  We show that the skeleton of the Deligne-Mumford-Knudsen moduli stack of
stable curves is naturally identified with the moduli space of extended
tropical curves, and that this is compatible with the "naive" set-theoretic
tropicalization map. The proof passes through general structure results on the
skeleton of a toroidal Deligne-Mumford stack. Furthermore, we construct
tautological forgetful, clutching, and gluing maps between moduli spaces of
extended tropical curves and show that they are compatible with the analogous
tautological maps in the algebraic setting.
