Semi-landmark File from A comparison of metrics for quantifying cranial suture complexity

Cranial sutures play critical roles in facilitating postnatal skull development and function. The diversity of function is reflected in the highly variable suture morphology and complexity. Suture complexity has seldom been studied, resulting in little consensus on the most appropriate approach for comparative, quantitative analyses. Here, we provide the first comprehensive comparison of current approaches for quantifying suture morphology, using a wide range of two-dimensional suture outlines across extinct and extant mammals (<i>n</i> = 79). Five complexity metrics (sinuosity index (SI), suture complexity index (SCI), fractal dimension (FD) box counting, FD madogram and a windowed short-time Fourier transform with power spectrum density (PSD) calculation) were compared with each other and with the shape variation in the dataset. Analyses of suture shape demonstrate that the primary axis of variation captured attributes other than complexity, supporting the use of a complexity metric over raw shape data for sutural complexity analyses. Each approach captured different aspects of complexity. PSD successfully discriminates different sutural features, such as looping patterns and interdigitation amplitude and number, while SCI best-captured variation in interdigitation number alone. Therefore, future studies should consider the relevant attributes for their question when selecting a metric for comparative analysis of suture variation, function and evolution.

颅缝（cranial sutures）在促进出生后颅骨发育与功能发挥中扮演关键角色。其功能多样性体现在形态与复杂度的高度变异之上。当前针对颅缝复杂度的研究较为匮乏，导致学界在开展比较性定量分析时，尚未就最优分析路径达成共识。

本研究以79份涵盖已灭绝与现生哺乳动物的二维颅缝轮廓样本为对象，首次全面对比了当前用于量化颅缝形态的各类方法。本次对比共纳入5种复杂度指标：弯曲度指数（sinuosity index, SI）、颅缝复杂度指数（suture complexity index, SCI）、盒计数法分形维数（fractal dimension box counting, FD）、马氏图法分形维数（FD madogram），以及搭载功率谱密度（power spectrum density, PSD）计算的窗式短时傅里叶变换。研究将上述指标两两比对，并与数据集内的形状变异特征进行关联分析。

颅缝形状分析结果显示，本次分析捕获的首要变异维度并非复杂度相关属性，这支持在颅缝复杂度分析中采用复杂度指标而非原始形状数据。不同分析方法各自捕捉复杂度的不同维度：功率谱密度可有效区分不同颅缝特征，例如环状模式、交错幅度与交错数量；而颅缝复杂度指数则仅能最优地捕捉交错数量的变异。因此，未来研究在选取用于颅缝变异、功能与演化比较分析的指标时，应结合其研究问题聚焦的相关特征进行决策。