Lead and slant on the geometry of coiling in gastropods

This is a Preprint and has not been peer reviewed. This is version 2 of this Preprint. You must log in to post a comment. There are no comments or no comments have been made public for this article. This is a Preprint and has not been peer reviewed. This is version 2 of this Preprint. Add a Comment You must log in to post a comment. Comments There are no comments or no comments have been made public for this article. Molluscan shells have been studied with various geometric models. Here I show that lead angle, the defining slope of a conical helix, emerges as a more useful parameter in morphometric analyses and (adaptationist) interpretation of covariation in coiling parameters. The widely used apical semiangle becomes redundant and uninformative, a passive consequence of taxon-specific lead angles and plasticity in growth (expansion rate). Treating coiled shells as conical helices, and extending to logarithmic slant helices (curves of precession), provides insights into ontogenetic allometry, irregular coiling, past models, and unifying fixed- and moving-frame approaches. https://doi.org/10.32942/X28Q23 Ecology and Evolutionary Biology, Evolution, Life Sciences, Other Ecology and Evolutionary Biology, Physical Sciences and Mathematics allometry, Developmental plasticity, Theoretical morphology, morphometrics, Mollusc, Molluscan shell, ontogeny, conical helix, slant helix, Conchology, Logarithmic spiral, Differential geometry Published: 2026-04-30 21:15 Last Updated: 2026-05-15 01:04 CC-By Attribution-NonCommercial-NoDerivatives 4.0 International Data and Code Availability Statement: Dataset: https://doi.org/10.5281/zenodo.19763621, Webapp: https://doi.org/10.5281/zenodo.19895626 Language: English