The body axis of vertebrates is an integrated cylinder of bones, connective tissue, and muscle. These structures vary among living and extinct vertebrates in their orientation, composition, and function in ways that render useless simplistic models of the selective pressures that may have driven the evolution of the axis. Instead, recent experimental work indicates that the vertebrate axis serves multiple mechanical functions simultaneously: bending the body, storing elastic energy, transmitting forces from limbs, and ventilating the lungs. On the biochemical level, research on human intervertebral discs has shown that collagens resist tension and torsion while proteoglycans bind water to resist compression. This molecular behavior predicts mechanical behavior of the entire joint, which, in turn helps determine the mechanical behavior of the vertebral column. The axial skeleton, in turn, is reconfigured by axial muscles that work by way of three-dimensional connective tissues that derive mechanical advantage for the muscle force by using the skin to increase leverage. Models may eventually help determine which evolutionary changes in the vertebrate body axis have had important functional and possibly adaptational consequences. Current reconstruction of the hypothetical stem lineage of early chordates and vertebrates suggests that the gradual mineralization of the vertebral elements, appearance of fin rays and new median fins, and transverse and then horizontal segmentation of the axial musculature are all features correlated with increases in swimming speed, maneuverability, and body size.

Soft-bodied animals are an answer to the problem, solved for each species over evolutionary time, to design a cylindrical, motile machine composed of pliant polymeric materials (collagen and glycoproteins) and actuated by a contractile polymer (actomyosin).

The vertebrate body is a cylindrical set of pliant collagenous membranes. Axial notochords and backbones occur where membranes intersect. The basis for all vertebrate architecture is the collagen fiber that best functions to resist tension. Axial compressive forces in notochords and backbones occur as tensile stresses in collagen fibers in intervertebral discs and zygapohyseal ligaments. Bone provides local stiffening where muscles pull. Large muscle masses apply large forces via tendons thus allowing for leverage in the function of axes of bodies and appendages. Although isolated species in invertebrate phyla have notochord- or backbone-like structures, only echinoderms and vertebrates have a central axis to resist axial compression. Design is a useful tool in forming scientific hypotheses.

The notochord can play an important mechanical role in shape changes during early morphogenesis of vertebrates. For example, osmotic inflation of notochords elongates and straightens the axis of frog early tail-bud embryos. In Xenopus laevis, the sheath of cross-helically arranged fibers around the notochord limits the shape changes it undergoes when inflating, causing the notochord to stiffen and straighten (Adams et al., 1990; Koehl et al., 1990). We used physical models of stage 24 X. laevis notochords to explore the mechanical consequences of different arrangements of the sheath fibers on the behavior of such curved hydraulic cylinders. All the models straightened upon inflation regardless of initial fiber angle (θ = angle of the fibers to long axis of the cylinder). Notochord models with θ > 54° lengthened and narrowed as they straightened; although they could push, the forces they exerted were limited by their tendency to buckle, which increased the greater the θ. In contrast, models with θ < 54° shortened and widened as they straightened and showed pronounced increases in flexural stiffness. The mean θ of X. laevis early tail-bud notochords is 54°, a fiber angle that permits an increase in the end-to-end distance of the model (along the anterior-posterior axis of the embryo) as it straightens and pushes when pressurized, but that is less prone to Euler and local buckling than are models with higher θ's. Nonetheless, a θ of 54° in notochords may simply be the result of osmotic swelling.

