INTRODUCTION

Gastropods are well diversified, geographically and temporally widespread organisms with a very large range of adaptations. Because of their calcified shell, they are among the most common material in the fossil record. Hence, they constitute an invaluable archive of global and regional biotic and abiotic changes on Earth and can provide important insights into patterns and processes of evolution. However, their contribution remains hampered by the rather simple, highly integrated morphology of their shells, which is not well suited to conventional biometric and phylogenetic methods. Indeed, the gastropod shell consists of a calcified, univalve conch, basically conic and coiled, with well-diversified outlines of the aperture, various colour patterns, and few distinctive and qualitative ornaments (Figure 1). Since colour patterns, mostly expressed as bands of various magnitude and number, are highly variable within the same species, they have little taxonomic value. Moreover, colour patterns are only exceptionally preserved among fossils. Most diagnostic characters of extant gastropod species rely mainly on soft tissues, i.e., sets of characters which are lost in fossil representatives.

The most important set of morphological characters of gastropods resides in the geometry of their shell. However, the shell geometry is difficult to capture by conventional descriptive, qualitative and discrete approaches. For instance, the investigation of the shell geometry has largely been limited to basic two-dimensional measurements such as width of aperture, shell diameter, or apical angle (Figure 1). Such characters poorly capture the subtle differences of shell geometry, and their relevance is thus rather limited. Due to its accretionary mode of growth, the gastropod shell preserves its entire post-hatching ontogeny. The ontogenetic changes of shell geometry constitute a potential additional relevant set of characters. However, to date, ontogenetic studies of molluscs remain rare, qualitative and descriptive; usually the mature stage of the shell is given the greatest emphasis. Hence, the developmental characteristic of mollusc shells remains largely under exploited. The mollusc shell is thus in need of an adequate, quantitative and descriptive method to better take advantage of its excellent fossil record in palaeontological and evolutionary studies.

Significant advances in the quantitative and three-dimensional characterization of the mollusc shell have been first achieved by the pioneer work of Raup (e.g., Raup and Michelson 1965; Raup 1966). The coiled conic shell of molluscs is a well-known case study of theoretical morphology (e.g., Okamoto 1988; Ackerly 1989a; Cortie 1989; see also review by McGhee 1999). Raup (1966) demonstrated that the nearly self-similar accretionary growth of the mollusc shell allows for simulation of most shell shapes by varying only four geometric parameters. However, Raup's parameters have some important limitations (see review of McGhee 1999): some of them are interdependent (Schindel 1990), the four parameters are constants and apply only to isometric growth (Goodfriend 1983; Gould 1991), and the detailed shape of the growing shell aperture is subsumed to an ellipse. Furthermore, Raup's model assumes the existence of a coiling axis, which is not true for some mollusc shells (e.g., heteromorph ammonoids like Nipponites or vermetid gastropods).

Vermeij (1971) and Kohn and Riggs (1975) were the first to study gastropods in the context of the theoretical morphospace of Raup. The theoretical morphology of gastropods has also been investigated in various ways by Rex and Boss (1976), Harasewych (1982), Ekaratne and Crisp (1983), and Schindel (1990), among others. However, they were "forced" to modify Raup's parameters since determining them usually involves axial sectioning of the shell. Measuring the parameters of all these models is usually difficult and requires complicated techniques (e.g., Ackerly 1989b; Schindel 1990). All these models are a simplification of shell geometry, especially of aperture shape, based on 2-D measurements. Few morphometric studies have been devoted to the ontogeny of these accretionary organisms (e.g., Checa and Aguado 1992; Stone 1998). The most complete study is that of Stone (1998), which also compared the results between traditional measurements, parameters of mathematical modelling of shells, and a warp analysis of aperture trajectory centroids. However, gastropod ontogeny is reduced to the relative position of aperture centroid and therefore carries no information about aperture shape. It is also restricted to regularly coiled shells.

In his review about theoretical morphology of mollusc shells, McGhee (1999, p. 111) finally concluded "can a theoretical morphospace of helicospiral form be created that is both morphologically realistic and mensuratively simplistic?" Thanks to continuing improvements in three-dimensional computed image acquisition and analysis, a broad range of non-destructive methods is now available that enable the ontogenetic description and quantification of the gastropod shell geometry. The purpose of this study is to propose a method which captures the 3-D morphology of the coiled mollusc shell and exploits quantitative and continuous characters throughout ontogeny.