Methods for shape analysis of landmark data from articulated structures

Landmark-based geometric morphometric methods are powerful tools in the study of size and shape. These methods allow one to describe the shape of rigid structures using a set of variables that can be used for statistical hypothesis testing, and to generate graphical representations of shape differences as deformations. However, when the landmarks chosen for an analysis span multiple rigid structures that articulate, variation describing the position of landmarks on one structure relative to those on another is also present in the data. In this paper, I develop three novel methods to remove the effects of arbitrary positioning of articulated structures. The separate subset method constructs shape variables for each subset of landmarks separately, then combines the resulting information. The fixed angle method rotates one subset of landmarks so the angle between subsets is invariant among specimens, and then treats them as a rigid structure for the shape analyses. The orthogonal projection method estimates the distortion due to the effects of articulation motion, approximates it with a vector, and then removes this dimension from the shape data before statistical analysis. I describe each of these methods in detail, and demonstrate their use on a data set containing landmarks from skulls and lower jaws from several populations of the threespine stickleback, Gasterosteus aculeatus. The results using all methods are compared to previous findings and to each other, and the implications for studies of functional morphology are discussed.