphological grade) of terrestrial mammalian predators throughout the evolutionary history of that lineage. The hypothesis is then tested by analysing the scaling of humeral dimensions (interarticular length as a function of mid‐shaft antero‐posterior diameter and deltoid ridge/deltopectoral crest length as a function of interarticular length) and estimating maximal body mass for a number of lineages of such predators.

Possible constraints on body mass in terrestrial mammalian predators

The absence of a lion‐sized hyena from the guild of large terrestrial predators in Africa since the extinction of Pachycrocuta brevirostris on that continent 1.5 Ma (Turner & Antón 1996) suggests that ecological constraints, such as small size or low density of available prey or competition from members of other lineages, could limit body mass of a single lineage of terrestrial predators over a wide geographical area for more than a million years. But it would seem unlikely that ecological constraints imposed the same upper limit of approximately 200 kg on body masses of both the hyaenids in Africa and Eurasia during the Plio‐Pleistocene and the hyena‐like borophagine canids of the genus Epicyon in North America during the upper Miocene (Table 1). It would also seem an extraordinary coincidence if ecological constraints imposed the same upper limit on body mass of the saber‐toothed felids of the genus Homotherium (Table 1), which were similar to the living spotted hyena in the postcranial skeleton but differed greatly in cranial and dental morphology (Turner & Antón 1997), suggesting that they occupied a different ecological niche. Ecological constraints also fail to explain why no felid attained a body mass greater than 500 kg during the last 7 Ma, when the largest terrestrial predators of Africa, Eurasia, and North America were members of the Felidae (Turner & Antón 1997; Hunt 1998a), and all of the above continents supported a variety of herbivores weighing more than 1,000 kg (Owen‐Smith 1988).
The fact that maximal body masses were similar in lineages of predators with similar postcranial morphologies suggests a biomechanical constraint as the limiting factor. Munthe (1989) found that both the living spotted hyena and the extinct borophagine canids of the genus Epicyon had more robust (thicker at mid‐shaft at a given length) long bones (humerus, ulna, radius, femur and tibia) than the living grey wolf (Canis lupus), while closely resembling it in other postcranial features. The spotted hyena also resembles the grey wolf in hunting behaviour, being a social pursuit predator on large ungulates (Mech 1970; Kruuk 1972). The maximal body masses in both the Hyaenidae and the Epicyon were close to 200 kg, while the largest canine canid weighed only a little over 100 kg (Table 1). This evolutionary pattern suggests that body mass within a given lineage of terrestrial mammalian predators was limited by the ability of the long bones of its members to resist bending due to ground reaction force, the more robust bones allowing for the greater maximal body mass.

