Description and Analysis of Spatial Patterns in Geometric Morphometric Data

Abstract

The development of techniques for the acquisition of high-resolution 3D images, such as computed tomography and magnetic resonance imaging, has opened new avenues to the study of complex morphologies. Detailed descriptions of internal and external traits can be now obtained, allowing the intensive sampling of surface points. In this paper, we introduce a morphometric and statistical framework, grounded on Procrustes and Procrustes-like techniques as well as standard spatial statistics, to explicitly describe and incorporate the spatial pattern of these surface points into the analyses. We exemplified this approach by analyzing ontogenetic changes in a sample of human brain endocasts and inter-specific differences between primate skulls. An intensive sampling of points on 3D surfaces was performed by automatic techniques and the morphometric variation among specimens was measured by the residuals obtained after the alignment of points. Our results showed that shape changes in both examples are spatially structured. Different results were attained by using methods that incorporate or not the spatial structure in the evaluation of the effect of specific biological factors on shape variation. Particularly, these analyses indicated that the effect of biological factors acting at local scales can be confounded with more systemic factors (by example, the effect of the diet on the facial skeleton) if the spatial structure is not taken into account. Overall, our results suggest that the intensive description of shape differences among structures using densely sampled points on 3D surfaces combined with spatial statistical methods can be used to explore problems not widely addressed in morphological studies.

Morphometric Variation at Different Spatial Scales: Coordination and Compensation in the Emergence of Organismal Form

“…Only more distant landmarks are uncorrelated or even negatively correlated (due to the superimposition). Such a pattern of spatial autocorrelation is very common for morphometric data ( Mitteroecker and Bookstein 2007 ; Gonzalez et al 2019 ). Even though consistent with a model of completely unintegrated development, it can explain the results in many published studies on variational modularity ( Mitteroecker 2009 ).…”

“…This interpretation is not warranted for many kinds of measurements, particularly not for measurement point s (“landmarks”). Even if different anatomical components should lack any common control, nearby measurement points would still be correlated simply because of their spatial adjacency ( Mitteroecker and Bookstein 2007 ; Mitteroecker et al 2012 ; Bookstein 2015 ; Gonzalez et al 2019 ). However, a complete lack of coregulation would manifest at another level: If all parts vary completely independently, then their size variance accumulates at larger scales; morphological variation would be a function of the spatial scale at which it is studied.…”

Thirty years of geometric morphometrics: Achievements, challenges, and the ongoing quest for biological meaningfulness

“…A central problem in this context is the ignorance of spatial autocorrelation among morphometric measurements (Bookstein, 2015; Gonzalez et al, 2019; Mitteroecker & Bookstein, 2007). Adjacent parts of an organism cannot vary independently in their dimensions, just for spatial reasons.…”

Variation in cross-sectional indicator of femoral robusticity in Homo sapiens and Neandertals

“…The observed variable of a population may be spatially dependent, meaning that its value depends on the variable of a neighboring group. Many analyzed variables are spatially correlated for various reasons, such as gene flow or natural selection resulting from similar environments 27 , 43 , 104 . For example, spatial autocorrelation analysis has revealed variation in human cranial variables 44 .…”