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Multivariate statistics and geometric morphometrics

Multivariate statistics and geometric morphometrics

• Important ironical

• Important ironical note: – Bending energy matrix is a function of only the reference (concensus) form of the TPS deformation. – Partial warps are not features of the shape change. • Warps do not describe variation among individual forms, or deformations between forms. • Cannot be interpreted as components of the deformation. • Provide a useful coordinate system within the space in which shape change is analyzed and visualized. – Tangent space. – Projections of forms are partial-warp scores.

• Examples from Zelditch et al. (2004): – PCA (relative warps) of juveniles of 9 species of piranhas. – Data: matrix of partial warp scores on 1 st partial warp.

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