Bending stresses in the long bones of living Carnivora

Alexander (1974) argued that the ground reaction force acting on the long bones of the domestic dog (Canis familiaris) is greatest during strong jumps. However, his own observations (Alexander 1974) indicate that the peak ground reaction force, which is π/2 times greater than the average ground reaction force during the support phase of the stride (Alexander 1977), acting on each limb of a dog running at 8 m/s, was as great as that acting during a long jump by the same individual. Since the 8 m/s is well below the running speed of 12 m/s attained by that dog (Jayes & Alexander 1978), the ground reaction force acting on the long bones and, therefore, the stresses, its bending moments set up in those bones, are greatest at maximal running speed in the domestic dog and, probably, in other terrestrial predatory mammals as well. No data on the ground reaction force acting on the long bones during linear or centripetal (during turns) acceleration in carnivorans or any other terrestrial mammals are available. However, velocity curves for the African lion chasing its prey (Elliott et al. 1977, fig. 5) indicate that linear acceleration decreases as the lion approaches its maximal running speed, suggesting that the ground reaction force generated at maximal acceleration is no greater than that generated at maximal running speed.
Both the domestic dog and the domestic cat support ~30% of their body weight on each forelimb (~20% on each hind limb) (Rollinson & Martin 1981) and hold the humerus at a higher angle from the vertical in the middle of the support phase of the stride, when peak ground reaction force is generated, than the ulna and the radius (Biewener 1983, fig. 5; Day & Jayne 2007, table 6). Therefore, the ground reaction force is expected to exert a greater bending moment on the humerus than on any other long bone in the domestic dog and, probably, in any other terrestrial mammalian predator.
Data on the forelimb duty factor (duration of the support phase/duration of the stride of the forelimb) in two domestic dogs weighing 1.8 and 27 kg and running at 5 m/s (Biewener 1983, fig. 3) suggest that it scales as body mass0.09. To the best of the authors’ knowledge, these are the only published data on the scaling of limb duty factor at a given running speed as a function of body mass in Carnivora. In several species of African ungulates, ranging in size from the Thomson's gazelle (Gazella thomsonii) to the giraffe (Giraffa camelopardalis) and running at 7–14 m/s, the forelimb duty factor scales as body mass0.11 (Alexander et al. 1977). Assuming that the scaling of the forelimb duty factor in the domestic dog is representative of terrestrial Carnivora, the peak ground reaction force acting on the forelimb at a given running speed scales as body mass0.91 (proportional to body weight/forelimb duty factor) within the group.
Data on the scaling of humeral length and antero‐posterior mid‐shaft diameter as functions of body mass (Alexander et al. 1979, tables 1 and 2) suggest that the cantilever strength of the humerus (multiple of body weight, acting perpendicular to the shaft, the bone can support without breaking; Alexander 1977) scales as body mass−0.23 in terrestrial Carnivora. Data on the long bone angles in four domestic dogs with body mass range 1.8–30.5 kg (Biewener 1983, fig. 5) and in nine species of felids with body mass range 3.3–192 kg (Day & Jayne 2007) suggest that the angle from the vertical, at which the humerus is held in the middle of the support phase of the stride, is independent from body mass in terrestrial predatory mammals.
Table 2. Regression statistics.
RegressionnLeast squares (Model I)Reduced major axis (Model II)r
Slope95% CIInterceptSlope95% CIIntercept
Log10(humeral length) vs. log10(A–P diameter ) in ‘Felinae’150.769± 0.056 1.2510.775± 0.056 1.2430.993
Log10(humeral length) vs. log10(A–P diameter ) in Caninae 90.721± 0.104 1.3690.730± 0.104 1.3580.987
Deltoid ridge length vs. humeral length in Felidae 80.645± 0.105–5.2040.654± 0.105–7.6750.987
Deltoid ridge length vs. humeral length in Epicyon 30.538± 0.027–3.1700.538± 0.027–3.1711.000
Therefore, peak stress, set up in the humerus by the bending moment of the ground reaction force at a given running speed, should scale as body mass0.14 (proportional to ground reaction force/(body weight*cantilever strength)) in terrestrial predatory mammals. This would result in a decreasing safety factor for the humerus with increasing body mass, until a member of a morphologically uniform lineage of terrestrial mammalian predators, such as the genus Panthera, could no longer attain the maximal running speed of its smaller relatives.

