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.阐明器官间的连接模式，是识别不同类群（taxa）间解剖同源性（anatomical homologies）的核心前提，同时也是揭示形态发生（morphogenetic）过程、以及调控支系（clade）形态多样化的相关约束机制的关键所在。 这一点对于以离散骨骼单元构成骨架的生物类群研究尤为重要，例如节肢动物、脊椎动物与棘皮动物。 然而，聚焦于形态分异度（morphological disparity）的研究中，极少有将连接模式视为形态组织层级之一，或是借助恰当工具构建比较框架的工作。 本研究聚焦于不规则海胆类中形态分异度最高的支系——无口目（Atelostomata）的顶盘（apical plates）连接模式展开分析。该支系包含约1600个化石现生种（占古生代后海胆类物种的25%左右），并展现出极高的形态分异度。 我们借助图论（graph theory）的工具与统计方法，对顶盘连接模式展开分析。为描述并探究顶盘间连接模式的多样性，我们将每种连接模式抽象为图结构：其中顶盘被编码为节点（nodes），节点间以边（edges）两两相连。随后，我们构建了以连接模式为核心的形态空间（morphospace）比较框架，对自然界中观测到的顶盘模式分异度进行映射与分析。 主要研究结果表明：无口目各类群间及类群内部的顶盘模式均存在极高分异度，且模式数量有限；整体而言，相较于随机生成的连接模式，天然顶盘连接结构均为小型、紧凑且简洁的结构。 顶盘模式演化的核心特征显示，存在受系统发育决定的强形态发生约束机制。 与之相对，无口目内部的演化辐射事件伴随形态分异度的显著提升，这表明支系起源阶段部分约束机制得到了解除。