The F-conjecture for moduli spaces of stable curves

Let $\overline{\mathcal{M}}_{g,n}$ be the moduli space of stable curves, and let an F-curve be a one-dimensional codimension-$3g-4+n$ boundary stratum. A line bundle is F-nef if it has nonnegative intersection with every F-curve, and F-ample if it has positive intersection with every F-curve. F-conjecture. A line bundle on $\overline{\mathcal{M}}_{g,n}$ is nef if and only if it is F-nef. Equivalently, it is ample if and only if it is F-ample. This conjecture would completely determine the F-cone of $\overline{\mathcal{M}}_{g,n}$; the source attributes it to Gibney, Keel, and Morrison and says it is a conjecture, without giving a resolution.