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1.
SCAPULAR SHAPE AND PRIMATE CLASSIFICATION   总被引:1,自引:0,他引:1  
Certain quantitative features of the primato scapula bear no obvious mechanical relevance to such functions of the bone as are known to be significant in the employment of the forelimb during progression. Statistically these "residual" features are but weakly correlated with those of established locomotor significance and do not show a correspondingly regular pattern of contrast between Primates in different locomotor categories.
These features would, therefore, appear not to be adapted to locomotor function. Consequently, unless they have other functional significance or are linked genetically with other adaptive characters, their parallel variation may indicate genetic relationship. Thus, residual metrical features of this type may be of significance in primate classification. This is in contrast to features of proved locomotor significance whose concurrent appearance in several groups probably represents the result of parallel selection acting in unrelated species.
Eight such features examined in thirty genera (covoring most of the primate order) differentiate significantly between genera within subfamilies and somewhat fewer features differentiate between the components of progressively higher taxonomic groups. But the degree of overlap between genera is such as to minimize the value of individual dimensions in classifying an unknown specimen. It would, however, seem likely that the combination of these dimensions by multivariate techniques might effect a more efficient separation of forms within the primate order.  相似文献   

2.
A background to assessments of the ecological adaptations of fossil primates is the relationship of the detailed shape of bones in living forms to their known locomotor patterns, and this has been here attempted for the shoulder. Within the locomotion of the primates the function of the shoulder varies according to the extent to which the trunk is suspended by the arms. An analysis of the differences in the shoulder muscles has shown that much of their quantitative variation is mechanically in phase with these functional differences. A series of features of the shoulder bones, chosen because of their association with the mechanically meaningful features of the musculature, have been found to vary (a) in association with the known contrasts in locomotion and (b) in such a way as to render more efficient mechanically the associated muscular structure. Investigation of bony dimensions “residual” to such a study has shown that they are not highly correlated with primate locomotion but are, in contrast, associated with the commonly accepted taxonomic grouping of the order. The combination by discriminant functions of such sets of “locomotor” and “residual” dimensions reveals unsuspected information for living primates and might well allow more precise definition of the functional and taxonomic status of a fossil. The experimental testing of functional inferences from morphology is a necessary part of such studies, and preliminary reports of experimental stress analysis utilising the photoelastic technique confirm and reinforce their validity.  相似文献   

3.
One trait that distinguishes the walking gaits of most primates from those of most mammalian nonprimates is the distribution of weight between the forelimbs and hindlimbs. Nonprimate mammals generally experience higher vertical peak substrate reaction forces on the forelimb than on the hindlimb. Primates, in contrast, generally experience higher vertical peak substrate reaction forces on the hindlimb than on the forelimb. It is currently unclear whether this unusual pattern of force distribution characterizes other primate gaits as well. The available kinetic data for galloping primates are limited and present an ambiguous picture about peak-force distribution among the limbs. The present study investigates whether the pattern of forelimb-to-hindlimb force distribution seen during walking in primates is also displayed during galloping. Six species of primates were video-recorded during walking and galloping across a runway or horizontal pole instrumented with a force-plate. The results show that while the force differences between forelimb and hindlimb are not significantly different from zero during galloping, the pattern of force distribution is generally the same during walking and galloping for most primate species. These patterns and statistical results are similar to data collected during walking on the ground. The pattern of limb differentiation exhibited by primates during walking and galloping stands in contrast to the pattern seen in most nonprimate mammals, in which forelimb forces are significantly higher. The data reported here and by Demes et al. ([1994] J. Hum. Evol. 26:353-374) suggest that a relative reduction of forelimb vertical peak forces is part of an overall difference in locomotor mechanics between most primates and most nonprimate mammals during both walking and galloping.  相似文献   

