Modelling Echinoid Skeletal Growth and Form

Abstract

Echinoids have an endoskeletal system which is ideal for studying calcified structures such as development of vertebrate skeletons. However, understanding echinoid skeletal (test) growth has proven challenging to analyse solely on the basis of any one approach or process. Therefore, theoretical models have been developed to understand growth and form of echinoid tests. Herein, Holotestoid, a computational model of echinoid test growth is described. The model incorporates mathematical principles (e.g., close-packing), physical principles (e.g., interface between coalescing bubbles) and biological processes (e.g., echinoid ontogenic processes). It is the first computational model that emulates all five ontogenic processes involved in test growth (plate growth, plate addition, plate interaction, plate gapping, and visceral growth) using a geometrical representation and three analogies (coalescing bubble, circle-packing, and catenary chains). The emulated processes are used to predict plate size, plate shape, and test shape. The results from the simulations of the growth zones show that the ambulacral column angle (e.g., for A. punctulata α_am= 22° and for S. franciscanus α_am = 32°) is a crucial parameter that distinguishes between species when varied. The. comparison of simulated data with those from real specimens yielded high accuracies, thereby validating the model. The combination of the simulated processes produced patterns mimicking real biological specimens. The model was further used to investigate the test morphological disparity observed among echinoids, specifically between. regular echinoid (sea urchin) tests and irregular echinoid (sand dollar) tests. Both exhibit morphological similarities as imagines, however, they develop different test morphologies as adults. Thus, Holotestoid was used to explore the influence of each parameter on test height-todiameter ratio (h:d). The results showed that both ambulacral column widening and increase in total plate number cause the test h:d to decrease thereby leading to test flattening. Whereas the absolute size of the apical system and peristome does not influence test h:d, however, their growth with respect to column length caused an increase in the test h:d. These results provide an explanation of how the different test shapes were obtained.