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.]
This document corresponds to the worked example of the paper Detecting phylogenetic signal and adaptation in papionin cranial shape by decomposing variation at different spatial scales (Grunstra et al.). The dataset is a set of 70 2D landmarks on the midsagittal plane of the skull in 67 primates from 18 species (16 papionin taxa, 2 outgroups). The example below describes how to decompose shape variation into total, outline, and residual shape (approach 1) or into large-scale and small-scale shape (approach 2). For further details, please read the associated paper. Data preparation Install and load packages in R. library("prWarp") library("geomorph") Load the dataset papionin. This dataset comprises the coordinates of 70 two-dimensional landmarks for the 67 specimens as a 3D array. data("papionin") # load dataset species <-papionin$species # species papionin_ar <-papionin$coords # landmark coordinates k <-dim(papionin_ar)[1] # number of landmarks n_spec <-dim(papionin_ar)[3] # number of specimens n_species <-length(levels(species)) # number of species Approach 1: Total, outline, and residual shape variation In this approach the total shape variation is decomposed into the variation of outline shape and residual shape. The outline shape corresponds to a subset of the full landmark set, in which all landmarks that demarcate the boarders between bones (i.e., landmarks on sutures and synchondroses) are free to slide. The residual shape corresponds to the slid landmark coordinates of the full dataset after warping them to the mean outline shape using TPS interpolation.
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