4.
Univariate and multivariate study of 22 dimensions describing overall body proportions in 34 primate genera, has shown that these quantities effect a separation between the principal taxonomic divisions of the Primates: Prosimii, Ceboidea, Cercopithecoidea and Hominoidea. The last three do not, however, link to form a single unit, and the separation between the Ceboidea and Cercopithecoidea is imperfect. Some grouping within these major divisions appears, in certain aspects, to be of functional (locomotor), rather than of purely taxonomic, significance. For instance, within the Prosimii, the genera Microcebus, Galago and Tarsius (the two latter being saltatory forms, while leaping is a component of the locomotor pattern of the first) are associated, while within the apes, the Asiatic forms Hylobates, Symphalangus and Pongo (all brachiators) tend to be grouped, as also do the African forms Pan and Gorilla (both, to a large extent, secondarily terrestrial in habit).
The measures especially prominent in effecting this pattern of discrimination are: relative foot length, relative lower limb length and length of foot relative to lower limb length.
Similar, if less clearly defined results emerge if groups of dimensions relating to individual body regions (forelimb, hindlimb, head and trunk) are analysed separately.
The apparent failure of compounds of the measures of the limbs to give an anticipated close reflection of locomotor function stems possibly from the fact that the available dimensions are of an overall nature rather than a reflection of specific biomechanical functions. Such sub-division, according with locomotor pattern as seems to emerge from this study, appears, in fact, to be little more than that implied in current taxonomic schemata.  相似文献   

5.
Primate appendicular limb bones were measured on the cross-sectional geometry at the mid-length of the humerus and femur and on the external dimensions of long bones of the same individuals. Cross sections were directly measured by means of computer tomography or direct sectioning. The morphometry of bones and locomotor behaviour is discussed from the viewpoint of the functional differentiation between the fore- and hindlimbs. The primate group which daily adopted a relatively terrestrial locomotor type demonstrates robust forelimb bones compared with the group which adopted a fully arboreal locomotor type. In contrast, the arboreal group showed relatively large and long hindlimb bones. The difference resembled the previously reported comparison between terrestrial and arboreal groups among wholly quadrupedal mammals. Humans were more similar to the arboreal group than to the terrestrial group. Parameters of the cross-sectional geometry showed a slightly positive allometry in total primate species. Slopes of the parameters were explained by the influence of muscle force.  相似文献   

6.
Postcranial limb bones were compared among primates of different locomotor types. Seventy-one primate species, in which all families of primates were included, were grouped into nine locomotor types. Osteometrical data on long bones and data on the cross-sectional geometry of the humerus and the femur were studied by means of allometric analysis and principal component analysis. Relatively robust forelimb bones were observed in the primate group which adopted the relatively terrestrial locomotor type compared with the group that adopted the arboreal locomotor type. The difference resembled the previously reported comparison between terrestrial and arboreal groups among all quadrupedal mammals. The degree of arboreality in daily life is connected with the degree of hindlimb dominance, or the ratio of force applied to the fore- and hindlimb in positional behaviour and also with the shape, size and robusticity of limb bones.  相似文献   

7.
The aberrant features of the genus Daubentonia, such as the superficially rodent-like dentition, the globose and foreshortened brain case, and the filiform third manual digit have long been known. But the current assessment of the genus as lemuriform, and within that group as closest to the indriids, depends upon greater weight being placed upon other characteristics such as the cranial arterial pattern, the molariform teeth, and the developmental characteristics of the dentition. Prior multivariate morphometric studies have shown that though the shoulder structure of Daubentonia is uniquely different from that of all other primates, the structure of its pelvis may not be especially different from that of many relatively non-specialized primates. A large series of studies have been summated here in which many different anatomical regions (shoulder, arm, forearm, forelimb as a whole, pelvis, femur, hindlimb as a whole, forelimb and hindlimb combined, and total bodily proportions including limbs, trunk, and head) have been characterized osteometrically in a wide range of primate genera. The resulting data sets have been studied by discriminant function analyses. The differences that have been found are large enough that it can be confidently asserted that in its postcranial skeleton, Daubentonia is more different from the primates as a whole than is any other primate genus. These differences are big enough that their statistical and biological significance is not at all in doubt, notwithstanding the very small numbers of available specimens of this rare genus. They are so great that functional implications exist though they cannot, in our present state of knowledge of the habits of the genus, be ascribed with any certainty. They are so great indeed, paralleling the enormous differences of Daubentonia from other primates in its dentition, skull and cheiridia, that we may prefer to keep open minds about its taxonomic placement.  相似文献   

