Biology Reference
In-Depth Information
FIGURE 1.2
4
Truss measurement
scheme of external body form of a teleost:
(A) well-defined endpoints of measure-
ments; (B) a selection of 30 lengths,
arranged in a truss.
3
5
2
6
15
1
7
14
16
8
13
12
11
10
9
(A)
9
14
5
10
12
17
19
15
11
2
29
20
6
24
1
25
22
30
21
26
28
16
7
27
4
3
8
23
13
(B)
18
The classical measurement scheme can be greatly improved without altering its basic
mathematical framework, by the box truss (
Figure 1.2
)
a scheme developed by Strauss,
Bookstein and colleagues (
Strauss and Bookstein, 1982; Bookstein et al., 1985
). This set
of measurements samples more directions of the organism, the measurements are more
evenly spaced, and there are also many short measurements. Moreover, all the endpoints
of the measurements are biologically homologous anatomical loci
landmarks. But even
though the truss is a clear improvement over classical measurement schemes when it comes
to describing shape differences, the result is still just a list of numbers (i.e. the lengths of the
truss elements), with all the attendant problems of visualization and communication.
One general problem shared by both those measurement schemes is that they fail to
collect all the information available from the endpoints of the measurements. The truss
scheme shown in
Figure 1.2
contains 30 measurements, but 30 is only a fraction of the
120 that could be made among the same 16 landmarks (
Figure 1.3
). Of course, many of
the 120 are redundant, and several of them span large regions of the organism, making it
difficult to localize where changes occur. Additionally, we would need extraordinarily
large samples in order to test hypotheses about shape and the results would be incredi-
bly difficult to interpret because there would be 120 pieces of information (e.g. regression
