Environmental Engineering Reference
In-Depth Information
coarse
Discriminant axis
M = 0.55 D - 0.45 S
A
A
A
A
A
A
A
A
Substratum
A
A
B
B
A
B
B
B
B
B
B
B
fine
B
B
B
A
B
Distance from source
(a)
+ve
A
A
A
0.6
0.3
A
A
B
A
A
B
A
*
A
A
B
B
A
A
A
A
A
B
B
A
A
A
A
A
B
A
B
A
A
d.f.1
-ve
+ve
0.1
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
d.f.2
(b)
-ve
Figure 6.1.
(a) Illustration of discriminant analysis. Groups A and B are not distinct in
terms of either distance from source or substratum, but it is possible to separate the two
groups along the discriminant axis M using a combination of both parameters where
M
0.55 D 0.45 S. It is possible to separate multiple groups and parameters using this
approach. (b) Illustration of how discriminant functions (d.f.1 and 2) are used to
determine probabilities of end group inclusion. The probability that the site * belongs to
each group is proportional to its distance from the group centroid and the number of
sites in the group.
ΒΌ
The probabilities of the test site belonging to each biological end group are
used to calculate the expected fauna. For each taxon, the proportion of sites
within each end group that contain that taxon is combined with the probability
probability of the taxon occurring are summed across all probable end groups,
