  The standard differential scaling of proportions in limb long bones (length
against circumference) is applied to a phylogenetically wide sample of the
Proboscidea, Elephantidae and the Asian (Elephas maximus) and African elephant
(Loxodonta africana). In order to investigate allometric patterns in
proboscideans and terrestrial mammals with parasagittal limb kinematics, the
computed slopes (slenderness exponents) are compared with published values for
mammals and studied within a framework of theoretical models of long bone
scaling under gravity and muscle forces. Limb bone allometry in E. maximus and
the Elephantidae are congruent with adaptation to bending and/or torsion
induced by muscular forces during fast locomotion, as in other mammals, whereas
limb bones in L. africana appear adapted for coping with the compressive forces
of gravity. Consequently, hindlimb bones are expected to be more compliant than
forelimb bones in accordance with in vivo studies on elephant locomotory
kinetics and kinematics, and the resultant negative limb compliance gradient in
extinct and extant elephants, which contrasts to other mammals, suggests an
important locomotory constraint preventing achievement of a full-body aerial
phase during locomotion. Differences in ecology may be responsible for the
subtle differences observed between African and Asian elephant locomotion, and
the more pronounced differences in allometric and mechanical patterns
established in this study.
  Key words: long bone scaling models; standard differential scaling; limb
gradient functions; proboscideans; extinct and extant elephants
