Transcript Chapter 18

CHAPTER 18
Weighted Averaging
Tables, Figures, and Equations
From: McCune, B. & J. B. Grace. 2002. Analysis of
Ecological Communities. MjM Software Design,
Gleneden Beach, Oregon http://www.pcord.com
How it works
Matrix A contains abundances of :
p species in
n sample units
Vector of p species weights, wj.
Calculate an ordination score vi for each plot i:
p
a
vi =
ij
wj
j=1
p
a
j=1
ij
A new set of species weights can be calculated from the
site scores:
n
a
wj =
ij
vi
i=1
n
a
i=1
ij
Table 18.1. Example data matrix with 2 plots  3 species.
sp 1
sp 2
sp 3
sum
plot A
4
1
0
5
plot B
0
2
4
6
sum
4
3
4
Table 18.2. Weights assigned to each species, the
weights indicating tolerance of wet to dry sites.
Sp 1
Sp 2
Sp 3
Dry site
indicator
Medium site
indicator
Wet site
indicator
weight = 0
weight = 50
weight = 100
Calculate a moisture score vi for each plot i as an
average of the abundances weighted by the moisture
indicator values.
For example, plot B gets a score of 83.3.
0( 0) + 2(50) + 4(100)
vB =
= 500 / 6 = 83.3
6
B
A
Sample units 0
10
1
Species
0
83
100
2
50
3
100
Figure 18.1. Example of ordination by weighted
averaging.