Toward a minimal model for $H_\ast(\overline{\mathcal{M}})$

The modular operad $H_\ast(\overline{\mathcal{M}}_{g,n})$ of the homology of Deligne-Mumford compactifications of moduli spaces of pointed Riemann surfaces has a minimal model governed by higher homology operations on the open moduli spaces $H_\ast(\mathcal{M}_{g,n})$. Using Getzler's elliptic relation, we give an explicit construction of the first family of such higher operations.