Disadvantages of reduced maximal running speed for a terrestrial predator

Reduced maximal running speed (relative to its smaller relatives) would have probably been a major disadvantage to any predator on terrestrial mammals as large as or larger than itself. For predation on species that rely on high‐speed flight for anti‐predator defence, reduced maximal running speed would have reduced the ability of an ambush predator to catch up to its prey before becoming exhausted and a pursuit predator's ability to keep up with its prey throughout the chase. With a 15 m distance between predator and prey and velocities of both being 0 m/s at the beginning of the chase, the lion has a hunting success of 40% against wildebeest (Connochaetes taurinus) and zebra (Equus burchelli), which have maximal running speeds (13.5–15 m/s) similar to that of their predator (13.5 m/s), but 0% against the much faster Thomson's gazelle (maximal running speed 25 m/s; figs 5, 6 in Elliott et al. 1977). Lions do capture Thomson's gazelles at shorter initial predator–prey distances or when the predator starts running before the prey does (figs 6, 8 in Elliott et al. 1977).
For predation on species that rely on counterattack with horns, hooves, or front teeth or on a combination of counterattack with slow speed flight for anti‐predator defence, reduced maximal running speed would have reduced the ability of a predator to catch up to its prey before the latter could take up a strong defensive position and the predator's ability to evade the prey's counterattack. Lions in the Savuti area of the Chobe National Park, Botswana, prey on both the Cape buffalo (Syncerus caffer) and the giraffe, both of which possess formidable defensive weapons (horns and/or hooves) (Schaller 1972), but have a much higher hunting success rate against the slower Cape buffalo (Joubert 1994).
The above arguments would certainly apply to the extinct mammalian predators that resembled Panthera, Crocuta, or Canis in skeletal morphologies and, presumably, hunting behaviours. The hunting behaviours of the extinct predators, such as the Amphicyoninae (Carnivora) or the Oxyaeninae and the Hyaenodontinae (Creodonta), that were unlike any living carnivoran in their skeletal morphologies are more difficult to reconstruct. However, these predators probably used variations on the ambush and/or pursuit hunting behaviours used by the living carnivorans (Sorkin 2006). Similarly, the extinct herbivores, on which these predators preyed, probably used variations on the flight and/or the counterattack anti‐predator defences used by the living ungulates.
It has been suggested that Pachycrocuta brevirostris, the largest known hyaenid, and Hyainailouros sulzeri, one of the largest known hyaenodontid creodonts, were scavengers, rather than active predators (Turner & Antón 1996; Agustí & Antón 2002). However, among the three living hyaenids with dental and skeletal adaptations for scavenging (the spotted, striped and brown hyenas (Crocuta crocuta, Hyaena hyaena, and Parahyaena brunnea)), the largest (the spotted hyena) is the most active predator (Van Valkenburgh et al. 2003). Not only were Pachycrocuta brevirostris and Hyainailouros sulzeri among the largest members of their respective lineages, but they were also among the largest terrestrial carnivores in their respective habitats (Turner & Antón 1996; Agustí & Antón 2002) and, therefore, were unlikely to have depended on the kills of other predators and carrion for sustenance. Instead, the giant hyaenid and the giant hyaenodontid probably obtained most of their food by active hunting and supplemented it by scavenging (based on Van Valkenburgh et al. 2003).
Therefore, in any lineage of terrestrial mammalian predators there would have, probably, been a strong selective pressure against exceeding the body mass above which members of the lineage could no longer attain the maximal running speed of their smaller relatives. The upper limit on body mass, imposed by this biomechanical constraint, would have depended on the stress set up by the bending moment of the ground reaction force in the humerus of a predator of a given body mass running at the maximal running speed characteristic of its lineage. A lineage of terrestrial mammalian predators with the less stressed humeri would have attained the greater maximal body mass.

Factors affecting bending stress in the humerus

The stress, set up by the bending moment of the ground reaction force in a long bone, is determined by the magnitude of the bending moment and by the cantilever strength of the bone. In a terrestrial mammalian predator of a given body mass running at the maximal running speed characteristic of its lineage, the magnitude of the bending moment would be determined by the length of the moment arm of the ground reaction force, a shorter moment arm resulting in a smaller bending moment and, therefore, lower stress. The moment arm of the ground reaction force acting on the humerus is measured from the distal end of the bone to the point on its shaft, at which the net pull of humeral flexors, which counteract the ground reaction force acting on the forelimb during the first half of the support phase of the stride, is applied (Fig. 1). These muscles include latissimus dorsi, teres major, acromio‐ and spinodeltoids, and ectopectoralis (Reighard & Jennings 1925; Gambaryan 1974, p. 252; Evans & Christensen 1979). The point, at which their net pull is applied, probably lies close to the mid‐shaft of the humerus, but is difficult to pinpoint. How far distally the humeral flexors insert should be indicative of how far distally their net pull is applied. The most distal point of insertion of the humeral flexors in the domestic cat (Felis cattus) is the distal end of the confluence of the deltoid and pectoral ridges (the deltoid tuberosity sensu Crouch & Lackey 1969, plate 16: 2), on which both the acromiodeltoid and the ectopectoralis insert (Reighard & Jennings 1925, fig. 81). The insertion of the humeral flexors in the domestic dog is similar to that in the domestic cat, although the deltoid and pectoral ridges are not clearly marked (Evans & Christensen 1979, figs 4–71, 6–49).
Fig. 1. The moment arm (MA) of the ground reaction force (GRF) acting on the humerus of a running lioness during the first half of the support phase of the forelimb stride. HF – net pull of the humeral flexors.
A given bending moment of the ground reaction force will set up a lower stress in a humerus of greater cantilever strength. The cantilever strength of a long bone is determined, primarily, by the bone's length and mid‐shaft antero‐posterior diameter and by the animal's body mass (Alexander 1977), provided that the bone's marrow cavity diameter/external diameter ratio is independent of body mass. Data from Currey & Alexander (1985, table 1) suggest that for the humerus of terrestrial Carnivora this ratio scales as body mass –0.05. Because of the strong correlation between the mid‐shaft antero‐posterior diameter of long bones, including the humerus, and body mass in a wide variety of terrestrial mammals (Alexander et al. 1979), the scaling relationship between the mid‐shaft antero‐posterior diameter and the length of the humerus within a lineage of terrestrial mammals is indicative of the cantilever strength of the bone at a given body mass in members of that lineage.

