Data from: Empirical and theoretical study of Atelostomate (Echinoidea, Echinodermata) plate architecture: using graph analysis to reveal structural constraints

Describing patterns of connectivity among organs is essential for identifying anatomical homologies among taxa. It is also critical for revealing morphogenetic processes and the associated constraints that control the morphological diversification of clades. This is particularly relevant for studies of organisms with skeletons made of discrete elements such as arthropods, vertebrates, and echinoderms. Nonetheless, relatively few studies devoted to morphological disparity have considered connectivity patterns as a level of morphological organization or developed comparative frameworks with proper tools. Here, we analyze connectivity patterns among apical plates in Atelostomata, the most diversified clade among irregular echinoids. The clade comprises approximately 1600 fossil and Recent species (e.g., 25% of post-Paleozoic species of echinoids) and shows high levels of morphological disparity. Plate connectivity patterns were analyzed using tools and statistics of graph theory. To describe and explore the diversity of connectivity patterns among plates, we symbolized each pattern as a graph in which plates are coded as nodes that are connected pairwise by edges. We then generated a comparative framework as a morphospace of connections, in which the disparity of plate patterns observed in nature was mapped and analyzed. Main results show that apical plate patterns are both highly disparate between and within atelostomate groups and limited in number; overall, they also constitute small, compact, and simple structures compared to possible random patterns. Main traits of the evolution of apical plate patterns reveal the existence of strong morphogenetic constraints that are phylogenetically determined. In contrast, evolutionary radiations within atelostomates were accompanied by a clear increase in disparity, suggesting a release of some constraints at the origin of clades.

解析器官间的连接模式，对于识别不同类群间的解剖学同源性至关重要，同时也为揭示形态发生过程以及调控演化支形态多样化的相关约束机制提供关键依据。这一点对于以离散骨骼单元构成骨架的类群研究尤为重要，例如节肢动物、脊椎动物和棘皮动物。然而，在聚焦形态分异度（morphological disparity）的相关研究中，极少有将连接模式视为形态组织层级的案例，也鲜有借助恰当工具构建比较框架的工作。本研究聚焦不规则海胆类（irregular echinoids）中多样性最高的演化支——无气门亚目（Atelostomata）的顶体板（apical plates）连接模式。该演化支包含约1600个化石与现生物种（占古生代后海胆类物种总数的25%左右），且呈现出极高的形态分异度。本研究借助图论工具与统计方法分析顶体板的连接模式：为描述并探究顶体板间连接模式的多样性，我们将每种连接模式抽象为图结构，其中顶体板被编码为节点，板间的连接关系以边来表示。随后我们构建了以连接关系为维度的形态空间比较框架，对自然界中真实存在的顶体板模式的分异度进行映射与分析。主要研究结果显示：无气门亚目类群间及类群内部的顶体板模式均存在极高的分异度，且这类模式的数量相对有限；整体而言，相较于随机生成的连接模式，真实的顶体板连接结构均为小型、紧凑且简洁的结构。顶体板模式演化的核心特征表明，存在受系统发育调控的强形态发生约束机制；与之相对，无气门亚目内部的演化辐射事件伴随形态分异度的显著提升，这暗示演化支起源阶段部分约束机制得到了解除。