Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

A new developmental model for growth of the echinoid test is based on a review of the growth patterns in regular echinoids. Echinoids are structurally composed of a tessellation of hundreds to thousands of individual plates. The two major aspects of echinoid growth are treated separately. (1) New plates are added in accordance with the Ocular Plate Rule and plate addition is hypothesized to be constitutively active but inhibited by a morphogen originating in coronal plates. Morphogen production is modeled as an inverse function of plate size and the concentration of inhibiting morphogen at a plate nucleation point is inversely proportional to the distance from surrounding plate centers. Plate addition is triggered whenever the inhibiting morphogen concentration falls below a threshold value. (2) The growth of individual plates is described using the Bertalanffy growth equation to model change in plate perimeter. The geometric model is based on a spherical frame of reference, and all calculations of position and growth are modeled over the surface of the sphere (i.e., along geodesics). The data structure defined to maintain the geometric parameters is based on a spherical Delaunay triangulation of plate centers, and the edge geometry approximated by the dual Voronoi polygonalization. Echinoid plates are thus modeled as Voronoi polygons covering the sphere. Growth is modeled by the increasing radius of the sphere and the changing topology of the plates as new plates are added and existing plates grow. Final form of the complete test is generated by an affine deformation of the sphere. The growth model is implemented as the program EFORECHINOID, coded in the object-oriented programming language C++ with significant usage of the Standard Template Library (STL) for efficient coding and memory management. Most parameters are available to a user via a Graphical User Interface (GUI), and output of 3-dimensional simulations is via standard 3-D AutoCAD[trademark] Drawing Exchange Format (DXF) files. Program efficiency is O(nlogn) and reasonably parameterized growth simulations with several hundred time steps can be performed in a matter of minutes per run. / text

Echinoids are important grazers in the near-shore ecosystem and can significantly effect their ecology. The sea urchin Parechinus angulosus occurs inter- and subtidally along the southern African coast. Within this range it consumes an extremely wide variety of algae. Since algal cell walls have an almost species specific chemical composition, the question arises as to how it can digest the algae that it consumes. In order to investigate the digestive mechanisms employed by P. angulosus, an ultrastructural study of the gut was undertaken to characterize the tissue and identify functional regions in the gut. Ten structural and storage polysaccharides commonly found in macroalgae were used as substrates to assay the digestive polysaccharidases of the sea urchin. The enteric bacteria of the sea urchin were isolated and tested separately for polysaccharidase activity using the same substrates. The results shown that the gut of Parechinus angulosus is regionally specialized, with the foregut primarily responsible for the production of hydrolytic enzymes, while the hindgut is primarily absorptive. The occurrence of lamellar bodies, heterolysosomes, cytoplasmic blebs and paddle cilia among other characteristic features of the digestive epithelium are described and discussed. Two levels of enzyme activity are apparent. Generally the urchin could hydrolyze the reserve polysaccharides, but only partially hydrolyze the structural polysaccharides, of red and green algae. P.angulosus was unable to digest alginic acid, the main structural polysaccharide of brown algae. Mixed cultures of bacteria utilized only the reserve polysaccharides of red and green algae. Significantly, the bacteria were able to hydrolyze alginic acid. Enteric bacteria also showed agarolytic activity. Parechinus angulosus has the ability to digest red and green algae. No lysozyme activity was detected. The enteric bacteria can digest the same algal reserve polysaccharides and so may compete for carbon in the gut. However, in the case of brown algae, bacteria have a potentially important endosymbiotic role as agents of digestion. These results correspond with food preference studies which have shown that, although P.angulosus consumes the kelp Ecklonia maxima, in the western Cape, it is amongst its least preferred food species. The reasons for this are its unpalatability and the urchin's inability to digest brown algae. The digestibility of algal material can be an important factor in determining algal-herbivore interactions.