Biology Reference
In-Depth Information
5.4 EDMA applied to the study of growth
As demonstrated previously for the study of form difference, adoption
of an arbitrary coordinate system is undesirable when studying
growth, as the results obtained can be misleading. When studying
growth, we have representative forms from various age groups, and the
goal is to determine the locations where growth occurs. This goal can-
not be attained using coordinate system-based approaches, as results
will change with the coordinate system adopted and there is no way to
know which coordinate system is preferred in any given analysis. The
approach presented here provides coordinate system-free, valid infor-
mation about growth patterns.
Nearly all aspects of EDMA developed in previous chapters can be
applied to the study of growth. Consequently, the essential ideas
required to use EDMA in the study of growth have already been pre-
sented. We reinforce that knowledge by presenting an outline of the
method again, this time using growth data and a specific notation for
growth analyses. Let us begin with a single form, A , at two points dur-
ing ontogeny, time 1 and time 2. The morphology of A at the first point
in time is referred to as A 1 while the morphology of A at the second
point in time is referred to as A 2 . Data are collected for three two-
dimensional landmarks at each point in time. For example, the
coordinates from these three points could be collected as:
FM (A 1 ) and FM (A 2 ) denote the form matrices corresponding to these
landmark data. Recall that FM ij (A 1 ) is the distance between landmarks
i and j in object A 1 and that FM ij (A 2 ) is the corresponding distance in
object A 2 . Using the landmark coordinate data given above, we obtain
the following form matrices:
01 1
10
0
3
2 136
.
.
FM A
()
.
1
FM A
()
3
0
3 010
1
2
1
1 41
.
0
2 136
.
3 010
.
0
Search WWH ::




Custom Search