Scaling of the appendicular skeleton of the giraffe (Giraffa camelopardalis)

Giraffes have remarkably long and slender limb bones, but it is unknown how they grow with regard to body mass, sex, and neck length. In this study, we measured the length, mediolateral (ML) diameter, craniocaudal (CC) diameter and circumference of the humerus, radius, metacarpus, femur, tibia, and metatarsus in 10 fetuses, 21 females, and 23 males of known body masses. Allometric exponents were determined and compared. We found the average bone length increased from 340 ± 50 mm at birth to 700 ± 120 mm at maturity, while average diameters increased from 30 ± 3 to 70 ± 11 mm. Fetal bones increased with positive allometry in length (relative to body mass) and in diameter (relative to body mass and length). In postnatal giraffes bone lengths and diameters increased iso‐ or negatively allometric relative to increases in body mass, except for the humerus CC diameter which increased with positive allometry. Humerus circumference also increased with positive allometry, that of the radius and tibia isometrically and the femur and metapodials with negative allometry. Relative to increases in bone length, both the humerus and femur widened with positive allometry. In the distal limb bones, ML diameters increased isometrically (radius, metacarpus) or positively allometric (tibia, metatarsus) while the corresponding CC widths increased with negative allometry and isometrically, respectively. Except for the humerus and femur, exponents were not significantly different between corresponding front and hind limb segments. We concluded that the patterns of bone growth in males and females are identical. In fetuses, the growth of the appendicular skeleton is faster than it is after birth which is a pattern opposite to that reported for the neck. Allometric exponents seemed unremarkable compared to the few species described previously, and pointed to the importance of neck elongation rather than leg elongation during evolution. Nevertheless, the front limb bones and especially the humerus may show adaptation to behaviors such as drinking posture. J. Morphol. 276:503–516, 2015. © 2014 Wiley Periodicals, Inc.     

Primate limb bones and locomotor types in arboreal or terrestrial environments

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.     

Fabricational morphology of oblique ribs in bivalves

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.     

Body size, locomotion, and long bone cross-sectional geometry in indriid primates.

The geometry of the midshaft cross-sections of the femur and humerus of five indriid species was analysed. Internal (marrow cavity) and external diameters were measured on X-rays in the anteroposterior (a-p) and mediolateral (m-l) planes; cross-sectional areas, second moments of area, and section moduli were calculated using formulae for a hollow ellipse. Cortical thickness, robusticity indices (relating external diameters to the length of the bones), and a-p/m-l shape variables were also calculated. Model II regression was supplemented by analyses of correlation between size and shape. Indriids are saltatory, i.e., their locomotion is dominated by the hind limbs. Accordingly, the femur is more rigid than the humerus, and it shows a consistent difference between the a-p and m-l planes in measures related to bending strength. Cortical thickness varies considerably both within and across species. The type specimen of the new species Propithecus tattersalli is virtually indistinguishable from P. verreauxi on the basis of its long bone cross-sectional geometry. Femoral robusticity is uncorrelated with size, but humeral robusticity decreases significantly with increasing size. Femoral shape variables (a-p/m-l) are all negatively correlated with body size, indicating that m-l dimensions of the femur increase at a faster rate than do a-p dimensions. The highly loaded plane of movement seems to be more reinforced in the smaller species. Contrary to static biomechanical scaling predictions of positive allometry, all cross-sectional parameters scale relatively close to isometry. It is concluded that either changes in locomotor performance must compensate for the weight-related increase in forces and moments or that the larger-bodied animals operate appreciably closer to the limits of their safety margins.     

On birds: scale effects in the neognath hindlimb and differences in the gross morphology of wings and hindlimbs

Scale effects on whole limb morphology (i.e. bones together with in situ overlying muscles) are well understood for the neognath forelimb. However, scale effects on neognath gross hindlimb morphology remain largely unexplored. To broaden our understanding of avian whole limb morphology, I investigated the scaling of hindlimb inertial properties in neognath birds, testing empirical scaling relationships against the model of geometric similarity. Inertial property data – mass, moment of inertia, centre of mass distance, and radius of gyration – were collected from 22 neognath species representing a wide range of locomotor specializations. When scaled against body mass, hindlimb inertial properties scale with positive allometry. Thus, in terms of morphology, larger bodied neognaths possess hindlimbs requiring disproportionately more energy to accelerate and decelerate relative to body mass than smaller bodied birds. When scaled against limb length, hindlimb inertial properties scale according to isometry. In the subclade Land Birds (sensu Hackett et al.), hindlimb inertial properties largely scale according to positive allometry. The contrasting results of positive allometry vs. isometry in neognaths are due to how hindlimb length scales against body mass. Negative allometry of hindlimb inertial properties, which would reduce terrestrial locomotion costs, would probably make the hindlimb susceptible to mechanical failure or too diminutive for its many ecological functions. Comparing the scaling relationships of wings and hindlimbs highlights how locomotor costs influence the scaling of limb inertial properties. © 2013 The Linnean Society of London, Biological Journal of the Linnean Society, 2013, 110 , 14–31.     

