  There is a forgetful map from the mapping class group of a punctured surface
to that of the surface with one fewer puncture. We prove that finitely
generated purely pseudo-Anosov subgroups of the kernel of this map are convex
cocompact in the sense of B. Farb and L. Mosher. In particular, we obtain an
affirmative answer to their question of local convex cocompactness of K.
Whittlesey's group.
  In the course of the proof, we obtain a new proof of a theorem of I. Kra. We
also relate the action of this kernel on the curve complex to a family of
actions on trees. This quickly yields a new proof of a theorem of J. Harer.
