We approximate intersection numbers [formula presented] on Deligne–Mumford’s moduli space M_g,n of genus g stable complex curves with n marked points by certain closed-form expressions in d₁, …, d_n. Conjecturally, these approximations become asymptotically exact uniformly in d_i when g → ∞ and n remains bounded or grows slowly. In this note we prove a lower bound for the intersection numbers in terms of the above-mentioned approx-imating expressions multiplied by an explicit factor λ(g, n), which tends to 1 when g → ∞ and d₁ + · · · + d_n−2 = o(g).