The mechanical scaling of hydrostatic skeletons: Ontogeny of earthworms, Lumbricus terrestris

Soft-bodied organisms with hydrostatic skeletons range enormously in body size, both during the growth of individuals and when different species are compared. Therefore, body size is potentially an important variable determining the mechanical function of hydrostatic skeletons. This study used the ontogenetic changes in the morphology and mechanical performance of earthworm Lumbricus terrestris to examine the mechanical scaling of hydrostatic skeletons. Hydrostatic skeletons differ fundamentally from jointed skeletons in their ability to grow isometrically while maintaining similarity in both static and dynamic stresses. The peristaltic crawling of L. terrestris was kinematically similar when the motions were normalized by body length, and the shape changes of individual segments approximated dynamic strain similarity. However, even though large worms exerted greater axial and radial burrowing forces than small worms on an absolute scale, large earthworms were less forceful for their size (relative to small earthworms) than was predicted by traditional scaling theory. This result does not appear to be explained by differences in mechanical advantage. An index was derived for the calculation of mechanical advantage in leverless organisms; it indicated that, because earthworms grow isometrically, mechanical advantage was also constant as a function of body size. In summary, although both hydrostatic skeletons and jointed skeletons are capable of the same mechanical functions (e.g. maintenance of posture, antagonism of muscles and transfer of muscle forces to the environment), the mechanism of mechanical function is sufficiently distinct that the specific scaling rules that apply to jointed skeletons usually do not transfer to hydrostatic skeletons. Force production was the only variable that changed as a function of body size; otherwise, body size was not an important determinant of mechanical function of earthworm skeletons. No one quantitative scaling "rule" will apply to all hydrostatic skeletons, but this study has provided a general conceptual framework that is applicable to most of the cylindrical hydrostatic skeletons of soft-bodied organisms.