Differentiation between fore- and hindlimb bones and locomotor behaviour in primates

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.     

Scale Effects between Body Size and Limb Design in Quadrupedal Mammals

Recently the metabolic cost of swinging the limbs has been found to be much greater than previously thought, raising the possibility that limb rotational inertia influences the energetics of locomotion. Larger mammals have a lower mass-specific cost of transport than smaller mammals. The scaling of the mass-specific cost of transport is partly explained by decreasing stride frequency with increasing body size; however, it is unknown if limb rotational inertia also influences the mass-specific cost of transport. Limb length and inertial properties – limb mass, center of mass (COM) position, moment of inertia, radius of gyration, and natural frequency – were measured in 44 species of terrestrial mammals, spanning eight taxonomic orders. Limb length increases disproportionately with body mass via positive allometry (length ∝ body mass^0.40); the positive allometry of limb length may help explain the scaling of the metabolic cost of transport. When scaled against body mass, forelimb inertial properties, apart from mass, scale with positive allometry. Fore- and hindlimb mass scale according to geometric similarity (limb mass ∝ body mass^1.0), as do the remaining hindlimb inertial properties. The positive allometry of limb length is largely the result of absolute differences in limb inertial properties between mammalian subgroups. Though likely detrimental to locomotor costs in large mammals, scale effects in limb inertial properties appear to be concomitant with scale effects in sensorimotor control and locomotor ability in terrestrial mammals. Across mammals, the forelimb''s potential for angular acceleration scales according to geometric similarity, whereas the hindlimb''s potential for angular acceleration scales with positive allometry.     

Scaling of long bones in ruminants with respect to the scapula

The significance of the scapula for locomotion is becoming more and more established. Studies of locomotion in small and medium‐sized mammals show a considerable amplitude of the scapula and a large contribution to step length. Taking this into account, long bone studies of forelimb movement restricted to the ‘arm’ miss one important segment. A regression model (reduced major axis) was used for analysis of a sample of 77 species of ruminants. This sample was divided according to (1) phylogenetic relationships and (2) habitat. The proximal elements of the limbs, scapula and humerus in the anterior extremity, femur in the hindlimb, show a similar scaling in the different analyses. The changes to limb proportions in the different subsamples are caused by the variability of the distal segments. The anterior extremity scales with a higher coefficient than the hindlimb in all analyses. Concepts like elastic or geometric similarity are inadequate for long bone scaling when the full range of body size in the sample is used. Taking all analyses into account, the differences in limb proportions are due more to phylogenetic relationships than to habitat.     

Allometry of cetacean forelimb bones

This study examines the allometric scaling relationships of the cetacean humerus, radius, and ulna. Bone lengths and diameters were measured for 20 species of odontocete and three species of mysticete cetaceans, representing eight of the nine extant cetacean families. The scaling of individual bone proportions (bone length vs. cranio-caudal diameter, bone length vs. dorso-ventral diameter), and of individual bone dimensions against estimated body mass, are compared to models of geometric and elastic similarity. The geometric similarity model describes the scaling relationship of bone length vs. cranio-caudal diameter and body mass vs. cranio-caudal diameter for the humerus only; geometric similarity also describes the scaling relationship of body mass vs. bone length for all three bones. None of the scaling relationships fits the elastic similarity model. The scaling relationships of bone length vs. dorso-ventral diameter for all three bones, and bone length vs. cranio-caudal diameter for the radius and ulna, exhibit negative allometry, indicating that large bones are less robust than small bones. Negative allometry of structural support elements has not been previously described for terrestrial mammals or plants. The high relative swimming speeds of small delphinids may generate sufficient stresses to require more robust bones relative to those of larger whales. © 1994 Wiley-Liss, Inc.     

