JOHNSON, A.S.*; ELLERS, O.E.; WRIGHT, M.; STRANGES, P.B.; Bowdoin College, Maine; Bowdoin College, Maine; Bowdoin College, Maine; Bowdoin College, Maine: Implications of transport processes and 2/3 power metabolic scaling to Bertalanffy and bimodal growth in sea urchins

We measured basal respiratory rate of sea urchins Strongylocentrotus droebachiensis as a function of whole body drip weight. Respiratory rate scaled with the 0.67 (�0.01 s.e.) power of weight, which was statistically indistinguishable from 2/3, but which was not equal to 3/4. A simple calculation using the Fick diffusion equation and estimated transfer surface area and diffusion distances showed that simple diffusion, with the aid of ciliary stirring adjacent to surfaces, was sufficient to describe oxygen transport in sea urchins (which after all have no circulatory system). Growth studies on this same species showed that the Bertalanffy function fitted growth data very well for sizes between 5 mm and 70 mm diameter. Specifically, a plot of linearized weight change versus linearized weight yields a straight line, as is expected by a Bertalanffy description of growth. In the Bertalanffy function anabolism is assumed to scale with the 2/3 power of weight largely because of the 2/3 power metabolic scaling. In many field studies, and in common experience, urchin researchers have often found some version of bimodal growth in which smaller urchins grow less rapidly. Such bimodal growth is not predicted by a Bertalanffy function. Although this slower growth at smaller size may be due to changes in diet, we suggest another possibility, mainly that very small sea urchins are sufficiently within the boundary layer, or in crevasses, that delivery of oxygen to the surface of the urchins is restricted, thus slowing their growth. We suggest that biomechanical transport constraints may generally limit the rate at which biological engines run, which in turn influence growth rate via a modified anabolic term in the Bertalanffy growth function.