Predictions of the proposed hypothesis

In two lineages of terrestrial mammalian predators with deltoid ridges of similar relative lengths, members of the lineage with the shorter and, therefore, the more robust humerus at a given mid‐shaft antero‐posterior diameter would be expected to attain greater body mass than those of the more slender‐boned lineage.
In two lineages of terrestrial mammalian predators with humeri of similar robustness, members of the lineage with the longer deltoid ridge (including the deltoid tuberosity sensu Crouch & Lackey 1969) and, therefore, the shorter moment arm of the ground reaction force relative to the length of the humerus would be expected to attain the greater maximal body mass.
Both of these predictions are based on the assumption that humeral robustness and/or relative length of the deltoid ridge at a given body mass differ significantly between different lineages of terrestrial mammalian predators.

Falsification of the proposed hypothesis

The author has argued above that ecological constraints alone are insufficient to explain all of the observed differences in maximal body masses between different lineages of terrestrial mammalian predators. Yet, it seems entirely plausible that small size or low density of available prey or competition from members of other lineages could have prevented members of a given lineage of terrestrial mammalian predators from reaching the upper limit on their body mass, imposed by the proposed biomechanical constraint, throughout the evolutionary history of that lineage. Therefore, the finding, that members of a lineage of terrestrial mammalian predators attained greater maximal body mass than members of a morphologically similar lineage with the more robust humeri and the deltoid ridges of similar relative lengths or the humeri of similar robustness and the relatively longer deltoid ridges, would not by itself falsify the research hypothesis. Such a finding would be consistent with the hypothesis if paleoecological data suggested that body mass in the latter lineage was limited by ecological constraints throughout its evolutionary history. But, as argued above, ecological constraints alone were unlikely to have limited body mass in the Felidae during the last 7 Ma. Therefore, if members of a lineage of terrestrial mammalian predators morphologically similar to the living big cats with the humeri no more robust and the deltoid ridges no longer (relative to the lengths of the humeri) than those of the Felidae were found to attain greater maximal body mass than the felids, the hypothesis would be falsified.

Materials and methods

Institutional abbreviations

AMNH, F: AM (Frick American Mammals Collection), American Museum of Natural History, New York; FMNH, Field Museum of Natural History, Chicago; both in the USA; KNM, National Museums of Kenya, Nairobi, Kenya.

Data

The data on the interarticular length (between proximal and distal articular surfaces) and the antero‐posterior mid‐shaft diameter of the humerus in the extant species of terrestrial mammalian predators, with the exception of the two subspecies of the tiger (Panthera tigris altaica and P. tigris ssp.), the grey wolf (Canis lupus), and the dhole (Cuon alpinus), were taken from Bertram & Biewener (1990). Data on the latter three extant species and on all the extinct species were collected by the author, as were data on the interarticular length of the humerus and the length of its deltoid ridge/deltopectoral crest.
Interarticular length and antero‐posterior mid‐shaft diameter of the humerus were measured as described in Bertram & Biewener (1990), using a 300 mm digital caliper from ABS Import Tools Inc. (Chino, CA, USA) and a metal rule (for lengths over 310 mm). The length of the deltoid ridge (including the deltoid tuberosity sensu Crouch & Lackey 1969)/deltopectoral crest was measured from the most proximal point on the head of the humerus to the distal end of the ridge/crest only in those specimens in which the latter was clearly marked (Fig. 2). All individuals measured were adults, as indicated by the fusion of the humeral epiphyses to the diaphysis. For the extinct species, the values of humeral dimensions are arithmetic means of the measurements of each dimension in up to four humeri assigned to a particular species. For the extant species, both humeri (when available) were measured in up to five individuals. Humeral dimensions for each individual were averaged and those average values used to calculate the average interarticular length and mid‐shaft antero‐posterior diameter for each species.
Fig. 2. Humeri of terrestrial mammalian predators in anterior view, illustrating measurement of the deltoid ridge/deltopectoral crest length. □C is left, all others are right. The line with arrowheads at both ends represents the length of the deltoid ridge/deltopectoral crest in each specimen. This length was measured by placing one external measuring face of the caliper on the distal end of the deltoid tuberosity sensu Crouch & Lackey (1969) or the distal end of the deltopectoral crest and aligning the other external measuring face with the most proximal point on the head of the humerus, indicated by the horizontal line, while holding the caliper parallel to the shaft of the bone. □A. Panthera tigris female, FMNH 57172, measurements not included in the analysis. □B. Hemphillian Epicyon haydeni, F: AM 67603. □C. Patriofelis ferox, AMNH 1507. □D. Hyainailouros sp., cast of KNM‐ME 20 (R).

