Abstract It is a classic aim of quantitative and evolutionary biology to infer genetic architecture and potential evolutionary responses to selection from the variance–covariance structure of measured traits. But a meaningful genetic or developmental interpretation of raw covariances is difficult, and classic concepts of morphological integration do not directly apply to modern morphometric data. Here, we present a new morphometric strategy based on the comparison of morphological variation across different spatial scales. If anatomical elements vary completely independently, then their variance accumulates at larger scales or for structures composed of multiple elements: morphological variance would be a power function of spatial scale. Deviations from this pattern of “variational self-similarity” (serving as a null model of completely uncoordinated growth) indicate genetic or developmental coregulation of anatomical components. We present biometric strategies and R scripts for identifying patterns of coordination and compensation in the size and shape of composite anatomical structures. In an application to human cranial variation, we found that coordinated variation and positive correlations are prevalent for the size of cranial components, whereas their shape was dominated by compensatory variation, leading to strong canalization of cranial shape at larger scales. We propose that mechanically induced bone formation and remodeling are key mechanisms underlying compensatory variation in cranial shape. Such epigenetic coordination and compensation of growth are indispensable for stable, canalized development and may also foster the evolvability of complex anatomical structures by preserving spatial and functional integrity during genetic responses to selection.[Cranial shape; developmental canalization; evolvability; morphological integration; morphometrics; phenotypic variation; self-similarity.]

中文翻译：

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不同空间尺度的形态变化：生物体出现时的协调与补偿

摘要 定量和进化生物学的一个经典目标是从测量性状的方差-协方差结构中推断遗传结构和对选择的潜在进化反应。但是对原始协方差进行有意义的遗传或发育解释是困难的，并且形态学整合的经典概念并不直接适用于现代形态测量数据。在这里，我们提出了一种基于不同空间尺度的形态变化比较的新形态测量策略。如果解剖元素完全独立地变化，那么它们的方差会在更大的尺度上累积，或者对于由多个元素组成的结构：形态方差将是空间尺度的幂函数。偏离这种“变异自相似性”模式（作为完全不协调生长的无效模型）表明解剖组件的遗传或发育协同调节。我们提出了生物识别策略和 R 脚本，用于识别复合解剖结构大小和形状的协调和补偿模式。在对人类颅骨变异的应用中，我们发现颅骨组件的大小普遍存在协调变异和正相关，而它们的形状则以补偿性变异为主，导致颅骨形状在更大尺度上的强烈管道化。我们提出机械诱导的骨形成和重塑是颅骨形状补偿性变化的关键机制。这种表观遗传协调和生长补偿对于稳定、畅通的发育是必不可少的，并且还可以通过在对选择的遗传反应期间保持空间和功能完整性来促进复杂解剖结构的可进化性。发展渠道；可进化性；形态整合；形态测量学；表型变异；自相似。]