The Study of Growth - An Invariant Approach to Statistical Analysis of Shapes - page 213

CHAPTER 5
The Study of Growth
“The form of an organism is determined by its rate of growth in various
directions”
D'Arcy Thompson (1992)
Up to this point we have limited our discussion to the description and
comparison of two forms. Growth analysis stems directly from the
methods we have already developed in the last chapter and is simply a
special case of form comparison. Instead of comparing the form of one
group to the form of another group, we compare the form of one age
class to the form of another age class within the same group.
Consequently, the tools that we have presented thus far are adequate
for studying growth within a single group.
We define growth pattern as the composite of geometric changes in
biological structure occurring through ontogenetic time. In many prac-
tical situations, we are interested in comparing the growth pattern of
one group with the growth pattern of another. The issues of comparing
growth patterns lead to different challenges and problems necessitat-
ing further development of analytical techniques. This chapter
discusses the special difficulties faced in comparing growth patterns,
and develops relevant methods. This discussion is based in part on
ideas presented in Richtsmeier and Lele (1993).
The study of growth provides important information for many fields
of inquiry. In the study of dysmorphology or disease, a valid question
concerns the original source and reason for continuation or intensifi-
cation of the dysmorphology. Is the dysmorphology a product of an
initial developmental insult that is carried to a new developmental
stage by following a normal growth pattern? Or is growth affected such
that the dysmorphology is at least in part a product of an aberrant
growth pattern? The answer to this question might inform us about