Statistical analysis

Interarticular length was plotted as a function of antero‐posterior mid‐shaft diameter of the humerus on log10/log10 axes, with each species represented by a single data point. Linear regression lines and 95% confidence (for the regression line) and prediction (for a single data point) intervals were fitted to the data sets for the ‘Felinae’ (see results for the definition of the group) and the Caninae, using least squares (Model I) analysis. Deltoid ridge/deltopectoral crest length was plotted as a function of interarticular length of the humerus (without logarithmic transformation), and linear regression lines and 95% confidence and prediction intervals were fitted to the data sets for the Felidae and the genus Epicyon. The above statistical analyses were performed in SigmaPlot 2000 for Windows, version 6.00. Slopes and intercepts for the above regression lines were calculated using both the least squares (Model I) and the reduced major axis (Model II) analyses in Microsoft Excel 2000 and are listed in Table 2.

Body mass estimation

With the exception of the ‘Felinae’, the largest members of the lineages used to test the proposed hypothesis are extinct. The maximal body mass (mextinct) attained by an extinct species of terrestrial mammalian predator was estimated using the following equation:
mextinct=mliving×(lextinct/lliving)3
where lextinct is the maximal value of a linear skeletal dimension (‘skeletal dimension used to estimate body mass’ in Table 1) reported in the literature or measured by the author for that species and where lliving and mliving are the maximal reported values of that skeletal dimension and body mass, respectively, for the extant species of Carnivora that it most closely resembled in skeletal morphology and size (‘extant model for the largest known species of the lineage’ in Table 1). The maximal body mass estimates of the largest members of Amphicyoninae, Oxyaeninae, Hyaenodontinae and Borhyaenoidea were rounded off to hundreds of kilograms, while all other body mass estimates were rounded off to tens of kilograms. These estimates are listed in the last column of Table 1, labelled ‘max body mass (kg) of the lineage’.
This method has been previously used to make qualitative body mass estimates (‘size approaching that of a very large bear’, ‘lion‐sized’ and ‘jaguar‐sized’) of Proborhyaena gigantea, Epicyon haydeni, Pachycrocuta brevirostris, Homotherium spp. and Hoplophoneus occidentalis (Marshall 1978; Munthe 1989; Turner & Antón 1996; Turner & Antón 1997; Martin 1998b). Its accuracy depends on the similarity of body shapes and sizes between the extinct species and its extant model because it assumes that the two are isometric to each other (body mass proportional to any linear dimension3.00). Body mass scales as condylobasal skull length 3.13 in terrestrial Carnivora and Dasyuridae (Marsupialia) (Van Valkenburgh 1990) and as humerus length 2.93 and as femur length 2.92 in terrestrial Carnivora (Anyonge 1993). However, with the exception of Sarkastodon mongoliensis and Proborhyaena gigantea, the estimated maximal body masses of the extinct species in Table 1 do not exceed the reported maximal body masses of their extant models by more than a factor of two. Therefore, the assumption of isometry between the extinct species and their extant models probably resulted in an error of no more than ± 10% in the body mass estimates of the former, with the possible exception of the two above species. Given the dissimilarity of the probable body shapes of Sarkastodon mongoliensis, Proborhyaena gigantea, and Megistotherium osteothlastes (inferred from other members of their respective lineages) and of the known body shape of Amphicyon ingens to the body shape of any living carnivoran, any method used to estimate body masses of the largest individuals of these species would yield less reliable results than those for other species in Table 1.

Results

Felidae

Figure 3 shows the plot of humeral length as a function of antero‐posterior diameter in Felidae (genera Felis, Neofelis, Nimravides, Panthera, Pseudaelurus, Smilodon, and Uncia). All felids included in the analysis possessed moderately long (relative to body length) limbs with moderately robust distal segments and digitigrade hind feet (Savage 1977, table 5; Turner & Antón 1997). The data points for members of the genus Smilodon and for the P. spelaea/atrox lineage within the genus Panthera (probably subspecies of P. leo; Kurtén 1985) fall below the 95% prediction intervals for the linear regression line fitted to the data points for the rest of the felid species included in the analysis. This indicates that Smilodon and Panthera spelaea/atrox possessed significantly more robust humeri than the latter (which roughly correspond to the paraphyletic ‘Felinae’ in Martin 1998a). Members of the two lineages of robust‐boned felids are estimated to have attained maximal body masses at least 30% greater than that of the ‘Felinae’ (Table 1).