This paper reviews our current understanding of the relationship between the structures and properties of the tissues of the spine and their mechanical functions. Emphasis is on the human lumbar spine. Vertebrae consist of a core of cancellous bone (low density) surrounded by a shell of cortical bone (high stiffness); as a result they have high stiffness but low mass. The intervertebral disc is able to withstand compression because of the swelling pressure exerted by the nucleus pulposus which is constrained, radially, by the annulus fibrosus. Thus the disc acts as a thick-walled pressure vessel. Collagen fibers within the annulus provide reinforcement during compression, bending and torsion of the disc. Collagen fibers also provide tensile reinforcement and prevent tears spreading across ligaments. The ligamenta flava contain elastic fibers (low stiffness and low strength) with collagen fibers (high stiffness and high strength). In the unstretched ligamenta flava, the collagen fibers have almost random orientations but they become aligned as the ligament is stretched. This structure enables the high extensibility of elastic fibers to be exploited but protects them from damage at high strains. The structure of the interspinous ligament suggests that its main function is to attach the thoracolumbar fascia to the posterior spine. Thus the fascia is maintained in tension when stretched by the abdominal muscles. This and other observations indicate the importance of muscles for maintaining the stability of the spinal column.

The nucleus of the intervertebral disc in humans shows the most dramatic changes with age of any cartilaginous tissue. It originates from the notochord. In the foetus and infant, the nucleus contains actively dividing and biosynthetically active notochordal cells. The proteoglycans and other matrix components produced have a high osmotic pressure, imbibe water and maintain a hydrated structure which, though it has little mechanical strength, has a high swelling pressure which maintains disc turgor. In some species, the notochordal cells and the mucoid nucleus pulposus persist throughout adult life. However by about 4 yr of age in humans, the notochordal cells have disappeared to be replaced by those of chondrocytic appearance but of unknown origin. These cells continue to produce proteoglycans but also synthesize significant amounts of collagen. The nucleus becomes firmer and less hydrated and loses its transparent appearance. The cell density of the adult nucleus is very low with cells occupying less than 0.5% of tissue volume; each cell thus has to turn over and maintain a large domain of extracellular matrix. The density of living cells decreases with age, possibly because of problems with nutrient supply to this large avascular tissue. Proteoglycan concentration also falls, and nucleus hydration decreases markedly, the disc discolours and in many cases clefts and fissures form. In most adults, the disc nucleus degenerates eventually to a stage where it can no longer fulfil its mechanical role.

Synopsis.Tadpoles are exceptional among vertebrates in lacking vertebrae along most of their body axis. Their caudal myotomes are also unusually simple for free-living vertebrates. This overall morphological simplicity, in theory, makes tadpoles good models for exploring how vertebrates control undulatory movements. We used electromyography (EMG), high speed ciné, computational fluid dynamics (CFD), and mechanical tissue testing to understand how Rana tadpoles regulate their locomotion.

Bullfrog (Rana catesbeiana) tadpoles have several patterns of muscle activity, each specific to a particular swimming behavior. Ipsilateral muscles in the tail were active either in series or simultaneously, depending on the tadpole's velocity, and linear and angular acceleration. When R. catesbeiana larvae swam at their natural preferred tail beat frequency, muscles at the caudal end of their tail were inactive. Mechanical tests of tissue further suggest that the preferred tail beat frequency closely matches the resonance frequency of the tail thus minimizing the energetic cost of locomotion.

CFD modeling has demonstrated that the characteristically high amplitude oscillations at a tadpole's snout during normal rectilinear locomotion do not add to drag, as might be supposed, but rather help generate thrust. Mechanical testing of the tadpole tail fin has revealed that the fin is viscoelastic and stiffer in small rather than large deformations. This property (among others) allows the tail to be light and flexible, yet stiff enough to generate thrust in the absence of a bony or cartilaginous skeleton.

Many recent studies have documented predator-induced polyphenism in tadpole tail shape. We suggest that this developmental plasticity in locomotor structures is more common in tadpoles than in other vertebrates because tadpoles do not need to reform skeletal tissue to change overall caudal shape.

Tadpole tail fins and tip, in the absence of any skeleton, are fragile and often scarred by predators. Based on the high incidence of tail fin injury seen in tadpoles in the wild, we suggest that the tadpole tail fin and tip may play an ecological role that goes beyond serving as a propeller to help tadpoles stay beyond predators' reach. Those soft tissue axial structures, by failing under very small tensile loads, may also allow tadpoles to tear free of a predator's grasp.

