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）间解剖同源性的核心前提，同时也是揭示形态发生过程，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关键，例如节肢动物、脊椎动物以及棘皮动物（echinoderms）。然而，在聚焦形态差异度（morphological disparity）的相关研究中，仅有极少数将连接模式视为形态组织的一个层级，或是借助恰当工具构建了比较分析框架。

本研究针对不规则海胆类（irregular echinoids）中多样性最高的支系——柔海胆亚目（Atelostomata）的顶盘骨板（apical plates）连接模式展开分析。该支系涵盖约1600个化石种与现生种，占古生代后（post-Paleozoic）海胆物种总数的25%左右，且展现出极高的形态差异度。

研究借助图论（graph theory）的工具与统计方法，对骨板的连接模式进行分析。为描述并探究骨板间连接模式的多样性，我们将每种连接模式建模为一张图：其中骨板被编码为节点（nodes），骨板间的连接关系则以边（edges）来表征。随后，我们构建了以连接关系为核心的形态空间（morphospace）作为比较分析框架，对自然界中观测到的骨板连接模式差异度进行映射与分析。

主要研究结果表明：柔海胆亚目类群内部及类群间的顶盘骨板连接模式均存在极高差异度，且模式数量有限；整体而言，相较于随机生成的连接模式，天然骨板连接结构整体偏小、紧凑且结构简单。顶盘骨板连接模式的演化主要特征显示，存在受系统发育关系决定的强烈形态发生约束机制。与之相对，柔海胆亚目内部的演化辐射过程伴随形态差异度的显著提升，这暗示在支系起源阶段，部分形态发生约束得到了解除。