Biology Reference
In-Depth Information
CHAPTER 1
Introduction
“Nor must we forget that the biologist is much more exacting in his
requirements, as regards form, than the physicist; for the latter is usual-
ly content with either an ideal or a general description of form, while the
student of living things must be specific.”
D'Arcy Thompson (1992)
Natural scientists have long perceived and classified organisms pri-
marily on the basis of their appearance and structure, otherwise
known as their
form
. Beyond classification, students of biology study
form in order to understand those processes that underlie variation in
form, processes like disease, growth, and evolution. The true form of an
object does not change whether an organism is moving across a surface
(translation in mathematical terms) or spinning on an axis (rotation).
Our perception of the organism may change when orientation changes,
but perception is not our concern here. It follows that any quantitative
representation of a form should not change if the coordinate system
used to represent that form changes. Moreover, any comparison of
forms should give us equivalent results regardless of whether the oper-
ations of translation and rotation are used in these comparisons. These
simple observations underscore the importance of the principle of
invariance
in the study of form.
The invariance principle and its implications for the study of bio-
logical form have prompted us to write this topic. There are now many
morphometric methods available to the biologist who wants to study
form quantitatively, and computer programs for most of these methods
are easily obtained. However, until recently the invariance principle
and its implications for the study of biological form have not been care-
fully considered in the field of morphometrics. We have worked togeth-
er for over ten years developing a unique approach to the study of bio-