Predators with dog or hyena‐like body shapes

Figure 4 shows the plot of humeral length as a function of antero‐posterior diameter in the living Canidae (genera Canis, Cuon and Lycaon) and Hyaenidae (genera Crocuta and Hyaena), as well as in a number of extinct carnivorans that resembled them in overall body shape, possessing long (relative to body length) limbs with slender distal segments and digitigrade hind feet (Savage 1977, table 5; Munthe 1989; Turner & Antón 1997; Hunt 1998b). The data points for the members of the genera Epicyon (Canidae, Borophaginae) and Homotherium (Felidae), as well as those for the living Hyaenidae, fall below the 95% confidence intervals for the linear regression line fitted to the data points for the Caninae (Canidae), indicating that the humeri of the former were significantly more robust than that of an average canine canid. In fact, the humeri of Epicyon, Homotherium, and the living Hyaenidae were as robust as those of most felids (Fig. 5), but the deltoid ridges of Epicyon and the living Hyaenidae (represented by the spotted hyena) were significantly shorter than those of the Felidae (Fig. 6). (The distal end of the deltoid ridge was not clearly marked on any of the humeri of the Caninae and Homotherium examined by the author.) Epicyon, Homotherium, and the Hyaenidae are estimated to have attained maximal body masses 50–70% greater than the Caninae, but 40–50% less than the ‘Felinae’ (Table 1).
Fig. 3. Humeral length as a function of antero‐posterior diameter in Felidae.
Fig. 4. Humeral length as a function of antero‐posterior diameter in terrestrial mammalian predators with dog‐ or hyena‐like body shapes.
Fig. 5. Humeral length as a function of antero‐posterior diameter in Epicyon, Hyaenidae, Homotherium, ‘Hemicyon’ ursinus, and ‘Felinae’.
Fig. 6. Length of the deltoid ridge/deltopectoral crest as a function of humeral length in terrestrial mammalian predators.
Members of the genus Plithocyon (Ursidae, Hemicyoninae), to which Hunt (1998b) referred Hemicyon ursinus, are estimated to have attained a maximal body mass similar to those of Epicyon, Homotherium and the Hyaenidae (Table 1). The only complete humerus known for Plithocyon (that of ‘Hemicyon’ ursinus) is significantly less robust than that of an average canine canid (Fig. 4), but has a significantly longer deltoid ridge than those of the three species/chronospecies of Epicyon (Fig. 6).
The skeletal morphologies of the members of the remaining lineages of terrestrial mammalian predators to be considered in this paper were unlike that of any living terrestrial mammalian predator. Nevertheless, these lineages are of great importance to the testing of the proposed hypothesis because they include the largest terrestrial mammalian predators known. The humeral dimensions of the members of these lineages and the estimates of the maximal body masses, they attained, will be compared to those of the Felidae, the lineage that includes the largest living terrestrial mammalian predators.

