UBC Theses and Dissertations
Functional design and scaling of the jumping mechanism of the African desert locust Katz, Stephen L.
Current models for scaling of skeletal morphology were examined to test their applicability to the ontogenetic growth of an exoskeletal animal, the African Desert Locust (Schistocerca gregaria). It was found that the tibial leg segments of both the mesothoracic (ie. non-jumping) and the metathoracic (jumping) legs scaled in a manner that produced relatively longer, more slender skeletal elements as the animal grew. Metathoracic tibial length scaled to tibial diameter raised to the power 1.21. This result deviates both from isometric (ie. geometric similarity) and distortive (constant stress, elastic similarity) allometric models. The mechanical properties of the metathoracic tibiae were measured using a dynamic, 3-point bending technique. The flexural stiffness of metathoracic tibiae scaled to body mass raised to the power of 1.53. This was intermediate to the predictions made by constant stress and elastic similarity models. Thus, the mechanical properties scaled in a manner similar to predictions of mechanical scaling expectations in spite of the morphological, developmental programme. The uncoupling between morphological scaling and structural, mechanical properties is accomplished by scaling the tensile modulus of the cuticle. This strategy of altering the properties of the building material is distinct from strategies employed by vertebrate animals. Calculations indicate that the energy stored in the substantial deflection of the adult, metathoracic tibiae during the jump may be as high as 10% of the total kinetic energy of the jump. Using the models that generated relationships between morphology and body size proposed by McMahon (1973, 1984) and the relationships between morphology and performance described by Hill (1950), predictions of how jumping performance measures may change as a function of body mass were tested. Performance was quantified using a high sensitivity, three dimensional forceplate. Performance parameters quantified included the force, acceleration, take-off velocity, kinetic energy and power output. With the exception of power output, each measure of performance scaled to body mass in a manner consistent with the predictions of the elastic similarity model. Power output scaled to body mass in a manner consistent with the predictions of the constant stress similarity model. The elastic similarity model is approximated by the performance of the locust in spite of the morphological design that deviates from that model's predictions. These results indicate that the jump has separate functions in the flightless, juvenile instars and in the flying adult stage of the life history. Juvenile locusts produce take-off velocities of between .9 and 1.2 m/s that are relatively size independent. The take-off velocity in juveniles produces a distance of ballistic travel that averages between 20 and 30 cm. In adults, the take-off velocity is also relatively size independent at a level approximately twice as high as in juveniles (ie 2.5 m/s). The data suggest that in juveniles, the jump is designed to achieve a characteristic distance travelled, and in adults the jump is designed to achieve a minimum velocity necessary to fly. Three rationales for the observed morphological programme are offered. The design may be a manifestation of a developmental constraint, it may be a response to scaling to force rather than explicitly to body mass, or it may be a design that takes advantage of the inherent deformability of long, slender beams. Thus, it may be that the tibiae, which have been treated as rigid levers, are in fact flexible springs.
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