  We prove that the ancestor Gromov-Witten correlation functions of
one-dimensional compact Calabi-Yau orbifolds are quasi-modular forms. This
includes the pillowcase orbifold which can not yet be handled by using
Milanov-Ruan's B-model technique. We first show that genus zero modularity is
obtained from the phenomenon that the system of WDVV equations is essentially
equivalent to the set of Ramanujan identities satisfied by the generators of
the ring of quasi-modular forms for a certain modular group associated to the
orbifold curve. Higher genus modularity then follows by using tautological
relations.
