Coiling in gastropods: a lead to synthesis

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, raising challenges to causal inferences. Here, I apply the familiar logarithmic helicospiral (logspiral) model for coiled shells, to assess its fit to data on gastropods, and to study allometry, covariation and constraint in coiling behavior, in light of adaptationist and proximate mechanistic explanations. I derive convenient expressions for the three-way relationship between expansion rate, apical angle and downward lead angle of spiral paths on shells. Combining several published datasets, I find that centerline spirals of gastropod shells follow isometrically growing conical logspirals. Allometry manifests in the relative growth of apertures. Both empirical patterns and theoretical arguments further suggest that the relation between apical angle and expansion rate, usually attributed to economical and mechanical demands, can equally be explained by taxon-specific lead angles and plasticity in growth rates. Consequently, the lead angle emerges as a more biologically meaningful coiling parameter that also unifies fixed- and moving-frame morphological models. I relate results to the longstanding methodological problem of confusing spire-height allometry with incorrect longitudinal origin of measurement, and to empirical patterns of covariation of coiling parameters and morphometric traits in gastropods. More generally, I demonstrate that geometry dictates particular "laws of form" that have practical use in data analyses and integration, and need to be fully acknowledged when seeking causal adaptationist or mechanistic explanations.