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Morphometric variation at different spatial scales: coordination and compensation in the emergence of organismal form


Mitteroecker, Philipp et al. (2020), Morphometric variation at different spatial scales: coordination and compensation in the emergence of organismal form, Dryad, Dataset,


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 co-regulation 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 und functional integrity during genetic responses to selection.


Online Appendix of the main mansucript, containing all the formulas and computational details as well as a description of the R package.

Midsagittal landmarks digitized on high-resolution CT scans of a geographically diverse sample of 24 adult human crania (16 females, 8 males). The landmark set comprises 30 anatomical landmarks and 57 semilandmarks.

We provide an R file including functions to compute bending energies, principal warps, partial warp scores, and the non-affine component of shape variation for 2D landmark configurations as well as functions to compute Mardia-Dryden distributions and self-similar distributions of landmarks. We also provide a worked example using the landmark data.

Usage Notes

Semilandmarks are the landmarks #: 5, 7, 9, 11, 13, 15, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 19, 21, 23, 25, 27, 29, 37, 43, 44, 45, 48, 54, 55, 63, 65, 64, 66, 69, 70, 60, 73, 74, 75, 77, 79, 81, 83, 85, 87, 89, 80, 82, 84, 86, 88, 90, 91, 93, 92


Austrian Science Fund, Award: FWF P29397