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.     

Skeletal allometry and interlimb scaling patterns in mustelid carnivorans

To address the effects of an evolutionary increase in body size on long bone skeletal allometry, scaling patterns relating body mass, bone length, limb length, midshaft diameters, and cross-sectional properties of the humerus and femur were analyzed for four species of scansorial mustelids. Humeral and, to a lesser extent, femoral allometry is consistent with expectations of elastic similarity: bone and limb length scale with negative allometry on body mass while bone robusticity (cross-sectional parameters against bone length) scales with strong positive allometry. Differences between fore- and hindlimb scaling patterns, however, are observed, with size-dependent increases in forelimb length and humeral strength and robusticity exceeding those of the hindlimb and femur. It is hypothesized that this greater fore- than hindlimb lengthening results in postural modifications that serve to straighten the hindlimb of larger bodied scansorial mustelids relative to smaller mustelids. Straightening of hindlimb joints would more precisely align the long axis of the femur with peak (vertical) ground reaction forces, thereby accounting for the reduction in relative bending stresses acting on the femur compared to the humerus. J. Morphol. 235:121–134, 1998. © 1998 Wiley-Liss, Inc.     

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.     

Post-hatching growth and development of the pectoral and pelvic limbs in the black noddy, Anous minutus

The black tern (Anous minutus) uses a semi-precocial growth strategy. Terrestrial locomotor capacity occurs soon after hatching, but pectoral limb development is delayed and flight is not possible until about post-hatching day 50. A growth series (hatchlings to fledglings) was used to explore how limb musculoskeletal development varied with body mass. In the pelvic limb, bone lengths scaled isometrically or with negative allometry. Gastrocnemius muscle mass and the failure load and stiffness of the tibiotarsus scaled isometrically. In the pectoral limb, pectoralis and supracoracoideus muscle masses increased with strong positive allometry that was mirrored by increases in wing bone strength and stiffness. Bending strength (sigma(ult)) and modulus (E) remained fairly constant throughout development to fledging for all limb bones. The moment of inertia (I) scaled with negative allometry for the tibiotarsus and with strong positive allometry in the wing bones. Differences in sigma(ult) and E of the tibiotarsus between pre-fledged chicks and adults was due, primarily, to increases in bone density rather than increases in the moment of inertia of the skeletal elements, whereas sigma(ult) of wing bones was a function of increases in both bone density and I. Early development of functional pelvic limbs in tree-nesting birds is relatively unusual, and presumably reflects a familial trait that does not appear to compromise breeding success in this species.     

Post-hatching growth and development of the pectoral and pelvic limbs in the black noddy, Anous minutus.

The black tern (Anous minutus) uses a semi-precocial growth strategy. Terrestrial locomotor capacity occurs soon after hatching, but pectoral limb development is delayed and flight is not possible until about post-hatching day 50. A growth series (hatchlings to fledglings) was used to explore how limb musculoskeletal development varied with body mass. In the pelvic limb, bone lengths scaled isometrically or with negative allometry. Gastrocnemius muscle mass and the failure load and stiffness of the tibiotarsus scaled isometrically. In the pectoral limb, pectoralis and supracoracoideus muscle masses increased with strong positive allometry that was mirrored by increases in wing bone strength and stiffness. Bending strength (sigma(ult)) and modulus (E) remained fairly constant throughout development to fledging for all limb bones. The moment of inertia (I) scaled with negative allometry for the tibiotarsus and with strong positive allometry in the wing bones. Differences in sigma(ult) and E of the tibiotarsus between pre-fledged chicks and adults was due, primarily, to increases in bone density rather than increases in the moment of inertia of the skeletal elements, whereas sigma(ult) of wing bones was a function of increases in both bone density and I. Early development of functional pelvic limbs in tree-nesting birds is relatively unusual, and presumably reflects a familial trait that does not appear to compromise breeding success in this species.     

Modern humans are not (quite) isometric

Allometric relationships are important sources of information for many types of anthropological and biological research. The baseline for all allometric relationships is isometry (or geometric similarity), the principal that shape is invariant of size. Here, we formally test for geometric similarity in modern humans, looking at the maximum lengths of four long bones (humerus, radius, femur, and tibia). We use Jolicoeur's multivariate allometry method to examine globally distributed samples of human populations, both collectively and individually. Results indicate that humans are not geometrically similar, although morphological deviations from isometry are small.     

