McMaster University, Department of Biology, 1280 Main Street West, Hamilton, ON, Canada L8S 4K1.
J Theor Biol. 2011 Sep 21;285(1):113-25. doi: 10.1016/j.jtbi.2011.06.019. Epub 2011 Jul 2.
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.
常规海胆骨骼，或称为壳，其由壳板图案和整体形状组成，仅通过单一方法或过程来分析具有挑战性。在此，我们提出了一种计算模型 Holotestoid，它模拟了壳生长过程中涉及的四个宏观结构发生过程（壳板生长、壳板添加、壳板相互作用和壳板间隙）。我们设计了一种用于分析壳的几何表示，并描述了如何使用类比（气泡相互作用和紧密堆积）来模拟这些过程。在计算模型中，模拟过程用于确定壳板的大小和形状，并将其组合起来模拟生长区。我们通过改变一个参数，即步带柱角度，为棘皮动物中的多棘海胆和扁形海胆模拟了生长区。我们定量比较了模拟形态的形态特征与真实标本的形态特征，以检验计算模型。此外，我们通过改变三个参数，即步带柱角度、口面半径与顶系半径比以及顶系半径与柱长比，为楯形目海胆、五角海胆和五齿刻肋海胆模拟了生长区。Holotestoid 可用于解释海胆壳形态差异。
