Using a mathematical model to test the null hypothesis of optimal shell construction by four marine gastropods

A previous analysis (Heath 1985; Biol J Linn Soc 24. 165-174) tested and re jected the null hypothesis that gastropods construct their shells with opti mal efficiency. The ratio volume of material used to volume of space enclos ed (V-shell:V-space) was used as a measure of inefficiency of construction and shown to exhibit smooth parabolic curves if plotted as a function of wh orl overlap. In the present analysis, in contrast, it is demonstrated that inefficiency of a particular combination of mode and rate of shell construc tion, consisting of variable interapertural areas and rapidly expanding who rl cross sections, is described by polynomial curves with inflection points . As an empirical test of this theoretically derived observation, V-shell:V -space of shells of four species of marine gastropods [Architectonica persp ectiva (L., 1758), Cittarium pica (L., 1758), Euspira heros (Say, 1822), an d Telescopium telescopium (L., 1758)] was calculated, using a mathematical model. By varying the vertical component of aperture trajectories [i.e. tra nslation (T)] in the mathematical model, hypothetical forms representing a range of possible whorl overlap were simulated graphically and, for each fo rm, V-shell:V-space was calculated. Plots of V-shell:V-space as a function of whorl overlap were described accurately by polynomial curves with inflec tion points, and each real shell yielded a nonoptimal V-shell:V-space, exhi biting approximately 75% less whorl overlap than its most efficiently const ructed, hypothetical form. Inflection points of inefficiency curves represe nt critical points at which the reduction of space provided begins to excee d significantly the amount of material saved with increasing whorl overlap, and nonoptimal shell forms might represent compromises between efficient c onstruction and function.