8.
Among the characteristics that are thought to set primate quadrupedal locomotion apart from that of nonprimate mammals are a more protracted limb posture and larger limb angular excursion. However, kinematic aspects of primate or nonprimate quadrupedal locomotion have been documented in only a handful of species, and more widely for the hind than the forelimb. This study presents data on arm (humerus) and forelimb posture during walking for 102 species of mammals, including 53 nonhuman primates and 49 nonprimate mammals. The results demonstrate that primates uniformly display a more protracted arm and forelimb at hand touchdown of a step than nearly all other mammals. Although primates tend to end a step with a less retracted humerus, their total humeral or forelimb angular excursion exceeds that of other mammals. It is suggested that these features are components of functional adaptations to locomotion in an arboreal habitat, using clawless, grasping extremities.  相似文献   

9.
Several features that appear to differentiate the walking gaits of most primates from those of most other mammals (the prevalence of diagonal-sequence footfalls, high degrees of humeral protraction, and low forelimb vs. hindlimb peak vertical forces) are believed to have evolved in response to requirements of locomotion on thin arboreal supports by early primates that had developed clawless grasping hands and feet. This putative relationship between anatomy, behavior, and ecology is tested here by examining gait mechanics in the common marmoset (Callithrix jacchus), a primate that has sharp claws and reduced pedal grasping, and that spends much of its time clinging on large trunks. Kinematic and kinetic data were collected on three male Callithrix jacchus as they walked across a force platform attached to the ground or to raised horizontal poles. The vast majority of all walking gaits were lateral-sequence. For all steps, the humerus was retracted (<90 degrees relative to a horizontal axis) or held in a neutral (90 degrees ) position at forelimb touchdown. Peak vertical forces on the forelimb were always higher than those on the hindlimb. These three features of the walking gaits of C. jacchus separate it from any other primate studied (including other callitrichids). The walking gaits of C. jacchus are mechanically more similar to those of small, nonprimate mammals. The results of this study support previous models that suggest that the unusual suite of features that typify the walking gaits of most primates are adaptations to the requirements of locomotion on thin arboreal supports. These data, along with data from other primates and marsupials, suggest that primate postcranial and locomotor characteristics are part of a basal adaptation for walking on thin branches.  相似文献   

10.
The distribution of peak vertical forces between the forelimbs and the hind limbs is one of the key traits distinguishing primate quadrupedal locomotion from that of other mammals. Whereas most mammals generate greater peak vertical forelimb forces, primates generate greater peak vertical hind limb forces. At the ultimate level, hind limb dominance in limb force distribution is typically interpreted as an adaptation to facilitate fine-branch arboreality. However, the proximate biomechanical bases for primate limb force distribution remain controversial. Three models have been previously proposed. The Center of Mass (COM) Position model attributes primates’ unique mode of limb loading to differences in the position of the whole-body COM relative to the hands and feet. The Active Weight Shift model asserts that primates actively redistribute body weight to their hind limbs by pitching the trunk up via the activation of hind limb retractor muscles. Finally, the Limb Compliance model argues that primates selectively mitigate forelimb forces by maintaining a compliant forelimb and a flat shoulder trajectory. Here, a detailed dataset of ontogenetic changes in morphology and locomotor mechanics in Bolivian squirrel monkeys (Saimiri boliviensis) was employed as a model system to evaluate each of these proposed models in turn. Over the first 10 months of life, squirrel monkeys transitioned from forelimb dominant infants to hind limb dominant juveniles, a change that was precipitated by decreases in peak vertical forelimb forces and increases in peak vertical hind limb forces. Results provided some support for all three of the models, although the COM Position and Active Weight Shift models were most strongly supported by the data. Overall, this study suggests that primates may use a variety of biomechanical strategies to achieve hind limb dominance in limb force distribution.  相似文献   

11.
The musculature of the shoulder, arm, and forearm was studied in 19 genera of squirrels, representing the Pteromyinae (flying squirrels) and all 7 tribes of the Sciurinae (tree and ground squirrels). The objective was to locate derived anatomical features of functional or phylogenetic significance and to determine how much morphological variation underlies the diverse locomotor behavior of squirrels, which includes terrestrial and arboreal bounding, climbing, digging, and gliding. The fossil evidence suggests that arboreality is primitive for squirrels, and in fact tree squirrels appear to represent the primitive sciurid morphology. Ground squirrels are less uniform and exhibit a few derived features, including a clavobrachialis muscle not seen in other squirrels. Pygmy tree squirrels, which have evolved independently in three tribes, exhibit convergence of forelimb anatomy, including the loss or reduction of several muscles in the shoulder and forearm. The forelimb anatomy of flying squirrels is the most derived and differs from that of tree squirrels in details of shoulder, arm, and forearm musculature. Some of these muscular differences among squirrels have phylogenetic significance, being shared by closely related genera, but none has significance above the tribal level. Many of the differences suggest a variety of changes in function that are amenable to further study. J. Morphol. 234:155–182, 1997. © 1997 Wiley-Liss, Inc.  相似文献   