Predators with a deltopectoral crest

Figure 7 shows the plot of humeral length as a function of antero‐posterior diameter in several lineages of terrestrial mammalian predators that possessed a deltopectoral crest (as described in the Amphicyoninae by Hunt 1998a, fig. 11: 2F), rather than separate deltoid and pectoral ridges, on the humerus. With the exception of the Amphicyoninae (Carnivora, Amphicyonidae, genera Amphicyon, Ischyrocyon, Pliocyon, and Ysengrinia), this resulted in a greater antero‐posterior diameter for a given humeral length than in all other lineages of terrestrial mammalian predators included in the analysis. Members of the lineages of terrestrial mammalian predators that possessed a deltopectoral crest also resembled one another in possessing short (relative to body length) limbs with robust distal segments and plantigrade hind feet (Sinclair 1905; Riggs 1934; Denison 1938; Savage 1977, table 5; Hunt 1998a; Martin 1998b).
Fig. 7. Humeral length as a function of antero‐posterior diameter in terrestrial mammalian predators that possessed a deltopectoral crest and Felidae.
Data points for the Oxyaeninae (Creodonta, Oxyaenidae, genera Oxyaena and Patriofelis) and the Borhyaenoidea (Marsupialia, genera Prothylacynus and Thylacosmilus) with estimated body masses above 25 kg fall farther below the 95% prediction intervals for the linear regression line fitted to the data points for the ‘Felinae’ than do the data points for Smilodon and Panthera spelaea/atrox. This indicates that large oxyaenines and borhyaenoids possessed more robust humeri than any felid. The lengths of the deltopectoral crest in the Oxyaeninae and the Borhyaenoidea were similar to that of the deltoid ridge in the Felidae (Fig. 6). But in Patriofelis ferox, the largest oxyaenine for which the postcranial skeleton is known, the scar on the deltoid (lateral) edge of the deltopectoral crest, on which most of the fibres of the deltoid muscles probably inserted, was located more distally than a similar scar on the deltoid ridge in a felid of comparable size (the tiger) (Fig. 8A, B). (The only known humerus of a borhyaenoid comparable to Patriofelis ferox in size (Thylacosmilus atrox) is too poorly preserved to determine the location of the deltoid scar.) This suggests that the net pull of the humeral flexors was applied more distally and, therefore, the moment arm of the GRF was shorter in the oxyaenine than in a felid with the humerus of the same length. Despite the high degree of uncertainty associated with the maximal body mass estimates for the Oxyaeninae and the Borhyaenoidea in Table 1, it seems certain that the largest members of both lineages exceeded the largest known felids in body mass by at least 30%.
Fig. 8. Left humeri of Panthera tigris, Patriofelis ferox and Amphicyon sp. in lateral view, showing the location of the deltoid scar (DS). □A. Panthera tigris female, FMNH 57172. □B. Patriofelis ferox, AMNH 1507. □C. Amphicyon sp., F: AM 68108.
The largest members of the Amphicyoninae also exceeded the largest known felids in body mass by least 30% (Table 1). Most data points for amphicyonines, including the largest one (Amphicyon ingens), fall within the 95% prediction intervals for the ‘Felinae’, indicating that their humeri were as robust as those of most felids and less robust than those of Smilodon and Panthera spelaea/atrox. But in all amphicyonine species included in the analysis, the deltopectoral crest was significantly longer than the deltoid ridge in an average felid and in A. ingens – significantly longer than the deltoid ridge in any species of the Felidae (Fig. 6). The deltoid scar was also located more distally in Amphicyon than in either a felid or an oxyaenine of comparable size (Fig. 8).

Hyaenodontinae

Figure 9 shows the plot of humeral length as a function of antero‐posterior diameter in Hyaenodontinae (Creodonta, Hyaenodontidae). Both the wolf‐sized (Hyaenodon horridus) and the tiger‐sized (Hyainailouros sp.) members of this lineage, included in the analysis, possessed enormous skulls and short (relative to body length) limbs with moderately robust distal segments and digitigrade hind feet (Mellet 1977; Savage 1977, table 5; Ginsburg 1980). The data point for the largest hyaenodontine species, for which a complete humerus is known (Hyainailouros sp.), falls within the 95% confidence intervals for the linear regression line fitted to the data points for the ‘Felinae’, indicating that its humerus was as robust as that of an average felid and, therefore, less robust than those of Smilodon populator and Panthera atrox. The lengths of the deltoid ridge in the Hyaenodontinae and the Felidae were also similar (Fig. 6). However, the deltoid scar was located more distally in Hyainailouros sp. than in a felid of comparable size (the tiger) (Fig. 10). The largest known hyaenodontine equalled or exceeded the largest known felids in body mass (Table 1).
Fig. 9. Humeral length as a function of antero‐posterior diameter in Hyaenodontinae and ‘Felinae’.
Fig. 10. Right humeri of Panthera tigris and Hyainailouros sp. in lateral view, showing the location of the deltoid scar (DS). □A. Panthera tigris female, FMNH 57172. □B. Hyainailouros sp., cast of KNM‐ME 20 (R).