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.     

Mechanics of locomotion and jumping in the horse (Equus): in vivo stress in the tibia and metatarsus

Principal stresses acting in the midshaft cortices of the tibia and metatarsus of the horse were determined from in vivo rosette strain gauge recordings for overground locomotion at different gaits, as well as for jumping and acceleration. Bone stresses were correlated with limb kinematics and ground reaction forces. The results for these two hind limb bones were compared to earlier determinations of locomotor stress in the forelimb radius and metacarpus (Biewener, Thomason & Lanyon, 1983b). Peak stresses generally increased with increasing speed; however, because of greater bending, stresses in the tibia were substantially higher (45%) than in the metatarsus over the range of steady state speeds. Bending of the tibia resulted from significant off-axis loading by the ground reaction force. In contrast, the metatarsus was loaded in compression due to its close alignment with the ground reaction force. Peak stresses as high as - 53 MPa (caudal cortex) in the tibia and -38 MPa (plantar cortex) in the metatarsus acted at a canter. Increased skeletal stress was matched by a corresponding increase in ground reaction force and a decrease in hind limb duty factor. In both bones, peak stresses were significantly greater and differed in their distribution during jumping and acceleration, compared to peak stresses during steady speed locomotion. Maximal values of - 126 MPa (cranial cortex) in the tibia and - 117 MPa (dorsal cortex) in the metatarsus were developed during jumping. These stresses are similar in magnitude to those reported for a range of different sized mammals during strenuous activity and correspond to a safety factor to yield failure of 1.5 to 3. Though generally consistent within an individual bone, the distribution and magnitude of stresses varied about 20% among individuals. This variation was greater for the metatarsus because of its lesser curvature, which diminishes the bone's ability to control for bending in a fixed direction.     

太行山猕猴第Ⅶ颈椎变量的异速生长分析

以肱骨最大长为参照,对成年太行山猕猴第Ⅶ颈椎变量进行了异速生长分析。结果表明,椎体后高、椎体上矢径、全宽呈正异速生长;椎体下横径接近等速生长;椎体前高、椎体下矢径、椎体上横径、椎孔矢径、椎孔横径、矢径呈负异速生长。     

On the allometry of long bones in dogs (Canis familiaris)

The allometric relations of diameter and length of humerus, ulna, femur, and tibia of 108 specimens, from 63 different breeds of dogs and 12 specimens of wolves, were calculated by means of model II of regression or major axis method. Only for the tibia were the values of wolves included in the cluster formed for dog breeds. Consequently, separate lines of regression were calculated for the other bones. Results agree in general with the exponents predicted by the theory of geometric similarity; however, the slope obtained for femur (0.865) differed significantly from this. Morphology of the long bones of the legs does not differentiate dogs and wolves; this probably reflects secondary convergence among wolves with relatively modern breeds of dogs.     

Allometry between length and cross-sectional dimensions of the femur and tibia in Homo sapiens sapiens

Allometric equations relating length and cross-sectional geometric properties of the femur and tibia are generated using skeletal remains from three recent human population samples. Approximate isometry, or geometric similarity, is found both within and between samples. Cross-sectional areas scale to approximately length2, while second moments of area scale to approximately length4. It is shown that this is consistent with the maintenance of equivalent mechanical stress in long bones of different length under dynamic loadings in vivo. Other evidence indicates that bending and torsional loadings are more critical than axial loadings in the determination of lower limb bone cross-sectional dimensions.     

Skeletal growth and function in the California gull (Larus californicus)

Although the bones of rapidly growing animals are composed of weak tissue, they often must function in locomotor activity. We address the conflict between development and skeletal function by analysing the ontogeny of skeletal strength in the California gull, Larus californicus. Changes in shape and mechanical properties of the femur, tibia, tarsometatarsus, humerus, ulna and carpometacarpus were analysed in a complete post-hatching growth series. During post-hatching growth, strength and stiffness of the skeletal tissue increases six- to ten-fold. At hatching, long bones of the wing are relatively weak and they remain so throughout the major portion of the growth period. However, in the hind limb, relatively thick bones in juveniles compensate for the weak tissue such that the force required to break the bones remains constant relative to body mass. This difference between hind limb and wing parallels the development of locomotor function; young gulls begin to walk within a day or two of hatching, but they do not fly until they are fully grown. Thus, in the bones of the hind limb, the conflict between rapid growth and skeletal function is solved by negative allometry of bone thickness.
After young gulls reach adult size, the breaking strength of the wing bones increases three- to four-fold, the mass of the pectoralis muscle triples and the surface area of the wing doubles. The one aspect of wing development that is not delayed until shortly before fledging is linear growth of the bones. Bones of the wing increase in length at a rapid and relatively constant rate from the time of hatching to the attainment of adult size. Relatively early initiation of linear growth of the wing bones suggests that the rate at which bones grow in length may be the rate limiting factor in wing development.     

