Compactifying de Sitter Naturally Selects a Small Cosmological Constant

We study compactifications of D-dimensional de Sitter space with a q-form flux down to D - Nq dimensions. We show that for (N - 1)(q - 1) >= 2 there are double-exponentially or even infinitely many compact de Sitter vacua, and that their effective cosmological constants accumulate at zero. This population explosion of Lambda << 1 de Sitters arises by a mechanism analogous to natural selection.