A PLS Regression Framework for Spatially-dense Geometric Morphometrics to Analyze Effects on Shape and Shape Characteristics: Applied to the Study of Genomic Ancestry and Sex on Facial Morphology

摘要

Shape-regression is an important technique in geometric morphometrics for investigating the effects of various independent variables on biological morphology represented using landmark configurations (dependent variables). Spatially-dense (in contrast to the traditional sparse) landmark configurations, typically cover the complete shape with thousands of landmarks such that salient features of the shape are not overlooked. Furthermore, as proposed in this chapter, spatially-dense configurations allow for the computation and representation of shape variation in terms of local shape characteristics such as curvature, area, and normal displacement. One challenge in using spatially-dense data is the large number of correlated dependent variables in comparison to the number of observations, leading to model instability when using an ordinary least squares regression. This problem has been addressed by using the more advanced technique of partial least squares regression (PLSR), which uses the correlation between the dependent variables for model stabilization, and have investigated genomic ancestry and sex in relation to 3D facial morphology. Briefly, the effect on facial morphology with respect to a particular landmark is measured as the magnitude or Euclidean distance of its displacement in 3D space. The effect-size or strength of the relationship is reported as the variance explained by the PLSR model. Statistical significance is tested under permutation for multivariate regressions. While the effect and effect-size provide insight into which parts of the face are being affected it fails to summarize and convey how facial characteristics are changing. Therefore, the PLS regression framework has been expanded to analyze local effects on normal displacement, curvature, and area. The results are in agreement with general expectations for differences in facial shape due to sex and genomic ancestry. The incorporation of normal displacement, curvature, and area provide additional and valuable biological insight and feedback of the effects on facial morphology due to sex and genomic ancestry.