.
This exercise explores the consequences of having different characters
highly correlated. Suppose that five OTUs A, B, . . . , E are being clustered
based upon five characters x1, x2, x3, x4, and x5. The matrix of characters,
X, is
x1 x2 x3 x4 x5
A 1 1 2 1 3
B 2 3 2 3 6
C 6 8 4 7 2
D 8 9 4 3 1
E 6 6 3 9 9
a. Perform hierarchical clustering of these five OTUs, and note the topology
of the dendrogram.
b. Determine the correlation coefficients for each pair of variables, and represent
values for highly correlated characters by a single column vector
(combining values for each OTU using a statistic of your choice).
c. Now use the composite character defined in part b and the remaining
columns from matrix X to form a new matrix having a lesser number of
characters, and again perform hierarchical clustering. Compare the topology
of the dendrogram to the one observed in part a.
d. Criticize or defend the approach used in part c.