There are a natural collection of rational curves (deep) in the boundary of $\overline{M}_{g,n}$, the so called 1-strata, the irreducible components of the locus of (pointed) curves with at least 3g-3 +n -1 singular points. Together with Gibney and Morrison, I conjecture that a divisor is ample iff it has positive intersection with each of these curves, and moreover, in char p, that a divisor is semi-ample (ie. the linear system of some positive multiple is free of base-points) iff it has non-negative intersection with each of these curves. I'll explain our main result, which is that the conjecture holds in general iff it holds for $g=0$, and strong evidence for the $g=0$ case.