Curvature, length, and cross-sectional geometry of the femur and humerus in anthropoid primates

The aims of this study were to describe the curvature of anthropoid limb bones quantitatively, to determine how limb bone curvature scales with body mass, and to discuss how bone curvature influences static measures of bone strength. Femora and humeri in six anthropoid genera of Old World monkeys, New World monkeys, and gibbons were used. Bone length, curvature, and cross-sectional properties were incorporated into the analysis. These variables were obtained by a new method using three-dimensional morphological data reconstructed from consecutive CT images. This method revealed the patterns of curvature of anthropoid limb bones. Log-transformed scaling analyses of the characters revealed that bone length and especially bone curvature strongly reflected taxonomic/locomotor differences. As compared with Old World monkeys, New World monkeys and gibbons in particular have a proportionally long and less curved femur and humerus relative to body mass. It is also revealed that the section modulus relative to body mass varies less between taxonomic/locomotor groups in anthropoids. Calculation of theoretical bending strengths implied that Old World monkeys achieve near-constant bending strength in accordance with the tendency observed in general terrestrial mammals. Relatively shorter bone length and larger A-P curvature of Old World monkeys largely contribute to this uniformity. Bending strengths in New World monkeys and gibbons were, however, a little lower under lateral loading and extremely stronger and more variable under axial loading as compared with Old World monkeys, due to their relative elongated and weakly curved femora and humeri. These results suggest that arboreal locomotion, including quadrupedalism and suspension, requires functional demands quite dissimilar to those required in terrestrial quadrupedalism.     

Ontogenetic and individual variation in size, shape and speed in the Australian agamid lizard Amphibolurus nuchalis

The present study investigates relationships among size, shape and speed in the Australian agamid lizard Amphibolurus nuchalis . Maximal running speed, body mass, snout-vent length, tail length, fore- and hind limb spans and thigh muscle mass were measured in 68 field-fresh individuals spanning the entire ontogenetic size range (1.3 48 g). Relative lengths of both foreand hind limbs decrease with increasing body mass (= negative allometry), whereas relative tail length and thigh muscle mass increase with body mass (= positive allometry). Repeatable and significant differences in maximal running speed exist among individuals. Maximal running speed scales as (body mass)^0.161, and 59% of the variation in maximal speed was related to body mass. Based on the results of the present and previous studies, data on scaling of body proportions alone appear inadequate to infer scaling relationships of functional characters such as top speed.
Surprisingly, individual variation in maximal speed is not related to individual variation in shape (relative limb, tail and body lengths). These components of overall shape are not independent; individuals tended to have either relatively long or relatively short limbs, tails and bodies for their body mass. Even the significant difference in multivariate shape between adult males and females has no measurable consequences for maximal speed. Speeds of field-fresh animals did not vary on a seasonal basis, and eight weeks of captivity had no effect on maximal running speeds. Gravid females and long-term (obese) captive lizards were both approximately 12% slower than field-fresh lizards.     

Comparative limb bone scaling in turtles: Phylogenetic transitions with changes in functional demands?

Several terrestrial vertebrate clades include lineages that have evolved nearly exclusive use of aquatic habitats. In many cases, such transitions are associated with the evolution of flattened limbs that are used to swim via dorsoventral flapping. Such changes in shape may have been facilitated by changes in limb bone loading in novel aquatic environments. Studies on limb bone loading in turtles found that torsion is high relative to bending loads on land, but reduced compared to bending during aquatic rowing. Release from torsion among rowers could have facilitated the evolution of hydrodynamically advantageous flattened limbs among aquatic species. Because rowing is regarded as an intermediate locomotor stage between walking and flapping, rowing species might show limb bone flattening intermediate between the tubular shapes of walkers and the flattened shapes of flappers. We collected measurements of humeri and femora from specimens representing four functionally divergent turtle clades: sea turtles (marine flappers), softshells (specialized freshwater rowers), emydids (generalist semiaquatic rowers), and tortoises (terrestrial walkers). Patterns of limb bone scaling with size were compared across lineages using phylogenetic comparative methods. Although rowing taxa did not show the intermediate scaling patterns we predicted, our data provide other functional insights. For example, flattening of sea turtle humeri was associated with positive allometry (relative to body mass) for the limb bone diameter perpendicular to the flexion-extension plane of the elbow. Moreover, softshell limb bones exhibit positive allometry of femoral diameters relative to body mass, potentially helping them maintain their typical benthic position in water by providing additional weight to compensate for shell reduction. Tortoise limb bones showed positive allometry of diameters, as well as long humeri, relative to body mass, potentially reflecting specializations for resisting loads associated with digging. Overall, scaling patterns of many turtle lineages appear to correlate with distinctive behaviors or locomotor habits.     