Synopsis. The lateral hypaxial musculature (LHM) of salamanders may serve as a useful model for understanding the functions of LHM in tetrapods more generally. Salamanders have between two and four layers of LHM, arranged segmentally in myomeres. These layers produce three primary mechanical actions: they bend the body, pressurize the body, and produce or resist torsion about the long axis of the body. The optimum muscle fiber angle for forceful bending is 0° to the long axis, the optimum angle for pressurization is 90°, and the optimum angle for torsion is 45°. For generating bending and torsional moments, lateral (superficial) muscle layers have greater mechanical advantage than medial (deep) layers. For increasing body pressure, by contrast, medial layers have greater mechanical advantage. A comparison of muscle fiber angles in aquatic and terrestrial salamanders reveals that some aquatic salamanders have one muscle layer with a low fiber angle which may represent a specialization for swimming. Overall, however, the fiber angles in the LHM of terrestrial and aquatic salamanders are surprisingly similar. In contrast, the pattern of fiber angles in caecilians is different, suggesting that these amphibians use their LHM differently. The fiber angle models and morphological observations presented here form a framework which may be useful in future studies of lateral hypaxial musculature.

Movements of the pelvis have recently been found to contribute to ventilation in both crocodilians and birds. Alligators have a kinetic pelvis in which the ischiopubic and ischiotruncus muscles rotate the pubic bones ventrally to increase abdominal volume and thereby facilitate inspiration. In birds, the entire pelvis rocks on the axial skeleton to produce ventilation. Although the mechanisms of pelvic aspiration are very different in crocodilians and birds, it is unusual among vertebrates for the pelvic musculoskeletal system to play an active role in inspiration. This observation raises the possibility that the pelvic musculoskeletal system may have played an important role in the ventilation of basal archosaurs. Based on the mechanism of pelvic aspiration in crocodilians and the structure of gastralia in basal archosaurs, we suggest that an ischiotruncus muscle pulled the medial aspect of the gastralia caudally, and thereby helped to produce inspiration by increasing the volume of the cuirassal basket. The proposed mechanism of cuirassal breathing in non-avian theropods leads us to suggest that the phase relationship of the ventilatory and locomotor cycles in running theropods was the opposite of that observed in running birds. Furthermore, we suggest that the ventilatory cycle of flying pterosaurs was entrained to the locomotor cycle with a phase relationship that was the opposite of that observed during flight in modern birds.

One of the most prominent characteristics of early vertebrates is the elongate caudal fin bearing fin rays. The caudal fin represents a fundamental design feature of vertebrates that predates the origin of jaws and is found in both agnathans and gnathostomes. The caudal fin also represents the most posterior region of the vertebrate axis and is the location where fluid, accelerated by movement of the body anteriorly, is shed into the surrounding medium. Despite the extensive fossil record of the caudal fin, the use of caudal characters for systematic studies, and the importance of tail function for understanding locomotor dynamics in fishes, few experimental studies have been undertaken of caudal fin function. In this paper I review two experimental approaches which promise to provide new insights into the function and evolution of the caudal fin: three-dimensional kinematic analysis, and quantitative flow measurements in the wake of freely-swimming fishes using digital particle image velocimetry (DPIV). These methods are then applied to the function of the caudal fin during steady swimming in fishes with heterocercal and homocercal morphologies: chondrichthyians (leopard sharks) and ray-fined fishes (sturgeon and bluegill sunfish). The caudal fin of leopard sharks functions in a manner consistent with the classical model of heterocercal tail function in which the caudal surface moves at an acute angle to the horizontal plane, and hence is expected to generate lift forces and torques which must be counteracted anteriorly by the body and pectoral fins. An alternative model in which the shark tail produces a reactive force that acts through the center of mass is not supported. The sturgeon heterocercal tail is extremely flexible and the upper tail lobe trails the lower during the fin beat cycle. The sturgeon tail does not function according to the classical model of the heterocercal tail, and is hypothesized to generate reactive forces oriented near the center of mass of the body which is tilted at an angle to the flow during steady locomotion. Functional analysis of the homocercal tail of bluegill shows that the dorsal and ventral lobes do not function symmetrically as expected. Rather, the dorsal lobe undergoes greater lateral excursions and moves at higher velocities than the ventral lobe. The surface of the dorsal lobe also achieves a significantly acute angle to the horizontal plane suggesting that the homocercal tail of bluegill generates lift during steady swimming. These movements are actively generated by the hypochordal longitudinalis muscle within the tail. This result, combined with DPIV flow visualization data, suggest a new hypothesis for the function of the homocercal tail: the homocercal tail generates tilted and linked vortex rings with a central jet inclined posteroventrally, producing an anterodorsal reactive force on the body which generates lift and torque in the manner expected of a heterocercal tail. These results show that the application of new techniques to the study of caudal fin function in fishes reveals a previously unknown diversity of homocercal and heterocercal tail function, and that morphological characterizations of caudal fins do not accurately reflect in vivo function.

