  Much of the information about the multi-valley structure of disordered spin
systems can be convened in a simple tree structure -- a barrier tree -- the
leaves and internal nodes of which represent, respectively, the local minima
and the lowest energy saddles connecting those minima. Here we apply several
statistics used in the study of phylogenetic trees to barrier trees that result
from the energy landscapes of p-spin models. These statistics give information
about the shape of these barrier trees, in particular about balance and
symmetry. We then ask if they can be used to classify different types of
landscapes, compare them with results obtained from random trees, and
investigate the structure of subtrees of the barrier trees. We conclude that at
least one of the used statistics is capable of distinguishing different types
of landscapes, that the barrier trees from p-spin energy landscapes are quite
different from random trees, and that subtrees of barrier trees do not reflect
the overall tree structure, but their structure is correlated with their
``depth'' in the tree.
