Multivariate Data
Analysis of Biological Data
Ryan McEwan and Julia Chapman
Department of Biology
University of Dayton
ryan.mcewan@udayton.edu
Biological phenomenon are very often “multivariate” in nature…meaning that many
different variables must be considered simultaneously to understand the system
A classic example is a species by plot matrix (see below)
For example, if you wanted to compare the animal/insect/plant
communities between burned and unburned grassland
You might install plots like this.
Then measure the plants/animals/microbes, etc, within the plots.
Then you want to compare them…
But…the data set….
You may also be interested in environmental parameters…measured in the
same plots…
Traditional Statistical Approaches Just wont Do!
How to proceed?
(a) Display the compositional information
(a) Display the compositional information
(a) Display the compositional information
Note these are
summary values!
(a) Display the compositional information (could be environmental data)
(a) Display the compositional information (stacked charts could be good)
How to proceed?
(a) Display the compositional information
(b) Summarize- perhaps through
diversity indicies!
How to proceed?
(a) Display the compositional information
(b) Summarize- perhaps through
diversity indicies!
(c) Cluster analysis
Figure 1. Correlation, Group Average (UPGMA)
Information Remaining (%)
100
S83
S84
A83
SP84
A84
S89
S90
A89
A90
SP90
A92
S92
S86
S88
A86
SP88
75
50
25
0
Figure 2. Sorenson, UPGMA
Information Remaining (%)
100
S83
S84
A83
A84
SP84
S89
S90
S86
A86
SP88
S88
SP90
A89
A90
S92
A92
75
50
25
0
Figure 3. Correlation, Nearest Neighbor
Information Remaining (%)
100
S83
A83
SP84
A84
S84
S90
S89
A89
A90
SP90
S86
S88
S92
A92
A86
SP88
75
50
25
0
Figure 4. Sorenson, Nearest Neighbor
Information Remaining (%)
100
S83
A83
A84
SP84
A89
A90
SP90
A86
SP88
S84
S88
S86
S89
S92
S90
A92
75
50
25
0
Figure 5. Correlation, Farthest Neighbor
Information Remaining (%)
100
S83
S84
A83
SP84
A84
S86
S88
S89
S90
A86
SP88
A89
A90
SP90
S92
A92
75
50
25
0
Figure 6. Sorenson, Farthest Neighbor
Information Remaining (%)
100
S83
S84
A83
A84
SP84
S86
S89
S90
A86
SP88
S88
SP90
A89
A90
S92
A92
75
50
25
0
Figure 7. Ward’s Method
Information Remaining (%)
100
S83
S84
A83
SP84
A84
S89
S90
A89
A90
SP90
S92
A92
S86
S88
A86
SP88
75
50
25
0
Figure 8. Ward’s Distance
Information Remaining (%)
100
S83
S84
A83
A84
SP84
S86
S89
S90
A86
SP88
S88
SP90
A89
A90
S92
A92
75
50
25
0