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

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.