  In arXiv:1503.08402v2 Gelander described a new compactification of the moduli
space of finite area hyperbolic surfaces using invariant random subgroups. The
goal of this paper is to relate this compactification to the classical
augmented moduli space, also known as the Deligne-Mumford compactification. We
define a continuous finite-to-one surjection from the augmented moduli space to
the IRS compactification. The cardinalities of this map's fibers admit a
uniform upper bound that depends only on the topology of the underlying
surface.
