The logarithmic helicospiral has been the most widely accepted model of regularly coiled mollusc form since it was proposed by Moseley (1838) and popularised by Thompson (1942) and Raup (1966). It is based on an explicit assumption that shells are isometric and grow exponentially, and an implicit assumption that the external form of the shell follows the internal shape, which implies that the parameters of the spiral could, theoretically, be reconstructed from the external whorl profile. In this contribution, we show that these assumptions fail on all 25 gastropod species we examine. Using a dataset of 176 fossil and modern gastropod shells, we construct an empirical morphospace of coiling using the familiar three parameters of whorl expansion rate, translation rate, and rate of increasing distance from coiling axis, plus rate of aperture shape change, from their best-fit models. We present a case study of change in shell form through geological time in the austral family Struthiolariidae to demonstrate the utility of our approach for evolutionary paleobiology. We fit various functions to the four shell-coiling parameters, to demonstrate that the best morphological model is not the same for each parameter. We present a set of R routines that will calculate helicospiral parameters from sagittal sections through coiled shells and allow workers to compare models and choose appropriate sets of parameters for their own datasets. Shell form parameters in the Struthiolariidae highlight a hitherto-neglected hypothesis of relationship between Antarctic Perissodonta and the enigmatic Australian genus Tylospira that fits the biogeographic and stratigraphic distribution of both genera.

The dataset comprises 2D images, the majority taken with a dSLR camera, plus a small number of digital 'slices' through synchrotron micro-CT scans. The dSLR camera images were retrodeformed to remove lens distortion (see Collins & Gazley 2017 for details of method). 

The .tps file of landmarks was collected by one author (KSC) from the images included here.

Code files are provided as .Rmd files, which can be run in R Studio, and as html files which can be read in a browser without any coding knowledge.

To run the .Rmd files, you will need to download the .Rmd files and the .csv files and place them in a folder together. Extract the zip file, and place all of its contents inside a folder named 'data' inside the folder containing the .Rmd and .csv files.