  We present the redshift evolutions and distributions of the gamma-ray
luminosity and photon spectral index of flat spectrum radio quasar (FSRQ) type
blazars, using non-parametric methods to obtain the evolutions and
distributions directly from the data. The sample we use for analysis consists
of almost all FSRQs observed with a greater than approximately 7 sigma
detection threshold in the first year catalog of the Fermi Gamma-ray Space
Telescope's Large Area Telescope, with redshfits as determined from optical
spectroscopy by Shaw et al. We find that FSQRs undergo rapid gamma-ray
luminosity evolution, but negligible photon index evolution, with redshift.
With these evolutions accounted for we determine the density evolution and
luminosity function of FSRQs, and calculate their total contribution to the
extragalactic gamma-ray background radiation, resolved and unresolved, which is
found to be 16(+10/-4)%, in agreement with previous studies.
