TL;DR: It is demonstrated that inefficiency of a particular combination of mode and rate of shell construction, consisting of variable interapertural areas and rapidly expanding whorl cross sections, is described by polynomial curves with inflection points.
Abstract: A previous analysis (Heath 1985; Biol J Linn Soc 24: 165–174) tested and rejected the null hypothesis that gastropods construct their shells with optimal efficiency. The ratio volume of material used to volume of space enclosed (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 whorl overlap. In the present analysis, in contrast, it is demonstrated that inefficiency of a particular combination of mode and rate of shell construction, consisting of variable interapertural areas and rapidly expanding whorl 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 perspectiva (L., 1758), Cittarium pica (L., 1758), Euspira heros (Say, 1822), and Telescopium telescopium (L., 1758)] was calculated, using a mathematical model. By varying the vertical component of aperture trajectories [i.e. translation (T )] in the mathematical model, hypothetical forms representing a range of possible whorl overlap were simulated graphically and, for each form, 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 inflection points, and each real shell yielded a nonoptimal V
shell:V
space, exhibiting approximately 75% less whorl overlap than its most efficiently constructed, hypothetical form. Inflection points of inefficiency curves represent critical points at which the reduction of space provided begins to exceed significantly the amount of material saved with increasing whorl overlap, and nonoptimal shell forms might represent compromises between efficient construction and function.
TL;DR: Spermatozoa of the gastropodArchitectonica perspectiva Linné differ from those of other molluscs by having a long, transversely banded column interpolated between the base of the nucleus and the axoneme of the midpiece.
Abstract: Spermatozoa of the gastropodArchitectonica perspectiva Linne differ from those of other molluscs by having a long, transversely banded column interpolated between the base of the nucleus and the axoneme of the midpiece. The sperm head consists of a weakly helical nucleus (length 15µm) capped apically by a small, ovoid acrosome. Within the midpiece a cylindrical, mitochondrial sheath surrounds the banded column, and posteriorly, an axonemal complex (9+2 pattern axoneme associated with nine finely banded coarse fibres). Coarse fibres terminate near the annulus, leaving only the 9+2 axoneme to penetrate the glycogen piece. The posterior extremity of the end piece is paddle-shaped and contains only singlet microtubules. Total sperm length forA. perspectiva is 220 to 225µm. Available sperm data for the Architectonicidae indicate that some features may be diagnostic of the entire family (e.g. shape and substructure of the acrosome, coarse fibres and mitochondrial sheath), while others may prove useful at the subfamily or generic levels (morphology of midpiece, nucleus and annulus).