The Study of Growth - An Invariant Approach to Statistical Analysis of Shapes - page 238

species B; see Gould, 1977). We can continue to grow the adult form of
species B by applying the complete growth pattern or a specific portion
of the growth pattern for species B to the species B adult morphology,
producing a hypothetical form that we refer to as B´. B´ can be com-
pared to the adult form of species A. This comparison will determine
whether an extension of the growth pattern of species B can produce a
morphology consistent with that of species A.
To provide an example of how EDMA can be used to produce hypo-
thetical forms, we take the growth matrix obtained for Macaca
fascicularis facial growth and apply it to the landmark data repre-
senting the face of the youngest Cebus apella . The form matrix for the
starting form ( Cebus apella age 1) is:

Form matrix for the starting form FM Ca 1

0.00000
1.28355 0.00000

1.36297 0.77527 0.00000

1.55937 1.97504 1.34787 0.00000

2.67187 2.62567 2.23906 1.86376 0.00000

2.24435 2.33153 2.16739 1.96148 0.83985 0.00000

The “transformation matrix” used in this example is the growth matrix
obtained by comparing the young to the old Macaca fascicularis face
( GM MF ).

Transformation Matrix GM MF

0.00000
1.85100 0.00000
1.44800 1.30600 0.00000
1.46000 1.99800 2.13600 0.00000
1.45300 1.71500 1.81600 1.51800 0.00000
1.32900 1.66500 1.64100 1.26300 1.48300 0.00000
The matrix obtained by multiplying the chosen form matrix FM Ca 1 by
the transformation matrix ( GM MF ) represents the hypothetical form
matrix.