Holotestoid: a computational model for testing hypotheses about echinoid skeleton form and growth.

Regular echinoid skeletons, or tests, comprise plate patterns and overall shapes that have proven challenging to analyse solely on the basis of any one approach or process. Herein, we present a computational model, Holotestoid, that emulates four macrostructural ontogenic processes involved in test growth (plate growth, plate addition, plate interaction, and plate gapping). We devise a geometric representation for analysing tests and describe how we use analogies (bubble interactions and close-packing) to emulate the processes. In the computational model, the emulated processes are used to determine the plate size and plate shape and combined to simulate a growth zone. We simulated growth zones for Arbacia punctulata and for Strongylocentrotus franciscanus by changing the value for one parameter, the ambulacral column angle. We quantitatively compared morphological features for simulated forms to those for real specimens to test the computational model. Additionally, we simulated growth zones for A. punctulata, S. franciscanus, Eucidaris thouarsii, and Mellita quinquiesperforata by changing three parameters, ambulacral column angle, peristome radius to apical system radius ratio, and apical system radius to column length ratio. Holotestoid can be used to explain morphological disparity among echinoid tests.

COMPUTER-SIMULATED SHELL SIZE AND SHAPE VARIATION IN THE CARIBBEAN LAND SNAIL GENUS CERION: A TEST OF GEOMETRICAL CONSTRAINTS.

A computer graphical model of gastropod shell form is used to test a hypothesis of geometric constraint proposed to explain the disjunct distribution of shell forms observed in Cerion, a species-rich and geometrically varied genus of terrestrial gastropods. The mapping of computer-simulated forms into a morphospace of Cerion shells produces a continuum of sizes and shapes. Therefore, the absence of particular shell forms is not explained by geometric constraints. Two proposed modes of shell morphogenesis at extreme ranges in size ("dwarfs" and "giants") previously were thought to be exclusive routes to the construction of high-spired ("smokestack") forms. The present study shows that there are, in fact, multiple routes of transformation. In addition, these routes are geometrically reversible and interconnect the members of the shell-form continuum. Thus, the possible pathways followed during the course of evolution within this genus cannot be determined until an adequate phylogenetic hypothesis has been proposed.