Why do organisms evolve in the manner that they do‭? ‬Are there restrictions or constraints that influence the direction of evolutionary change‭? ‬Although in‭ ‬1917‭ ‬D’Arcy Thompson stated that‭ “‬Even now the zoologist has scarce begun to dream of defining in mathematical language even the simplest organic forms‭” ‬the same can be said today. More recently,‭ ‬mathematical modeling has been applied to general aspects of mollusk skeletogenesis through both ontogeny and phylogeny‭ (‬e.g.,‭ ‬Raup and Stanley,‭ ‬1981‭)‬. Our study is exploring how mathematical modeling of ontogenetic and phylogenetic change in Prunum,‭ ‬in combination with experimental studies,‭ ‬can be used to elucidate the mechanisms involved in the direction and magnitude of evolutionary-developmental change. We used X-radiographic images of Prunum species to delineate quantitative parameters that could in turn be used to model hypothetical and actual skeletal morphologies. These parameters were entered into the software program CerioShell‭ (‬Stone,‭ ‬1995‭)‬. We modeled hypothetical shell morphologies that could be used to interpret the boundaries of possible morphological change in Prunum. These results are being combined with experimental and descriptive studies in order to better understand macroevolutionary events in this clade.

A shell can be thought of as a structure that is a tube that travels over time through‭ ‬360‭ ‬degrees of space.  These revolutions or turns of a coiled shell are called whorls,‭ ‬which are considered to spiral around an imaginary central axis.  This axis runs through the central column of the shell and is known as the columella. The speed at which the whorls enlarge can vary,‭ ‬and a continuous line separates each whorl and is referred to as a suture.  In most shells,‭ ‬the largest whorl of a shell is the last whorl‭ (‬body whorl‭)‬.  ‭ ‬The spire is considered to be all the whorls except the last. The apex is the tip of the spire and the opposite end is referred to as the base. The animal extends out of its shell through an opening called the aperture.

Shells can be viewed in apical,‭ ‬basal,‭ ‬apertural and abapertural views. ‭(‬The‭ "‬usual‭" ‬orientation of a shell is an apertural view,‭ ‬with the aperture toward the viewer and with the apex pointing up.‭)‬

A method for counting whorls is seen below.  First,‭ ‬the shell should be viewed from the apical view and then it should be determined where the first suture begins.  A line can be then drawn dividing the shell into two parts.  Whorls are counted from this line,‭ ‬and are estimated to a quarter of a whorl.

A shell can be viewed as a series of apertures that travel through time and space as the animal accretes‭ (‬i.e. builds‭) ‬its shell.  It is possible to trace the path of the aperture via coordinates of the center of each whorl’s aperture as well as the horizontal and vertical radius of the aperture.

This trajectory can be graphically and mathematically represented.  Once a mathematical formulation is made,‭ ‬it is then possible to vary parameters and modify the mollusk’s skeletogenesis.
