  We describe the conditions under which a set of continuous variables or
characters can be described as an X-tree or a split network. A distance matrix
corresponds exactly to a split network or a valued X-tree if, after ordering of
the taxa, the variables values can be embedded into a function with at most a
local maxima and a local minima, and crossing any horizontal line at most
twice. In real applications, the order of the taxa best satisfying the above
conditions can be obtained using the Minimum Contradiction method. This
approach is applied to 2 sets of continuous characters. The first set
corresponds to craniofacial landmarks in Hominids. The contradiction matrix is
used to identify possible tree structures and some alternatives when they
exist. We explain how to discover the main structuring characters in a tree.
The second set consists of a sample of 100 galaxies. In that second example one
shows how to discretize the continuous variables describing physical properties
of the galaxies without disrupting the underlying tree structure.