12.
Most analyses on allometry of long bones in terrestrial mammals have focused on dimensional allometry, relating external bone measurements either to each other or to body mass. In this article, an analysis of long bone mass to body mass in 64 different species of mammals, spanning three orders of magnitude in body mass, is presented. As previously reported from analyses on total skeletal mass to body mass in terrestrial vertebrates, the masses of most appendicular bones scale with significant positive allometry. These include the pectoral and pelvic girdles, humerus, radius+ulna, and forelimb. Total hindlimb mass and the masses of individual hindlimb bones (femur, tibia, and metatarsus) scale isometrically. Metapodial mass correlates more poorly with body mass than the girdles or any of the long bones. Metapodial mass probably reflects locomotor behavior to a greater extent than do the long bones. Long bone mass in small mammals (<50 kg) scales with significantly greater positive allometry than bone mass in large (>50 kg) mammals, probably because of the proportionally shorter long bones of large mammals as a means of preserving resistance to bending forces at large body sizes. The positive allometric scaling of the skeleton in terrestrial animals has implications for the maximal size attainable, and it is possible that the largest sauropod dinosaurs approached this limit.  相似文献   

13.
A comparative study of the forelimbs of the semifossorial prairie dog, Cynomys gunnisoni , and the scansorial tree squirrel, Sciurus niger, was focused on the musculoskeletal design for digging in the former and climbing in the latter. Based on lever arm mechanics, it was expected that the forelimb of the prairie dog would show features appropriate to the production of relatively large forces and that of the fox squirrel to relatively great velocity. Force and lever arm measurements were made of select forelimb muscles at the shoulder, elbow, and wrist joints for a series of angles in both species. Contraction time and fatigue indexes were determined for the same forelimb muscles. Contrary to expectation, in the few cases in which significant (P less than .05) differences were found, the forces, lever arms, and torques (force times its lever arm) were greater in the smaller fox squirrel. The observed variation in the torques produced fits the demands on the forelimb during climbing and digging as estimated from films. Several forelimb muscles of the fox squirrel show significantly higher mean contraction times than do the homologous muscles of the prairie dog. There were no significant differences between the two species in the fatigability of the selected forelimb muscles, although the mean fatigue index was always higher (less fatigable muscle) in the prairie dog. Similarities in the forelimbs of these two sciurids suggest that only minor modifications may have been required of the ancestral forelimb in order for descendent forms to operate successfully as climbers and diggers .  相似文献   

14.
Hominoids and lorines are assumed to possess greater shoulder mobility than other primates. This assumption is based on morphological characteristics of the shoulder, rather than on empirical data. However, recent studies have shown that the glenohumeral joint of hominoids is not more mobile than that of other primates (Chan LK. 2007. Glenohumeral mobility in primates. Folia Primatol (Basel) 78(1):1–18), and the thoracic shape of hominoids does not necessarily promote shoulder mobility (Chan LK. 2007. Scapular position in primates. Folia Primatol (Basel) 78(1):19–35). Moreover, lorines differ significantly from hominoids in both these features, thus challenging the assumption that both hominoids and lorines have greater shoulder mobility. The present study aims to test this assumption by collecting empirical data on shoulder mobility in 17 primate species. Passive arm circumduction (a combination of glenohumeral and pectoral girdle movement) was performed on sedated subjects (except humans), and the range measured on the video images of the circumduction. The motion differed among primate species mostly in the craniodorsal directions, the directions most relevant to the animal's ability to brachiate and slow climb. Hylobatids possessed the highest craniodorsal mobility among all primate species studied. However, nonhylobatid hominoids did not have greater craniodorsal mobility than arboreal quadrupedal monkeys, and lorines did not have greater craniodorsal mobility than arboreal quadrupedal prosimians. Nonhylobatid hominoids and lorines had similar craniodorsal mobility, but this was due to a longer clavicle, more dorsal scapula, and lower glenohumeral mobility in the former, and a shorter clavicle, less dorsal scapula, and greater glenohumeral mobility in the latter. This study provides evidence for the reexamination of the brachiation, slow climbing, and vertical climbing hypotheses. Am J Phys Anthropol, 2008. © 2008 Wiley‐Liss, Inc.  相似文献   

