  Stability and diversity are two key properties that living entities share
with spin glasses, where they are manifested through the breaking of the phase
space into many valleys or local minima connected by saddle points. The
topology of the phase space can be conveniently condensed into a tree
structure, akin to the biological phylogenetic trees, whose tips are the local
minima and internal nodes are the lowest-energy saddles connecting those
minima. For the infinite-range Ising spin glass with p-spin interactions, we
show that the average size-frequency distribution of saddles obeys a power law
$<\psi(w) > \sim w^{-D}$, where w=w(s) is the number of minima that can be
connected through saddle s, and D is the fractal dimension of the phase space.
