  We use crossing parity to construct a generalization of biquandles for
virtual knots which we call Parity Biquandles. These structures include all
biquandles as a standard example referred to as the even parity biquandle.
Additionally, we find all Parity Biquandles arising from the Alexander
Biquandle and Quaternionic Biquandles. For a particular construction named the
z-Parity Alexander Biquandle we show that the associated polynomial yields a
lower bound on the number of odd crossings as well as the total number of real
crossings and virtual crossings for the virtual knot. Moreover we extend this
construction to links to obtain a lower bound on the number of crossings
between components of a virtual link.
