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.