Postnatal long bone growth in terrestrial placental mammals: Allometry,life history,and organismal traits

The ontogenetic allometry of long bone proportions is poorly understood in Mammalia. It has previously been suggested that during mammalian ontogeny long bone proportions grow more slender (positive allometry; length ∝ circumference^>1.0), although this conclusion was based upon data from a few small‐bodied taxa. It remains unknown how ontogenetic long bone allometry varies across Mammalia in terms of both taxonomy and body size. We collected long bone length and circumference data for ontogenetic samples of 22 species of mammals spanning six major clades and three orders of magnitude in body mass. Using reduced major axis bivariate regressions to compare bone length to circumference, we found that isometry and positive allometry are the most widespread patterns of growth across mammals. Negative allometry (i.e., bones growing more robust during ontogeny) occurs in mammals but is largely restricted to cetartiodactyls. Using regression slope as a proxy for long bone allometry, we compared long bone allometry to life history and organismal traits. Neonatal body mass, adult body mass, and growth rate have a negative relationship with long bone allometry. At an adult mass of roughly 15–20 kg, long bone growth shifts from positive allometry to mainly isometry and negative allometry. There were no significant relationships between ontogenetic long bone allometry and either cursoriality or basal metabolic rate. J. Morphol. © 2012 Wiley Periodicals, Inc.     

Energetic benefits and adaptations in mammalian limbs: Scale effects and selective pressures

Differences in limb size and shape are fundamental to mammalian morphological diversity; however, their relevance to locomotor costs has long been subject to debate. In particular, it remains unknown if scale effects in whole limb morphology could partially underlie decreasing mass‐specific locomotor costs with increasing limb length. Whole fore‐ and hindlimb inertial properties reflecting limb size and shape—moment of inertia (MOI), mass, mass distribution, and natural frequency—were regressed against limb length for 44 species of quadrupedal mammals. Limb mass, MOI, and center of mass position are negatively allometric, having a strong potential for lowering mass‐specific locomotor costs in large terrestrial mammals. Negative allometry of limb MOI results in a 40% reduction in MOI relative to isometry's prediction for our largest sampled taxa. However, fitting regression residuals to adaptive diversification models reveals that codiversification of limb mass, limb length, and body mass likely results from selection for differing locomotor modes of running, climbing, digging, and swimming. The observed allometric scaling does not result from selection for energetically beneficial whole limb morphology with increasing size. Instead, our data suggest that it is a consequence of differing morphological adaptations and body size distributions among quadrupedal mammals, highlighting the role of differing limb functions in mammalian evolution.     

Sagittal long bone curvature in birds

The maximum sagittal curvature of the long bones (humeras, radius, ulna, femur, tibiotarsus and tarsometatarsus) of 45 specimens of birds, belonging to 36 species, was measured and regressed to the corresponding body mass. Mathematical results show a tendency of curvature to scale with strong positive allometry. Within the species studied, those with more characteristic flapping flight tend to show relatively low values of curvature in the wing bones. To check the agreement of the present results with current hypotheses on the origin of long bone curvature, previous results on scaling of myological and cross-sectional parameters in birds are considered. Indirect evidence suggests that curvature tends to increase bone stresses. Hypotheses that consider curvature as a consequence of the mechanical action of muscle allocation and optimization of functional strains are discussed at length. The possible double genetic-epigenetic determinism of the curvature character is evoked.     

Allometry and curvature in the long bones of quadrupedal mammals

The allometric relationships between basic structural proportions in long bones are examined in the humerus, radius, femur and tibia for a diverse group of 42 terrestrial quadrupedal mammals that span a size range from 0.02–6000 kg. Non-linear scaling is found for length vs. diameter in the tibia and radius, suggesting that the mechanical constraints on the skeleton differ within large and small body-size mammals. Curvature normalized to mid-shaft radius scales differently in the different long bones. Curvature is poorly related to size in the proximal limb bones (humerus and femur) while it decreases systematically with size in the tibia (mass exponent −0.13). The scaling of normalized curvature in the radius is unique among long bones. Variability of curvature in the radius is reduced at any size in comparison to that found in the other long bones. Normalized curvature is constant within the small body size group (0.02 to approximately 100 kg) while it decreases sharply with size within animals over 100 kg body mass. The unusual scaling found in the radius is probably the result of this bone's close alignment with the extrinsic forces which act on it during locomotion. The change in scaling within the radius for animals of different size may be indicative of more general size-dependent mechanical trade-offs which are masked by the complex loading circumstances of the other long bones.     

