Landmark-based geometric morphometrics is a powerful approach to quantifying biological shape, shape variation, and covariation of shape with other biotic or abiotic variables or factors. The resulting graphical representations of shape differences are visually appealing and intuitive. This paper serves as an introduction to common exploratory and confirmatory techniques in landmark-based geometric morphometrics. The issues most frequently faced by (paleo)biologists conducting studies of comparative morphology are covered. Acquisition of landmark and semilandmark data is discussed. There are several methods for superimposing landmark configurations, differing in how and in the degree to which among-configuration differences in location, scale, and size are removed. Partial Procrustes superimposition is the most widely used superimposition method and forms the basis for many subsequent operations in geometric morphometrics. Shape variation among superimposed configurations can be visualized as a scatter plot of landmark coordinates, as vectors of landmark displacement, as a thin-plate spline deformation grid, or through a principal components analysis of landmark coordinates or warp scores. The amount of difference in shape between two configurations can be quantified as the partial Procrustes distance; and shape variation within a sample can be quantified as the average partial Procrustes distance from the sample mean. Statistical testing of difference in mean shape between samples using warp scores as variables can be achieved through a standard Hotelling's T2 test, MANOVA, or canonical variates analysis (CVA). A nonparametric equivalent to MANOVA or Goodall's F-test can be used in analysis of Procrustes coordinates or Procrustes distance, respectively. CVA can also be used to determine the confidence with which a priori specimen classification is supported by shape data, and to assign unclassified specimens to pre-defined groups (assuming that the specimen actually belongs in one of the pre-defined groups).
Examples involving Cambrian olenelloid trilobites are used to illustrate how the various techniques work and their practical application to data. Mathematical details of the techniques are provided as supplemental online material. A guide to conducting the analyses in the free Integrated Morphometrics Package software is provided in the appendix.