Synopsis. The axial musculature of all vertebrates consists of two principal masses, the epaxial and hypaxial muscles. The primitive function of both axial muscle masses is to generate lateral bending of the trunk during swimming, as is seen in most fishes. Within amphibians we see multiple functional and morphological elaborations of the axial musculature. These elaborations appear to be associated not only with movement into terrestrial habits (salamanders), but also with subsequent locomotor specializations of two of the three major extant amphibian clades (frogs and caecilians). Salamanders use both epaxial and hypaxial muscles to produce lateral bending during swimming and terrestrial, quadrupedal locomotion. However during terrestrial locomotion the hypaxial muscles are thought to perform an added function, resisting long-axis torsion of the trunk. Relative to salamanders, frogs have elaborate epaxial muscles, which function to both stabilize and extend the iliosacral and coccygeosacral joints. These actions are important in the effective use of the hindlimbs during terrestrial saltation and swimming. In contrast, caecilians have relatively elaborate hypaxial musculature that is linked to a helix of connective tissue embedded in the skin. The helix and associated hypaxial muscles form a hydrostatic skeleton around the viscera that is continuously used to maintain body posture and also contributes to forward force production during burrowing.

Synopsis.Constraint theory has suffered from its many and varying definitions and from repeated confusion with the action of selection. Constraints are difficult to isolate, more difficult to quantify, and their consequences may be simulated by the action of agents such as stabilizing selection. This paper presents an alternative method of constraint analysis using a simple one-dimensional measurement. A total of 29 skeletal elements from 15 species representing 11 orders of mammals were measured for length and normalized for body mass, after which means, standard deviations, and variances were generated. A coefficient of variation analysis was performed to normalize for mean element length. The axial skeleton was found to be less variable than the appendicular. The appendicular demonstrated a trend where the more distal elements were the most variable, and variation decreased with more proximal positions. The three most variable of the 29 elements were finger V, toe V, and metacarpal V. In summary, the axial skeleton was found to be more conservative in the lengths of its elements, the more distal appendicular elements were less constrained than proximal ones and these constraints were probably the results of genetic, developmental, and mechanical factors. It is also proposed that stabilizing selection played some role in maintaining the curb on length variance in these structures, based on mechanical performance. The results of this study are intended to promote discussion of alternative methods of constraint analysis.

The similarity in swimming style and external body shape between dolphins and scombrid fishes, especially tunas, is a textbook example of evolutionary convergence. I identify additional morphological features of the musculoskeletal system shared by dolphins and tunas. Specifically, these swimmers share a pattern of force transmission through a complex, three-dimensional system of collagenous fabrics, which are stiffened by muscular hydrostatic pressure. This force transmission system increases both the displacement advantage and moment arm of contracting axial muscle. These features represent a functionally significant design for steady swimming vertebrates.