金丝猴长骨的异速生长研究

文章利用14副成年金丝猴骨架(包括滇金丝猴Rhinopithecus bieti;黔金丝猴R.brelichi)对其长骨与体重间的异速生长进行了分析研究。结果表明,在金丝猴的生长发育过程中,前肢的生长速度大于后肢。这种形态特征与金丝猴在运动过程中攀爬垂直支撑物相联系。从肢间指数和生长系数看,金丝猴的前后肢与其它灵长类相比较,相对于体重来说比较短。这是在树上攀缘过程中使重心更接近支撑攀物和使身体稳定的一种适应。对躯干长(STL),肱骨、桡骨、股骨和胫骨经多维变量分析说明了金丝猴的长骨与体重之间的关系,长骨的结构特征与狮尾狒(Theropithecus)、狒狒(Papio)、叶猴(Presbytis)、猕猴(Mcaaca)及长鼻猴(Nasalis)更为接近。在金丝猴的运动特征上,我们据此推测,它们有一部分时间在地上活动,但休息、睡觉、寻食及逃避敌害等时在树上。因此,在运动中,跳跃、臂摆荡和悬吊不是它们的主要运动方式。     

The scaling of skeletal microanatomy in non-human primates

The study of scale-correlated changes in the external dimensions and cross-sectional geometry of primate long bones is fundamental to our understanding of primate limb bone structural adaptation. To date, however, there have been no studies of the effects of mechanical loading on patterns of skeletal scaling at the microstructural level. To remedy this, we analysed patterns of microanatomical scaling in the humeri and femora of 107 adult primates belonging to the families Galagonidae and Cercopithecidae. Seven species were included in our analysis. Proximal, midshaft, and distal sections of humeri and femora of each individual were examined and secondary osteonal and cortical area were measured. Secondary osteonal area scales positively allometrically with cortical cross-sectional area and with body mass. This pattern holds generally for humeri and femora—both within and across families. However, there are striking dissimilarities in the relative strengths of the allometric coefficients for humeri and femora measured for different families. These distinctions appear to be related to differences in the ways in which fore- and hindlimbs are loaded. Such differences highlight the promise of microstructural data and the importance of examining the confounding effects of locomotory behaviour in studies of skeletal scaling.     

The relative growth of the limb bones forHomo sapiens —As compared to anthropoid apes

For comparison with previously defined relative long bone lengths of growing anthropoid apes, the relative size increase of the raduus/humerus, tibia/femur and leg/arm lengths forHomo sapiens were determined. Results indicate thatHomo follows other Hominoidea during postnatal growth, maintaining general isometric patterns of relative long bone size increase within the proximal and distal segments of each limb. Variation between genera is primarily proportional, withHomo showing the relatively shortest radii and shorter tibae throughout growth. Between limbsHomo displays specializations toward disproportional increases of the lower limb, suggesting size required allometry for facilitative support. This research was partially supported by NIDR fellowship No. T-32-DE07047.     

Salient features in the locomotion of proboscideans revealed via the differential scaling of limb long bones

The standard differential scaling of proportions in limb long bones (length against circumference) was applied to a phylogenetically wide sample of the Proboscidea, Elephantidae and the Asian (Elephas maximus) and African (Loxodonta africana) elephants. In order to investigate allometric patterns in proboscideans and terrestrial mammals with parasagittal limb kinematics, the computed slopes between long bone lengths and circumferences (slenderness exponents) were compared with published values for mammals, and studied within a framework of the theoretical models of long bone scaling under gravity and muscle forces. Limb bone allometry in E. maximus and the Elephantidae is congruent with adaptation to bending and/or torsion induced by muscular forces during fast locomotion, as in other mammals, whereas the limb bones in L. africana appear to be adapted for coping with the compressive forces of gravity. Hindlimb bones are therefore more compliant than forelimb bones, and the resultant limb compliance gradient in extinct and extant elephants, contrasting in sign to that of other mammals, is shown to be a new important locomotory constraint preventing elephants from achieving a full‐body aerial phase during fast locomotion. Moreover, the limb bone pattern of African elephants, indicating a noncritical bone stress not increasing with increments in body weight, explains why their mean and maximal body masses are usually above those for Asian elephants. Differences in ecology may be responsible for the subtle differences observed in vivo between African and Asian elephants, but they appear to be more pronounced when revealed via mechanical patterns dictated by limb bone allometry. © 2010 The Linnean Society of London, Biological Journal of the Linnean Society, 2010, 100 , 16–29.