15.
Forelimb morphology is an indicator for terrestrial locomotor ecology. The limb morphology of the enigmatic tapir (Perissodactyla: Tapirus) has often been compared to that of basal perissodactyls, despite the lack of quantitative studies comparing forelimb variation in modern tapirs. Here, we present a quantitative assessment of tapir upper forelimb osteology using three‐dimensional geometric morphometrics to test whether the four modern tapir species are monomorphic in their forelimb skeleton. The shape of the upper forelimb bones across four species (T. indicus; T. bairdii; T. terrestris; T. pinchaque) was investigated. Bones were laser scanned to capture surface morphology and 3D landmark analysis was used to quantify shape. Discriminant function analyses were performed to reveal features which could be used for interspecific discrimination. Overall our results show that the appendicular skeleton contains notable interspecific differences. We demonstrate that upper forelimb bones can be used to discriminate between species (>91% accuracy), with the scapula proving the most diagnostic bone (100% accuracy). Features that most successfully discriminate between the four species include the placement of the cranial angle of the scapula, depth of the humeral condyle, and the caudal deflection of the olecranon. Previous studies comparing the limbs of T. indicus and T. terrestris are corroborated by our quantitative findings. Moreover, the mountain tapir T. pinchaque consistently exhibited the greatest divergence in morphology from the other three species. Despite previous studies describing tapirs as functionally mediportal in their locomotor style, we find osteological evidence suggesting a spectrum of locomotor adaptations in the tapirs. We conclude that modern tapir forelimbs are neither monomorphic nor are tapirs as conserved in their locomotor habits as previously described. J. Morphol. 277:1469–1485, 2016. © 2016 Wiley Periodicals, Inc.  相似文献   

16.
The internal organization of myofibers and connective tissues has important physiologic implications for muscle function and for naturalistic behavior. In this study of forelimb muscle morphology and primate locomotion, fiber architecture is examined in the intrinsic muscles of the shoulder (musculi deltoideus, infraspinatus, supraspinatus, subscapularis, teres major, and t. minor) and arm (m. coracobrachialis, biceps brachii, brachialis, and triceps brachii) in the semiterrestrial vervets (Chlorocebus aethiops) and arboreal red-tailed guenons (Cercopithecus ascanius). Wet weights and lengths of whole muscles, lengths of fasciculi and their associated proximal and distal tendons, and angles of pinnation were measured to estimate morphologic correlates of physiologic properties of individual muscles: force, velocity/excursion, energy expense, and relative isometric or isotonic contraction. Neither mean total-shoulder:total-arm ratios for muscle mass nor total reduced physiological cross-sectional area exhibited significant (P < 0.05) interspecific differences, thus emphasizing the importance of fine-tuning musculoskeletal analyses by the data collected here. The results generally support those previously published for quadriceps femoris and triceps surae of the hind limb in these species (Anapol and Barry [1996] Am. J. Phys. Anthropol. 99:429-447). The fiber architecture of the semiterrestrial vervets is largely suited for higher velocity while running on the ground. By contrast, the architectural configuration of red-tailed monkeys implies relatively isometric muscle contraction and passive storage of elastic strain energy for exploitation of the compliant canopy, where substrate components are situated beneath the sagittal plane of the animal. With respect to relative distribution of maximum potential force output among muscles of either shoulder or arm groups in these otherwise hind limb-dominated quadrupedal primates, statistically significant interspecific differences are best interpreted in light of braking, climbing, and, for vervets, the transition between ground and canopy.The interspecific differences shown here for the intrinsic muscles of the shoulder and arm underscore the significance of intramuscular morphology in reconciling structure and function with regard to locomotor behavior. Its analysis and interpretation lend support to consideration of "semiterrestrial" as a bona fide locomotor category uniquely different from what is practiced by dedicated arboreal and terrestrial quadrupeds that occasionally visit the habitat of one another. Data from a more committed terrestrial species would clarify this enigma.  相似文献   

