Fig. 7. Morphogenetic scaling and the archetype hypothesis.

A Simple transformations of shapes through diagonal and shear matrices as examples for the scaling of developed tissue/body shapes between species. In general, an arbitrary regular matrix M can be decomposed into the stretch operation U and the rotation R (i.e., M = RU), and thus linear transformations through regular matrices are regarded as a scaling operation of shapes along the direction of each eigenvector (of U). B Our results show that the rescaled tissue dynamics in the ξ-space are well conserved between chick and Xenopus. This flow can be regarded as an archetype, corresponding to the standard shape suggested by D’arcy Thompson’s pioneering work. The tissue deformation map for each species is obtained by applying a species-specific time-variant linear transformation to this common flow. Consequently, the tissue dynamics for both species are also mapped, or scaled, to each other through time-variant linear transformations.