Coordinating tiny limbs and long bodies: Geometric mechanics of lizard terrestrial swimming

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Abstract
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Although typically possessing four limbs and short bodies, lizards have evolved diverse morphologies, including elongate trunks with tiny limbs. Such forms are hypothesized to aid locomotion in cluttered/fossorial environments but propulsion mechanisms (e.g., the use of body and/or limbs to interact with substrates) and potential body/limb coordination remain unstudied. Here, we use biological experiments, a geometric theory of locomotion, and robophysical models to investigate body-limb coordination in diverse lizards. Locomotor field studies in short-limbed, elongate lizards (Brachymeles and Lerista) and laboratory studies of fully limbed lizards (Uma scoparia and Sceloporus olivaceus) and a snake (Chionactis occipitalis) reveal that body-wave dynamics can be described by a combination of standing and traveling waves; the ratio of the amplitudes of these components is inversely related to the degree of limb reduction and body elongation. The geometric theory (which replaces laborious calculation with diagrams) helps explain our observations, predicting that the advantage of traveling-wave body undulations (compared with a standing wave) emerges when the dominant thrust-generation mechanism arises from the body rather than the limbs and reveals that such soil-dwelling lizards propel via "terrestrial swimming" like sand-swimming lizards and snakes. We test our hypothesis by inducing the use of traveling waves in stereotyped lizards via modulating the ground-penetration resistance. Study of a limbed/undulatory robophysical model demonstrates that a traveling wave is beneficial when propulsion is generated by body-environment interaction. Our models could be valuable in understanding functional constraints on the evolutionary processes of elongation and limb reduction as well as advancing robot designs.

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Convergent evolution and character correlation in burrowing reptiles: towards a resolution of squamate relationships
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The affinities of three problematic groups of elongate, burrowing reptiles (amphisbaenians, dibamids and snakes) are reassessed through a phylogenetic analysis of all the major groups of squamates, including the important fossil taxaSineoamphisbaena, mosasauroids andPachyrhachis; 230 phylogenetically informative osteological characters were evaluated in 22 taxa. Snakes (includingPachyrhachis) are anguimorphs, being related firstly to large marine mosasauroids, and secondly to monitor lizards (varanids). Scincids and cordylids are not related to lacertiforms as previously thought, but to anguimorphs. Amphisbaenians and dibamids are closely related, andSineoamphisbaenais the sister group to this clade. The amphisbaenian–dibamid–Sineoamphisbaenaclade, in turn, is related to gekkotans and xantusiids. When the fossil taxa are ignored, snakes, amphisbaenians and dibamids form an apparently well-corroborated clade nested within anguimorphs. However, nearly all of the characters supporting this arrangement are correlated with head-first burrowing (miniaturization, cranial consolidation, body elongation, limb reduction), and invariably co-occur in other tetrapods with similar habits. These characters are potentially very misleading because of their sheer number and because they largely represent reductions or losses. It takes very drastic downweighting of these linked characters to alter tree topology: if fossils are excluded from the analysis, a (probably spurious) clade consisting of elongate, fossorial taxa almost always results. These results underscore the importance of including all relevant taxa in phylogenetic analyses. Inferring squamate phylogeny depends critically on the inclusion of certain (fossil) taxa with combinations of character states that demonstrate convergent evolution of the elongate, fossorial ecomorph in amphisbaenians and dibamids, and in snakes. In the all-taxon analysis, the position of snakes within anguimorphs is more strongly-corroborated than the association of amphisbaenians and dibamids with gekkotans. When the critical fossil taxa are deleted, snakes «attract» the amphisbaenian–dibamid clade on the basis of a suite of correlated characters. While snakes remain anchored in anguimorphs, the amphisbaenian–dibamid clade moves away from gekkotans to join them. Regardless of the varying positions of the three elongate burrowing taxa, the interrelationships between the remaining limbed squamates («lizards») are constant; thus, the heterodox affinities of scincids, cordylids, and xantusiids identified in this analysis appear to be robust. Finally, the position ofPachyrhachisas a basal snake rather than (as recently suggested) a derived snake is supported on both phylogenetic and evolutionary grounds.

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