Additive vs ultrametric: triangle inequality Additive vs ultrametric ...

Expected BSFs per
hundred bootstrap iterations
(by simulation)
0.7
1.5
6.7
A
B
C
6.7
1.5
1.5
6.7
D
E
F
G
H
I
Other methods for modeling distance matrices
Cluster analysis
methods
Ultrametric
2.5
Additive
2
1.5
3
1
5
0.5
4
1
2
0
4
3
5
2
1
Distance matrix
1 2 3 4 5
1 0.00 1.41 2.45 2.45 2.83
2 1.41 0.00 2.45 3.16 2.45
3 2.45 2.45 0.00 1.41 1.41
4 245 2.45 316 3.16 141 1.41 000 0.00 245 2.45
5 2.83 2.45 1.41 2.45 0.00
Data
matrix
Characters
Taxa a b c
1 1 2 1
2 2 1 1
3 3 3 2
4 2 4 2
5 3 2 3
Correlation matrix
a b c
a 1.00 0.16 0.79
b 0.16 1.00 0.37
c 0.79 0.37 1.00
PCo2 (34.5% %)
Dim2
PC2 (29.4%)
1
0.5
Ordination
methods
Principal coordinates
0
-0.5
-1
1
0.5
0
-0.5
-1
-1.5
4
2
3
5
-1 -0.5 0 0.5 1 1.5
PCo1 (60.6%)
Multidimensional scaling
1
0.5
0
-0.5
-1
1
5
-1.5 -1 -0.5 0 0.5 1
Dim1
Principal components
1
2
-1.5 -1 -0.5 0 0.5 1 1.5
PC1 (64.5%)
4
3
1
3
2
4
5
12