  The underdoped region of the cuprate's phase diagram displays many novel
electronic phenomena both in the normal and the superconducting state. Many of
these anomalous properties have found a natural explanation within the
resonating valence bond spin liquid phenomenological model of Yang-Rice-Zhang
(YRZ) which includes the rise of a pseudogap. This leads to Fermi surface
reconstruction and profoundly changes the electronic structure. Here we extend
previous work to consider the shift in critical temperature on $^{16}$O to
$^{18}$O substitution, The isotope effect has been found experimentally to be
very small at optimal doping yet to rapidly increase to very large values with
underdoping. The YRZ model provides a natural explanation of this behavior and
supports the idea of a pairing mechanism which is mainly spin fluctuations with
a subdominant $(\sim 10\%)$ phonon contribution.