17.
It is often claimed that the walking gaits of primates are unusual because, unlike most other mammals, primates appear to have higher vertical peak ground reaction forces on their hindlimbs than on their forelimbs. Many researchers have argued that this pattern of ground reaction force distribution is part of a general adaptation to arboreal locomotion. This argument is frequently used to support models of primate locomotor evolution. Unfortunately, little is known about the force distribution patterns of primates walking on arboreal supports, nor do we completely understand the mechanisms that regulate weight distribution in primates. We collected vertical peak force data for seven species of primates walking quadrupedally on instrumented terrestrial and arboreal supports. Our results show that, when walking on arboreal vs. terrestrial substrates, primates generally have lower vertical peak forces on both limbs but the difference is most extreme for the forelimb. We found that force reduction occurs primarily by decreasing forelimb and, to a lesser extent, hindlimb stiffness. As a result, on arboreal supports, primates experience significantly greater functional differentiation of the forelimb and hindlimb than on the ground. These data support long-standing theories that arboreal locomotion was a critical factor in the differentiation of the forelimbs and hindlimbs in primates. This change in functional role of the forelimb may have played a critical role in the origin of primates and facilitated the evolution of more specialized locomotor behaviors.  相似文献   

18.
The forelimb joints of terrestrial primate quadrupeds appear better able to resist mediolateral (ML) shear forces than those of arboreal quadrupedal monkeys. These differences in forelimb morphology have been used extensively to infer locomotor behavior in extinct primate quadrupeds. However, the nature of ML substrate reaction forces (SRF) during arboreal and terrestrial quadrupedalism in primates is not known. This study documents ML-SRF magnitude and orientation and forelimb joint angles in six quadrupedal anthropoid species walking across a force platform attached to terrestrial (wooden runway) and arboreal supports (raised horizontal poles). On the ground all subjects applied a lateral force in more than 50% of the steps collected. On horizontal poles, in contrast, all subjects applied a medially directed force to the substrate in more than 75% of the steps collected. In addition, all subjects on arboreal supports combined a lower magnitude peak ML-SRF with a change in the timing of the ML-SRF peak force. As a result, during quadrupedalism on the poles the overall SRF resultant was relatively lower than it was on the runway. Most subjects in this study adduct their humerus while on the poles. The kinetic and kinematic variables combine to minimize the tendency to collapse or translate forelimbs joints in an ML plane in primarily arboreal quadrupedal primates compared to primarily terrestrial quadrupedal ones. These data allow for a more complete understanding of the anatomy of the forelimb in terrestrial vs. arboreal quadrupedal primates. A better understanding of the mechanical basis of morphological differences allows greater confidence in inferences concerning the locomotion of extinct primate quadrupeds.  相似文献   

19.
20.
The cross-sectional properties of mammalian limb bones provide an important source of information about their loading history and locomotor adaptations. It has been suggested, for instance, that the cross-sectional strength of primate limb bones differs from that of other mammals as a consequence of living in a complex arboreal environment (Kimura, 1991, 1995). In order to test this hypothesis more rigorously, we have investigated cross-sectional properties in samples of humeri and femora of 71 primate species, 30 carnivorans and 59 rodents. Primates differ from carnivorans and rodents in having limb bones with greater cross-sectional strength than mammals of similar mass. This might imply that primates have stronger bones than carnivorans and rodents. However, primates also have longer proximal limb bones than other mammals. When cross-sectional dimensions are regressed against bone length, primates appear to have more gracile bones than other mammals. These two seemingly contradictory findings can be reconciled by recognizing that most limb bones experience bending as a predominant loading regime. After regressing cross-sectional strength against the product of body mass and bone length, a product which should be proportional to the bending moments applied to the limb, primates are found to overlap considerably with carnivorans and rodents. Consequently, primate humeri and femora are similar to those of nonprimates in their resistance to bending. Comparisons between arboreal and terrestrial species within the orders show that the bones of arboreal carnivorans have greater cross-sectional properties than those of terrestrial carnivorans, thus supporting Kimura's general notion. However, no differences were found between arboreal and terrestrial rodents. Among primates, the only significant difference was in humeral bending rigidity, which is higher in the terrestrial species. In summary, arboreal and terrestrial species do not show consistent differences in long bone reinforcement, and Kimura's conclusions must be modified to take into account the interaction of bone length and cross-sectional geometry.  相似文献   

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