Why morphometrics is special: the problem with using partial warps as characters for phylogenetic inference.

There has been a dispute among morphometricians (Fink and Zelditch, 1995; Zelditch, Fink, and Swiderski, 1995; Adams and Rosenberg, 1998; Rohlf, 1998; Swiderski, Zelditch, and Fink, 1998; Zelditch, Fink, Swiderski, and Ludrigan, 1998) on the possibility of using morphometric data, expressed as shape variables (particularly partial warps) extracted by geometric morphometrics methods, in phylogenetic analyses. Much has been said against and in favor of this particular combination of geometric morphometrics and cladistics, but the issue is not yet resolved. This is probably because the single point that makes the partial warps unsuitable as characters for cladistic analysis, was not thoroughly considered: the lack of biological signiŽcance in partial warps when treated as single univariate characters. To project amultidimensional space into a set of single dimensions by different rotations for parsimony analysis, the single dimensions must have biological signiŽcance by themselves (what cannot be expected from partial warps, Rohlf, 1998). This problem is derived from the shape nonmonotonicity theorem, originally published by Bookstein (1980), that asserts: “for any three triangles of landmarks, no twoofwhichhave exactly the same shape, and for anyorderingof three triangles, there exist indeŽnitelymany shapemeasures consistent with that ordering” (Bookstein, 1994, p. 206). In other words, the ordination patterns in shape space are not consistent for all possible shape variables, although the distances among shapes are always preserved. Our perception of the world is deeply dependent on the dimensions we can observe. Natural phenomena are usually expressed in a multivariate fashion, even though most of us are limited to visualizing things in a maximum of three dimensions. To understand the phenomena, we must reduce the dimensionality by projecting our observations in a plane or a space, according to some sensible criterion (multivariate analyses usually maximize some sort of variance). If we have to draw a tridimensional pen in two dimensions, the sensible choice is a lateral view where the silhouette of the pen can be discerned. If we choose a different view (e.g., end view) to project the pen, no one will be able to discern the pen from a ball. Zelditch et al. (1995), Fink and Zelditch (1995), and Swiderski et al. (1998) have demonstrated how shape variables (partial warps) obtained by geometric morphometrics can be coded for phylogenetic analysis. This short note shows how their method corresponds to an arbitrary set of projections and how different arbitrary choices affect the outcome of cladistic analysis of morphometric data.