  We study Nakai-Moishezon type question and Donaldson's "tamed to compatible"
question for almost complex structures on rational four manifolds. By extending
Taubes' subvarieties--current--form technique to $J-$nef genus $0$ classes, we
give affirmative answers of these two questions for all tamed almost complex
structures on $S^2$ bundles over $S^2$ as well as for many geometrically
interesting tamed almost complex structures on other rational four manifolds,
including the del Pezzo ones.
