  Let $X$ be a smooth projective surface and $D$ a smooth rational ample
divisor in $X$. We prove an all-genus generalization of the genus $0$ WDVV
equation for primary Gromov--Witten invariants of the local 3-fold
$\mathcal{O}_X(-D)$. The proof relies on a correspondence between all-genus
Gromov--Witten invariants and refined Donaldson--Thomas invariants of acyclic
quivers. In particular, the corresponding BPS invariants are expressed in terms
of Betti numbers of moduli spaces of quiver representations.
