Meeting Abstract
P1.45 Friday, Jan. 4 Limits on the body size and shape of animals SHARMA, N*; DHAWALE, N; VENKADESAN, M; National Centre for Biological Sciences, Bangalore; National Centre for Biological Sciences, Bangalore; National Centre for Biological Sciences, Bangalore neelimas@ncbs.res.in
Material strength of bone and muscle impose limits on body mass and on aspect ratio (width/height) as a function of body mass. Does the need for stability during standing and locomotion also impose limits on the size and shape of animals? We model standing animals as an inverted pendulum with neural feedback, and locomotion (seen head-on) as a passive rectangular box on uneven ground. The first model refines the existing upper limit on body mass based on strength of materials. The second predicts that small animals have to sprawl with a body shape that is “landscape” and not “portrait”, complementing the material strength theory that requires heavy animals to be “portrait”. The success or failure to maintain balance during standing is governed by the relative magnitude of two time scales; neural delays in sensorimotor feedback control versus the mechanical time scale associated with the inverted pendulum like body. Having smaller neural feedback delays than the mechanical time scale leads to an upper limit on the height. Using published allometry of height to mass we find an upper bound on mass that is comparable to the Apatosaurus, the heaviest known land animal. To understand how aspect ratio affects lateral stability of an animal, we compare two angles; the critical angle beyond which a passive rectangular box will fall versus the angle of tilt imposed by terrain unevenness, i.e. maximal height differences between points on the terrain that the box is resting on. The tilt depends on how terrain unevenness scales with the width of the box. We find that the aspect ratio has a lower bounded for a broad class of power law relationships of terrain unevenness as a function of base width. This suggests the hypothesis that small animals sprawl like a “landscape” because they face an unfavorably rough terrain.
