MODELING A GROWTH SERIES FOR AN ANTARCTIC FRESHWATER SNAIL

Gastropod fossils belonging to the superfamily Lymnaeoidea are found in the Neogene-aged Meyer Desert Formation (Sirius Group), Antarctica, about 500 km from the South Pole.  Other fossils include Nothofagus, Ranunculus, mosses, insects, bivalves and a fish.  The gastropods occur in a marlstone bed interbedded between diamictites which have been interpreted as lodgement tills.  The marlstone was washed through a 300 μm sieve to remove the finest fraction and the remaining sediment was sorted under a binocular microscope.  The gastropod shells consist of incomplete specimens representing growth stages from immature to submature individuals.  The purpose of this project was to reconstruct a complete growth series of snails, including adults which have not been found as fossils.  Computer models of snail growth are made by sweeping a generating plane around a 3D logarithmic spiral based on four parameters: shape of the generating curve (the snail's aperture), expansion of the generating curve¹, expansion of the logarithmic spiral in an xy-plane², and expansion of the logarithmic spiral in a third (z) direction³.  In order to provide input measurements, one of the larger and more complete submature snail specimens was selected and mounted on a glass slide.  The interior chambers of the shell were exposed by applying 10% HCl to create a cross section.  An image of the cross-section (30 x) was taken with a digital camera mounted to a binocular microscope.  Measurements were taken from the image and plotted in Excel to obtain equations for the three growth parameters.  These equations were used to write an AutoLISP program for AutoCAD that produces a mesh model of a Lymnaeoidea snail of any desired size.  Images ranging from an immature to mature snail were saved as dxf files and rendered using Studio VIZ 2006 to produce a complete growth series. The research was supported by NSF grant no. ANT - 0230696.

 

¹  a(θ) = a_oε_a^θ               a = axis length               ε = constant                  a_o : r_o : z_o = initial values

²  r(θ) = r_oε_r^θ                 r = radius length            θ = angle of rotation

³  z(θ) = z_oε_z^θ                z = vertical displacement