Lab 4 - Morphology and Principal Components Analysis

Morphology

• The study and description of an organism’s physical form and structure.

• In biological anthropology, morphology can be used to compare bones, teeth, and other anatomical structures.

Shape vs. size vs. form

• Shape: the geometry of an object irrespective of magnitude or orientation.

• Size: a linear or multidimensional measure of an object’s proportions or magnitude.

• Form: the combination of an object’s size and shape.

Geometric morphometrics

• A method for quantitatively analyzing morphology using geometric coordinates called landmarks.

• It allows researchers to compare complex shapes across specimens.

Landmarks

• Points in 2D or 3D space that describe particular anatomical features, expressed as Cartesian coordinates such as x, y, and z.

• At least three points are needed to describe a shape rather than just a line.

True landmarks vs. semi-landmarks

• True landmarks are identifiable anatomical points that can be located consistently across specimens.

• Semi-landmarks are points placed along curves where clear anatomical landmarks may be unavailable; they can be manually placed or allowed to slide.

Landmark clouds

• Collections of landmarks representing the shape of a specimen.

• Before comparing landmark clouds, researchers standardize them using Procrustes superimposition.

Procrustes superimposition (GPA)

• A method for standardizing landmark configurations by adjusting their scale, location, and orientation.

• It involves scaling, translation, and rotation so that shapes can be compared more meaningfully.

Procrustes distance

• A measure of the distance between corresponding landmarks after superimposition.

• A greater Procrustes distance indicates a greater difference in morphology at that point.

• Distances across landmarks can describe overall shape differences between specimens.

Principal components analysis (PCA)

• A statistical technique that organizes data along major axes of variation called principal components (PCs).

• It summarizes patterns across multiple variables and can be used to visualize morphological variation in a morphospace.

Morphospace

• A representation of the range of morphological variation across a sample.

• Specimens are positioned according to their values on principal components, allowing researchers to examine similarities, differences, and group separation.

Principal component 1 (PC1)

• The first principal component captures the greatest proportion of variation in the dataset.

• In many biological samples, most measurements increase along PC1 because size is often a major driver of morphological variation, but this must be checked using the loadings.

Principal component 2 (PC2)

• The second principal component captures the greatest proportion of variation remaining after PC1.

• It represents another pattern of variation, often involving differences in proportions or other combinations of measurements.

Eigenvalues

• The proportion of whole-sample variation captured by each principal component.

• Larger eigenvalues mean that a PC explains more of the dataset’s variation. Check eigenvalues first when interpreting a PCA plot.

Eigenvectors (loadings)

• The relative contribution of each variable or measurement to a principal component.

• Their values indicate the direction and relative importance of each variable in driving variation along that axis.

Interpreting positive and negative loadings

• Positive values indicate that a variable increases toward the positive end of a PC axis.

• Negative values indicate that it decreases toward the positive end. The absolute magnitude indicates relative importance: values closer to zero have less influence on that PC.

Eigenvalues vs. eigenvectors

• Eigenvalues tell you how much variation a PC captures.

• Eigenvectors or loadings tell you which variables contribute to that PC, how strongly they contribute, and the direction of their relationship with the axis.

Why is PCA useful for comparing morphology?

Multiple anatomical measurements can vary together, making individual measurements difficult to interpret separately. PCA summarizes major patterns of variation, helping researchers compare specimens and identify which measurements contribute most to differences between groups.