Integral points and effective cones of moduli spaces of stable maps

Consider the Fulton-MacPherson configuration space of n points on P^ 1, which is isomorphic to a certain moduli space of stable maps to P^ 1. We compute the cone of effective Sn-invariant divisors on this space. This yields a geometric interpretation of known asymptotic formulas for the number of integral points of bounded height on compactifications of SL2 in the space of binary forms of degree n (more than)3.