GAIA N' 15, LlSBONLISBON, DEZEMBROIDECEMBER 1998, pp. 241-255 (ISSN: 0871-5424) STRENGTH INDICATOR VALUES OF THEROPOD LONG BONES, WITH COMMENTS ON LIMB PROPORTIONS AND CURSORIAL POTENTIAL Per CHRISTIANSEN Zoological Museum, Department of Vertebrates. Universitetsparken 15, OK 2100 COPEN HAG EM 0. DENMARK E-mail: [email protected] ABSTRACT: Body mass and strength indicator values of the three hindlimb long bones have been calculated for a large number oftheropod dinosaurs and compared to extant mammals of varying size and locomotory capability_Small to medium sized theropods have strength indicator values comparable to fast-moving ungulates and carnivorans, whereas all large genera have considerably lower strength indicator values, roughly comparable to elephants and hippopotamuses. This suggests that their locomotory potential was reduced compared to the smaller forms. Limb bone ratios of a large number of extant mammals clearly differen­ tiate fast-moving forms, classified from their anatomy as subcursorial or cursorial, from forms capable of less rapid locomotion, classified as graviportal and mediportal. Limb bone ratios for theropods, however, somewhat contradict the above, as all theropods group among subcursorial mammals_ Calculations on estimated peak locomotory performance in­ dicates that even large theropods could have been fast moving without having to include a suspended phase in the stride, thus not subjecting their appendicular anatomy to large amounts of stress, due to their very long limbs. INTRODUCTION However, COOMBS (1978) analyzed a long list of anatomical characters in various tetrapods and Theropod dinosaurs were the only undoubtedly found that a number of these had probably de­ carnivorous terrestrial tetrapods for most of the veloped convergently and were found in all forms ca­ Mesozoic that, at least theoretically, were large and pable of fast locomotion. Thus, he concluded that powerful enough to succesfully hunt the great vari­ they were a prerequisite for fast locomotion, as dis­ ety of herbivorous dinosaurs. As such their ability to played by extant subcursorial and cursorial animals, move fast and hunt succesfully would appear self­ and could be used to identify good running capability evident. Most large extant tetrapod hunters are ei­ in extinct animals. By far most of these characters therfast-moving, such as the Carnivora, or use cryp­ were present in theropods, even large forms, includ­ tic tactics and ambush hunting for catching prey, ing hinge-like joints, long limbs, long and slender such as crocodiles and large snakes. Theropod di­ distal limb elements, greatly reduced fibula, meta­ nosaurs anatomically resembled the former to a tarsals interlocking into a single functional unit, pes much greater extent and thus it would appear likely with median symmetry, loss of outer pedal digits, that they also displayed a similar capability for run­ digitigrade stance and reduced forelimb (bipeds ning and hunting. The gracile nature of small thero­ only). Forelimb reduction is most pronounced pods has never generated much controversy as to among large non-avian theropod taxa, whereas dro­ their running ability. Substantial controversy has maeosaurids, oviraptorosaurs, troodontids, and in arisen, however, as to the locomotory potential of part, ornithomimids, have quite long forelimbs. The large theropods. Although some authors have cred­ hindlimb is still the largest and strongest, however. ited the largest theropods with top speeds of around Non-avian theropods retained just one non­ 20 m.s-' (BAKKER, 1986; PAUL, 1988), they have cursorial trait, a long femur. Unlike birds femoral re­ _most often been considered too large to have been traction was a very important part of forwards pro­ fast-moving and have usually been credited with a pulsion in most forms (PAUL, 1988; GATESY, 1990, walking gait only (e.g. LAMBE, 1917; NEWMAN, 1970; 1991 ). COLINVAUX, 1978; HALSTEAD & HALSTEAD, 1981; THULBORN, 1982; BARSBOLD, 1983). HOLTZ (1994) found that ornithomimids, troodon­ tids, elmisaurids, avimimids and, most importantly, 241 artigos/papers P. CHRISTIANSEN the large to gigantic tyrannosaurids, possessed an lometric trends to extant mammals (CHRISTIANSEN , unusual metatarsal structure, which he termed the 1999c). It is difficultto assess how this would further arctometatarsus, where the third metatarsal is be affected once extinct animals, which lack extant greatly reduced proximally and the three metatar­ anatomical analogs, such as non-avian theropods, sals interlock tightly. In certain arctometatarsalian were included. Still the approximation towards loco­ forms such as Elmisaurus OSM6LSKA (OSM6LSKA, motory dynamic similarity displayed by extant ani­ 1981) and Avimimus KURZANOV (KURZANOV, 