The Study of Growth - An Invariant Approach to Statistical Analysis of Shapes - page 237

linear distance. In such a graph, equivalent patterns of relative growth
in two groups are represented by a constant in the GDM , and the two
growth patterns are graphically represented as parallel vectors when
linear distances are plotted in natural log space (see Figure 5.4a ) . If
growth patterns differ between the two samples being compared, ele-
ments of the GDM are not uniform and vectors representing the
growth patterns are not parallel.
5.10 Producing hypothetical morphologies
from forms and growth patterns
An additional application of the methods provided in this chapter con-
cerns the production of hypothetical forms using growth patterns
quantified by EDMA. There are many instances where the creation of
hypothetical forms may be useful in research. Suppose that there is a
disease that results in dysmorphology. The mutation that causes this
disease has been identified, but it is unclear whether this mutation
causes a primary insult that continually affects systemic or localized
growth patterns of affected individuals or if the mutation results in a
prenatal developmental insult that causes a dysmorphology which is
then maintained by a normal growth pattern. Morphological data
could be used to explore these possibilities. For example, a growth
matrix calculated from a sample of normal individuals can be applied
to coordinate data representing the morphology of an affected individ-
ual. In a sense, we are “growing” an affected individual according to a
growth pattern derived from a sample of unaffected individuals. The
resulting form represents the morphology of an affected individual
who has followed a “normal” growth pattern. The hypothetical form
produced using this method can be statistically compared to age
matched affected and unaffected individuals to determine the differ-
ence in form. Similarly, the hypothetical form and samples of normal
and affected individuals can be analyzed using clustering or classifica-
tion techniques (see Chapter 6 ) to place the hypothetical form into the
group that it matches most closely. These analyses provide information
regarding the role of growth patterns in producing dysmorphology.
Another example of the use of this methodology for the production
of hypothetical forms concerns the testing of hypotheses about the role
of heterochrony in evolution. To offer a simplified sample, let us say
that species A has been described as evolving from species B through
the process of hypermorphosis (“going beyond” the morphology of