Discussion

Overall, the results, presented in this paper, agree with the predictions of the proposed hypothesis and justify the assumption, on which those predictions were based. Clearly, humeral robustness and/or relative length of the deltoid ridge/deltopectoral crest at a given body mass differ significantly between many lineages of terrestrial mammalian predators. For instance, both Smilodon fatalis and Panthera spelaea (the smaller of the species of Smilodon and P. spelaea/atrox included in the analysis) had more robust humeri than a very large Hemphillian species of Nimravides, which exceeded the two robust‐boned felids in both the antero‐posterior diameter and the length of the humerus and, probably, body mass (Fig. 3). Therefore, the robustness of the humeri of the even larger Smilodon populator and Panthera atrox was not due to their great size alone, but was also due to these species belonging to lineages within the Felidae that possessed significantly more robust humeri than other felids of the same body mass.
The results confirm the starting observation that, among predators with dog‐ or hyena‐like body shapes, lineages with the more robust humeri attained the greater maximal body masses, although the absence of data on the relative deltoid ridge length in the Caninae and Homotherium prevents the predictions of the proposed hypothesis from being fully tested for this category of predators. As predicted by the research hypothesis, among terrestrial mammalian predators with deltoid ridges of similar relative lengths (Felidae), lineages with the most robust humeri (Smilodon and Panthera spelaea/atrox) attained the greatest maximal body masses. Among terrestrial mammalian predators with humeri of similar robustness (Epicyon, Hyaenidae, ‘Felinae’, and Amphicyoninae), the lineage with the relatively longest deltoid ridge/deltopectoral crest (Amphicyoninae) attained the greatest maximal body mass, greater even than those of the lineages with the more robust humeri, but shorter deltoid ridges (Smilodon and Panthera spelaea/atrox). The Hyaenodontinae, which equalled or exceeded Smilodon and Panthera spelaea/atrox in maximal body mass despite possessing humeri no more robust than those of the rest of the Felidae, also appear to have possessed more distally inserted humeral flexors and, therefore, a shorter moment arm of the ground reaction force than the Felidae. The relatively long deltoid ridge of Plithocyon spp. appears to have ‘compensated’ for their slender humerus, allowing them to attain a maximal body mass similar to those of the more robust‐boned Epicyon spp. and the Hyaenidae. The Oxyaeninae and the Borhyaenoidea possessed more robust humeri and, probably, more distally inserted humeral flexors than Smilodon and Panthera spelaea/atrox and attained greater maximal body masses, again consistent with the predictions of the proposed hypothesis.
Two lineages of terrestrial mammalian predators, Hoplophoneus (Carnivora, Nimravidae) and Thylacosmilus (Marsupialia, Borhyaenoidea), possessed humeri as robust and deltopectoral crests as long as those of the Oxyaeninae and the Borhyaenoidea (Figs 6, 7), yet attained maximal body masses little greater than that of the living jaguar (Panthera onca, Table 1). This does not contradict the proposed hypothesis, because throughout the geographical and temporal ranges of these two lineages of saber‐toothed predators few, if any, species of herbivores weighed more than 1,000 kg (Scott 1937; Owen‐Smith 1988; Martin 1998b). Therefore, available evidence suggests that an ecological constraint (small size of available prey) prevented Hoplophoneus and Thylacosmilus from reaching the limit imposed on their body masses by the proposed biomechanical constraint, as has been proposed for Hoplophoneus and other Late Eocene–Oligocene nimravids of North America by Martin (1998b).

Conclusions

The research results presented in this paper support the hypothesis that increasing stress, set up in the humerus by the bending moment of the peak ground reaction force generated at maximal running speed, imposed an upper limit on body mass in a given lineage of terrestrial mammalian predators. These results also suggest that some lineages of such predators failed to reach those limits throughout their evolutionary histories because of the small size of available prey.

Acknowledgements

I am grateful to my graduate advisor V. L. Naples (Northern Illinois University) for her feedback and encouragement throughout the progress of this work and for her letters of recommendation to museum collection managers; to my former fellow graduate student J. Robins (Southeast Missouri State University) for teaching me to use SigmaPlot; to a former member of my dissertation committee G. T. Schwartz (Arizona State University) for providing me with Model II linear regression analysis software; to R. McN. Alexander (University of Leeds), A. A. Biewener (Harvard University), members of my dissertation committee J. M. Parrish, R. B. King, R. P. Scherer, and D. L. Gebo (Northern Illinois University), and reviewers for Lethaia K. Munthe and S. Viranta for providing valuable suggestions on improving the manuscript. This work forms part of the doctoral dissertation that was submitted to the Department of Biological Sciences of the Northern Illinois University and was supported, in part, by the National Science Foundation Graduate Research Fellowship.

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Volume 41Number 41 December 2008
Pages: 333347

History

Received: 12 January 2007
Accepted: 28 November 2007
Published online: 1 December 2008
Issue date: 1 December 2008

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Boris Sorkin [email protected]
Department of Biology, Appalachian State University, Boone, NC 28608, USA;

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