Constructing a Phenogram
Numerical phenetic methods organize taxa (operational taxonomic units, or OTUs) into groups
based on overall similarity. OTUs are grouped in such a way that there is a higher degree of
similarity within groups than between groups. That is, two OTUs within a group share more
character states than do two OTUs in different groups. The least inclusive (smallest) groups
represent the highest level of similarity. Successively more inclusive groups share successively
fewer character states, and the most inclusive group is the most heterogeneous, including all the
OTUs in the study.
This hierarchical pattern of grouping is expressed in a kind of branching diagram known as a
phenogram. The relationships of OTUs and groups in a phenogram reflect only similarity; no
evolutionary relationships are implied. To describe phylogenies (evolutionary relationships), a
cladogram is often used. This type of branching diagram shows the sequence of evolutionary
change in characters, the number of changes associated with each lineage, and the sequence of
lineage branching. Hence, the branches of a cladogram, unlike a phenogram, represent time.
A similarity matrix consists of pairwise comparisons between all the OTUs. One way to express
the similarity of two OTUs is the simple matching coefficient (SMC). The value of the SMC for
two OTUs (A,B) will be denoted:
SMCA,B = Number of characters for which (A,B) share the same state
Total number of characters
1)
For the “Cookophyte” data matrix, calculate the value of SMC for all pairs of
OTUs, and complete the following matrix:
A
2)
A
1
B
8/12
C
8/12
D
8/12
E
3/12
F
6/12
G
5/12
H
8/12
I
7/12
B
C
D
E
F
G
H
I
1
1
1
1
1
1
1
What is the most similar pair of OTUs? What is their SMC? What is the least
similar pair of OTUs and what is their SMC?
1
In the following problems, we will construct the phenogram for these data
3)
First link the two most similar OTUs at their level of similarity.
4)
What is the next highest SMC value in the similarity matrix? How many pairs of
taxa are this similar? Do any of these pairs overlap (is any OTU a member of
more than one such pair)?
5)
Link E and G at the appropriate level. Link C and F ant the appropriate level.
Because B and C are members of different clusters, we must determine the
relationships of all pairs of OTUs before joining these clusters.
6)
Now compare group (C,F) to group (B,I). there are four possible comparisons
between these groups. What is the value of S for each comparison?
C,B ____ C,I ____ F,B ____
Which value of S is highest? The OTUs with the greatest SMC are the nearest
neighbors between these groups.
7)
Link (B,I) and (C,F) at the nearest neighbor similarity value.
8)
The similarity matrix below collapses the original similarity matrix so that the two
clusters formed above are now treated as individual OTUs. To determine the
similarity of these clusters, the similarity of closest neighbors is used. Compare all
pairs of OTUs in different clusters, determine the closest neighbors, and fill in the
appropriate values below:
A
(B,C,I,F)
D
(E,G)
H
A
(B,C,I,F)
D
(E,G)
H
9)
What is the next highest SMC in the previous matrix? How many OTUs should be linked
together into a group at this level? Remember the nearest-neighbor rule: The similarity of
two groups equals the highest SMC value for between-group pairwise comparisons.
10) Finish the phenogram: This will take one step to cluster (E,G) with the cluster
(B,I,C,F,A,D,H) using the highest SMC value between pairs in these two clusters. Link
these groups at that level. Your phenogram is complete when all taxa are linked. Be sure
to show the level of similarity for each connection.