Take-off speed in jumping mantises depends on body size and a power limited mechanism

Abstract

Many insects such as fleas, froghoppers and grasshoppers use a catapult mechanism to jump and a direct consequence of this is that their take-off velocities are independent of their mass. In contrast, insects such as mantises, caddis flies and bush crickets propel their jumps by direct muscle contractions. What constrains the jumping performance of insects that use this second mechanism? To answer this question, the jumping performance of the mantis, Stagmomantis theophila, was measured through all its developmental stages, from 5 mg first instar nymphs to 1200 mg adults. Older and heavier mantises have longer hind and middle legs and higher take-off velocities than younger and lighter ones. The length of the propulsive hind and middle legs scaled approximately isometrically with body mass (exponent, 0.29 and 0.32 respectively). The front legs, which do not contribute to propulsion, scaled with an exponent of 0.37. Take-off velocity increased with increasing body mass (exponent, 0.12). Time to accelerate increased and maximum acceleration decreased but the measured power that a given mass of jumping muscle produced remained constant throughout all stages. Mathematical models were used to distinguish between three possible limitations to the scaling relationships; first, an energy-limited model (which explains catapult jumpers); second, a power-limited model; third, an acceleration-limited model. Only the model limited by muscle power explained the experimental data. Therefore, the two biomechanical mechanisms impose different limitations on jumping; those involving direct muscle contractions (mantises) are constrained by muscle power, catapult mechanisms by muscle energy.