Galactic arms, and devil's toenails: a synthesis of coiled morphology, applied to gastropods

Biological structures lie at intersections of function, construction, and history. Conversely, the geometry of structures modulates how these three aspects of organic form manifest in different taxonomic groups and ecological circumstances. Here, I apply the familiar logarithmic conispiral model for coiled shells, to assess its fit to data on gastropods, and to study covariation in coiling behavior. Treating shell centerlines as conical helices, and drawing on analogies from astronomy and robotics, the expansion angle of the helix, and its helical slope, or lead angle, emerge as convenient parameters for studying shell growth and its optimization, trait covariation, and ontogenetic allometry. I demonstrate that by combining several published datasets. Recent arguments on the inadequacy of logarithmic helicospirals contain a known methodological pitfall. Adopting the conihelical parameterization circumvents the problem altogether, demonstrating good fits of conihelical centerlines to data. Further analysis of aperture inclinations, relative to conihelical centerlines, highlights the constructional developmental role of the environment (here, substrate) as a general principle of natural history, on par with adaptation. More broadly, `laws of form' have practical use in data analyses and integration, and provide baseline references for ontogenetic allometry, growth gradients, and other morphological features (here, aperture inclination, and columellar folds).