Mathematical modeling of appendicular bone growth in glaucous‐winged gulls

Development of locomotor activity is crucial in tetrapods. In birds, this development leads to different functions for hindlimbs and forelimbs. The emergence of walking and flying as very different complex behavior patterns only weeks after hatching provides an interesting case study in animal development. We measured the diaphyseal lengths and midshaft diameters of three wing bones (humerus, ulna, and carpometacarpus) and three leg bones (femur, tibiotarsus, and tarsometatarsus) of 79 juvenile (ages 0–42 days) and 13 adult glaucous‐winged gulls (Larus glaucescens), a semiprecocial species. From a suite of nine alternative mathematical models, we used information‐theoretic criteria to determine the best model(s) for length and diameter of each bone as a function of age; that is, we determined the model(s) that obtained the best tradeoff between the minimized sum of squared residuals and the number of parameters used to fit the model. The Janoschek and Holling III models best described bone growth, with at least one of these models yielding an R² ≥ 0.94 for every dimension except tarsometatarsus diameter (R² = 0.87). We used the best growth models to construct accurate allometric comparisons of the bones. Early maximal absolute growth rates characterize the humerus, femur, and tarsometatarsus, bones that assume adult‐type support functions relatively early during juvenile development. Leg bone lengths exhibit more rapid but less sustained relative growth than wing bone lengths. Wing bone diameters are initially smaller than leg bone diameters, although this relationship is reversed by fledging. Wing bones and the femur approach adult length by fledging but continue to increase in diameter past fledging; the tibiotarsus and tarsometatarsus approach both adult length and diameter by fledging. In short, the pattern of bone growth in this semiprecocial species reflects the changing behavioral needs of the developing organism. J. Morphol., 2009. © 2008 Wiley‐Liss, Inc.     

Sizing the Jurassic theropod dinosaur Allosaurus: assessing growth strategy and evolution of ontogenetic scaling of limbs

Allosaurus is one of the most common Mesozoic theropod dinosaurs. We present a histological analysis to assess its growth strategy and ontogenetic limb bone scaling. Based on an ontogenetic series of humeral, ulnar, femoral, and tibial sections of fibrolamellar bone, we estimate the ages of the largest individuals in the sample to be between 13-19 years. Growth curve reconstruction suggests that maximum growth occurred at 15 years, when body mass increased 148 kg/year. Based on larger bones of Allosaurus, we estimate an upper age limit of between 22-28 years of age, which is similar to preliminary data for other large theropods. Both Model I and Model II regression analyses suggest that relative to the length of the femur, the lengths of the humerus, ulna, and tibia increase in length more slowly than isometry predicts. That pattern of limb scaling in Allosaurus is similar to those in other large theropods such as the tyrannosaurids. Phylogenetic optimization suggests that large theropods independently evolved reduced humeral, ulnar, and tibial lengths by a phyletic reduction in longitudinal growth relative to the femur.     

Residual stress distribution in rabbit limb bones

The presence of the residual stresses in bone tissue has been noted and the authors have reported that there are residual stresses in bone tissue. The aim of our study is to measure the residual stress distribution in the cortical bone of the extremities of vertebrates and to describe the relationships with the osteon population density. The study used the rabbit limb bones (femur, tibia/fibula, humerus, and radius/ulna) and measured the residual stresses in the bone axial direction at anterior and posterior positions on the cortical surface. The osteons at the sections at the measurement positions were observed by microscopy. As a result, the average stresses at the hindlimb bones and the forelimb bones were 210 and 149 MPa, respectively. In the femur, humerus, and radius/ulna, the residual stresses at the anterior position were larger than those at the posterior position, while in the tibia, the stress at the posterior position was larger than that at the anterior position. Further, in the femur and humerus, the osteon population densities in the anterior positions were larger than those in the posterior positions. In the tibia, the osteon population density in the posterior position was larger than that in the anterior position. Therefore, tensile residual stresses were observed at every measurement position in the rabbit limb bones and the value of residual stress correlated with the osteon population density (r=0.55, P<0.01).     

