  It has been observed that the sample mean of certain probability
distributions in Billera-Holmes-Vogtmann (BHV) phylogenetic spaces is confined
to a lower-dimensional subspace for large enough sample size. This non-standard
behavior has been called stickiness and poses difficulties in statistical
applications when comparing samples of sticky distributions. We extend previous
results on stickiness to show the equivalence of this sampling behavior to
topological conditions in the special case of BHV spaces. Furthermore, we
propose to alleviate statistical comparision of sticky distributions by
including the directional derivatives of the Fr\'echet function: the degree of
stickiness.
