HYDRODYNAMIC STRATEGIES IN THE MORPHOLOGICAL EVOLUTION OF SPINOSE PLANKTONIC-FORAMINIFERA

To counter gravitational settling, planktonic foraminifera adjust thei r buoyancies, in part by manufacturing low-density lipids or gases. Th e biochemical energy that a foraminifer expends in this way is a funct ion of the speed at which it would otherwise settle if it did not expe nd this energy. In turn, the settling speed varies with foraminifer sh ape. We consider here foraminifera that have acicular spines, for exam ple Orbulina universa and Globigerinoides sacculifer. Growing spines p roduces two counteractive effects: spines increase the weight of a for aminifer, and therefore tend to increase its settling speed; they also increase the fluid drag on the foraminifer, and therefore tend to dec rease its settling speed. If growing spines is part of an evolutionary strategy to impede settling, then it is reasonable to expect that the advantage of increasing drag by growing spines outweighs the disadvan tage of increasing weight.The complexity of foraminiferal shapes precl udes directly solving the equations of fluid motion for drag and settl ing speed. We therefore appeal to the efficacy of dimensional analysis to define a coefficient of drag C-D and a Reynolds number Re for spin ose foraminifera. Experiments that involve settling scaled models of f oraminifera (constructed from beeswax and pins) in viscous liquids are then used to confirm the forms of generalized dimensional formulae re lating the settling speed W to test radius R, spine number n, spine le ngth l, and spine radius r. Geometrically similar foraminifera whose s pine arrangements possess quasispherical symmetry settle according to an inverse relation between C-D and Re, homologous to Stokes's law for spheres. Fluid drag systematically increases with both n and l. For g iven R, l, and r, a minimum settling speed occurs at an intermediate s pine number no. Similarly, for given R, n, and r, a maximum settling s peed W-0 occurs at an intermediate spine length l(0). Results suggest that insofar as there is disadvantage in settling rapidly, there is ad vantage in remaining small; or, if growth of tests occurs, there is ad vantage in manufacturing many long thin spines. Investments of mass an d energy associated with this strategy must be weighed against those i nvolved in achieving neutral (or positive) buoyancy by other mechanism s, and limitations on lengths of spines imposed by their finite streng th. A comparison of the theory with modern foraminifera suggests that the geometries of adult Orbulina universa and Globigelinoides sacculif er, in the absence of external protoplasm, are well suited to impede s ettling. With external protoplasm, however, l is effectively decreased and the drag associated with spines is not sufficient to provide visc ous settling unless the protoplasm possesses positive buoyancy. For an individual at or near a state of neutral buoyancy, drag associated wi th spines decreases the sensitivity with which its settling speed resp onds to unavoidable changes in the buoyancy of its protoplasm related to metabolic activity, and to changes in the density and viscosity of sea water related to external factors. The effect is to hydrodynamical ly dampen vertical motions that would otherwise occur if the individua l did not possess spines. In contrast, the small drag associated with few short spines is advantageous to juveniles that must ascend from de ep to shallow waters during their ontogenies. A partitioning of finite spine mass into many moderate to short spines is less effective in pr oducing drag than one involving fewer long spines. Long spines, howeve r, are more susceptible to mechanical breakage due to the torque that viscous forces apply to them. Foraminifera with approximately 10 (or f ewer) spines that possess mechanical properties equivalent to those of spines of adult Orbulina universa and Globigerinoides sacculifer can withstand motions at speeds of only a few tenths of a centimeter per s econd (or more, depending on spine strength) without breakage. With in creasing numbers of spines, the resulting hydrodynamic interaction amo ng them has the effect of significantly reducing the chance of spine b reakage related to momentarily rapid motions; this is attributable to a decrease in the proportion of the spine length l exposed to signific ant viscous forces, whereby the torque on individual spines is decreas ed. External protoplasm also reduces the chance of breakage by decreas ing the length of spines exposed to surrounding fluid.