Bone length and muscle weight in mice subjected to genetic selection for the relative length of the tibia and radius

Mice which had undergone 5 generations of selection for high and low values of the tibia length/radius length ratio were compared with unselected controls at 10 weeks of age. The ratio responded to selection in both directions. The length of the radius was increased in the low line while the response in the high line was due to an increase in the length of the tibia and a small but statistically insignificant decrease in radius length. High and low line mice were heavier than the controls. The responses of the tibia and femur and of the radius and humerus were generally similar, suggesting the existence of an association between the genetic control of the lengths of the bones of a limb. There were also correlated responses in the weight of the tibialis anterior, biceps brachii and sternomastoid, and there is some evidence to suggest that the weight of a muscle may be influenced by the length of a bone to which it is attached.     

Analyzing ungulate long bones as a tool for habitat reconstruction

The long bones (humerus, radius, metacarpus, femur, tibia, metatarsus) of 51 extant bovid and 7 equid specimens were measured in order to test the hypothesis that they show adaptations to different habitats. We performed factor analyses (FAs) with principal component extraction method and plotted the extracted factors (Fs) in simple scatterplots. The preferred habitats (grassland, forest, mountainous regions) were labeled in the plots, and our results show three clearly separated clusters for F2 vs. F3. According to our interpretation, F1 reflects the body size of the specimens while F2 is most probably reflecting cursorial adaptations. F3 is largely affected by dimensional bone characteristics adapted to maneuver in the environment, and therefore, F3 is somehow linked to habitat. The investigated equids are plotting within the cluster of bovids preferring grassland habitats, which is surprising because of different constructions of the metapodials in perissodactyls and ruminants. Performed linear discriminant analyses (LDAs) are supporting our FA results. This approach combines biometrics with statistics and presents a tool, which easily can be applied helping to identify the paleo-habitat or the paleo-ecology of extinct bovids with implications on fossil localities.     

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.     

Postcranial variations in late Epigravettian and Neolithic human remains from Arene Candide cave (Liguria,Italy)

Late Epigravettian postcranial human remains from the Arene Candide cave (Finale Ligure, Savona, Italy) were compared with the Neolithic sample found in the upper levels of the same site. Data on length, diaphyseal circumference and diameter of clavicle, humerus, radius, femur and tibia were collected from male specimens having all these bones. The Epigravettian sample is characterized by significantly greater tibial length, robustness and platycnemia, significantly lower circumferences in the upper limb bones and the clavicle, and a high degree of asymmetry. Variations observed in lower limb bones are those expected on the basis of the different functional requirements of a hunting and gathering economy compared to a more sedentary, food producing economy. Differences in the upper limb bones and the clavicle are less explicable. However, considering that in spite of a more slender structure, the Epigravettian bones show evidence of vigorous use, variation in upper limb could result from qualitatively different involvements.     

Fine mapping dissects pleiotropic growth quantitative trait locus into linked loci

A recurring issue in studies of quantitative trait loci (QTLs) is whether QTLs that appear to have pleiotropic effects are indeed caused by pleiotropy at single loci or by linked QTLs. Previous work identified a QTL that affected tail length in mice and the lengths of various bones, including the humerus, ulna, femur, tibia, and mandible. The effect of this QTL on tail length has since been found to be due to multiple linked QTLs and so its apparently pleiotropic effects may have been due to linked QTLs with distinct effects. In the present study we examined a line of mice segregating only for a 0.94-Mb chromosomal region known to contain a subset of the QTLs influencing tail length. We measured a number of skeletal dimensions, including the lengths of the skull, mandible, humerus, ulna, femur, tibia, calcaneus, metatarsus, and a tail bone. The QTL region was found to have effects on the size of the mandible and length of the tail bone, with little or no effect on the other traits. Using a randomization approach, we rejected the null hypothesis that the QTL affected all traits equally, thereby demonstrating that the pleiotropic effects reported earlier were due to linked loci with distinct effects. This result underlines the possibility that seemingly pleiotropic effects of QTLs may frequently be due to linked loci and that high-resolution mapping will often be required to distinguish between pleiotropy and linkage.