  We discuss a link between the topological recursion relations derived
algebraically by Witten and the holomorphic anomaly equation of Bershadsky,
Cecotti, Ooguri and Vafa. This is obtained through the definition of an
operator ${\cal{W}}_s$ that reproduces the recursion relations for topological
string theory coupled to worldsheet gravity a la BCOV. This operator is
contained inside an algebra that generalizes the tt* equations and whose direct
consequence is the holomorphic anomaly equation itself.
