Meeting Abstract

71.2  Jan. 7  Implementation of a developmental model for growth of the post-metamorphic echinoid skeleton ZACHOS, Louis G.; The University of Texas at Austin zachos@mail.utexas.edu

The changes in shape of an echinoid skeleton or test during post-metamorphic ontogeny result from a precise interrelationship between growth of individual plates (accretion), introduction of new plates at the apical system (insertion), movement of plates towards the mouth (migration), and suturing of plates (annealing). The actual developmental mechanisms involved are unknown, but a heuristic model of echinoid growth can represent these interrelationships via realistic developmental pathways. I present a computer program of a model based on hypothetical signaling pathways represented by a set of functions describing nutrient diffusion, growth factor induction, lateral growth inhibition, and morphogen thresholds and gradients. The computer program applies these growth functions incrementally to produce a series of static models, each representing the growth state of every plate in the test at each time step. The test is modeled over a spherical coordinate system using Delaunay triangulation to create and maintain a plate reference system and a corresponding data structure to store individual plate geometries. Overall test growth (plate accommodation) is wholly dependent on insertion, accretion, migration, and annealing of the individual plates. Final test shape is derived from affine deformations applied to the spherical model. Varying the signaling parameters and rules of interaction results in a range of realistic models and suggests a basis for a phylogenetic hierarchy of growth mechanisms. Program results can be visualized as animations of growing model echinoids, which can be compared with actual ontogenetic series of representative species.