  We look at two contrasting spin-down models for isolated radio pulsars and,
accounting for selection effects, synthesize observable populations. While our
goal is to reproduce all of the observable characteristics, in this paper we
pay particular attention to the form of the spin period vs. period derivative
(P-Pdot) diagram and its dependence on various pulsar properties. We analyse
the initial spin period, the braking index, the magnetic field, various beaming
models, as well as the pulsar's luminosity. In addition to considering the
standard magnetic dipole model for pulsar spin-down, we also consider the
recent hybrid model proposed by Contopoulos & Spitkovsky. The magnetic dipole
model, however, does a better job of reproducing the observed pulsar
population. We conclude that random alignment angles and period dependent
luminosity distributions are essential to reproduce the observed P-Pdot
diagram. We also consider the time decay of alignment angles, and attempt to
reconcile various models currently being studied. We conclude that, in order to
account for recent evidence for the alignment found by Weltevrede & Johnston,
the braking torque on a neutron star should not depend strongly on the
inclination. Our simulation code is publically available and includes a
web-based interface to examine the results and make predictions for yields of
current and future surveys.
