General morphometric protocol Four simple steps to morphometric success

Four steps Data acquisition – images and landmarks Remove shape variation and generate shape variables – superimposition and TPS Perform statistical analyses to test biological hypotheses – standard multivariate analysis and resampling methods Produce graphical depiction of results – deformation grids, statistical plots, etc.

Data acquisition - images Transferring 3D to 2D depiction Many ways to go wrong Three things that don’t matter –Location in plane –Scale –Rotation

Problems to avoid Paralax – pitch and roll “bendiness” – look for straight lines and include points on these lines Articulated structures – can incorporate in analysis or remove as noise, but easiest to avoid problem in beginning

Avoiding image problems Standardize image acquisition procedure Independent quality check

Digitizing landmarks Homology Type 1, 2, and 3 - sliding semilandmarks Order is critical Checking for errors and outliers Symmetrical structures

Step two – remove nonshape variation and generate shape variables 3 types of nonshape variation – relative position, scale, rotation Remove by a process called superimposition via generalized Procrustes analysis or GPA

Variation in images

Translation

Rotation

Scaling Only shape variation left

Generate shape variables Thin plate spline Generates non-affine and affine components referred to as partial warps and uniform components

Affine and non-affine shape change

Shape coordinates Partial warps come in X and Y pairs, (2p-4) Uniform components also a pair, X and Y Combined referred to as the W (weight) matrix Scores are coordinates of a point along partial warp axes Nonsingular data matrix for multivariate analysis of shape

Relative warps Can use PCA on W matrix to generate relative warp scores and use these as data matrix Useful for visualization of major axis of shape variation