1987) mals of widely different sizes and morphology, the distal tarsals and proximal parts of metatarsals suggests that it is reasonable to suppose that this II-IV co-ossify into a tarsometatarsus, a condition wou ld have been the case for dinosaurs also. reminiscent of certain "alvarezsaurid theropods" When an animal moves, forces act on the limbs (BONAPARTE, 1996), although not Mononykus which are proportional to mg, where m is body mass PERLE, NORELL, CHIAPPE & CLARK (PERLE et al., and g is the gravitational constant. Peak stress in the 1994). long bones occur in the middle of a stride, where thJ) The arctometatarsalian genera have a longer greatest fraction of body mass is supported (ALEX­ metatarsus at any given limb length, a trait best inter­ ANDER, 1977a; BIEWENER, 1983), and it is conven­ preted as an adaptation to increased cursoriality, ient to divide the stress into two major components, and HOLTZ (1994) showed that it was not biome­ an axial component, setting up compressive stress chanically weaker despite its increased length. Fur­ in the diaphysis, and a transverse component, act­ thermore, virtually all non-avian theropods ing to distort the diaphysis about its long axis in the possessed a very similar appendicular anatomy parasagittal plane (ALEXANDER, 1977a; 1985; 1989; (BAKKER, 1986; PAUL, 1987, 1988, 1991; GATESY& 1991). MIDDLETON, 1997), and according to the Principle of The compressive stress is proportional to cross Uniformitarianism, this would imply that the large sectional area but is usually much less important theropods should have retained the ability to move than the transverse stress (ALEXANDER, 1989). As fast, albeit probably slower relative to body size the forces acting on the limbs are proportional to mg, (COOMBS, 1978). If an animal is capable of fast loco­ the peak transverse stress in the diaphysis is pro­ motion its limbs must be stronger, at any given size, portional to amgxJZ (ALEXANDER , 1977a, 1983a, than animals which move more slowly. Thus the 1985, 1989 1991; ALEXANDER & POND, 1992), strength of the limb bones constitutes an additional where Z is the section modulus of a cross section of parameter for evaluation of theropod locomotor ca­ bone for bending in a parasagittal plane, and x is the pability. Previously this has only been investigated distance from this cross section to the epiphysis. for very few species, probably due to difficulty of ob­ The value a is the fraction of body mass supported taining the necessary parameters, such as bone di­ by fore and hind limbs respectively, and applies on ly mensions and body mass. to quadrupedal animals. A higher value of Z thus re­ Most extant animals tend to move in a roughly dy­ duces peak stress at any given body mass and simi­ namical fashion when their Froude numbers (v2/gl) lar bone length. As such ALEXANDER (1983a; 1985; are alike, even when comparing animals of such dif­ 1989) argued that the reciprocal value Z/amgx ferent physical appearance as ostriches, humans would be a useful indicator of the ability ufthe bone~ and mammalian quadrupeds varying four orders of to resist mechanical failure, and a high value of magnitude in mass (ALEXANDER, 1976, 1989, 1991; Zlamgx indicates a potential for enhanced physical ALEXANDER & JAYES, 1983), although very small activity. Bone from a variety of extant animals ap­ mammals do not appear to conform to this principle pears not to have different mechanical properties (ALEXANDER, 1991). The Froude number is a dimen­ (BIEWENER, 1982; 1990) so the dimensions of a sionless number relating absolute speed (v) to a lin­ bone section appears to constitute a good measure ear dimension (I), in this case limb length, and for assessing its strength. gravitation (g). Dynamic similarity implies that any In orderforthis to apply to extinct animals one im­ differences between moving animals could be can­ portant, and often overlooked, factor must be ad­ celled out by a constant multiple of the linear dimen­ dressed. All structures, whether biological or man sions, time intervals or forces involved (ALEXANDER made, are constructed with a given factor of safety, & JAYES, 1983). which is the relationship between the yeld stress of However, extant animals are not strictly geomet­ the structure and peak stress experimented. Fortu­ ric in their physical proportions, but scale with in­ nately, among extant biological structures of support creasing allometry as linear dimensions increase the safety factors appearto vary remarkably litte and (e.g. PROTHERO & SERENO, 1982; ECONOMOS , are in the order of 2-4 (ALEXANDER, 1981 ; BIEWE­ 1983; BIEWENER, 1989a, 1989b; BERTRAM & BIEWE­ NER, 1989a, 1989b, 1990). It is not possible to as­ NER, 1990, CHRISTIANSEN, 1999a, 1999b):theropod sess if this was