The Spitzer Space Telescope Survey of the Orion A and B Molecular Clouds
  II: the Spatial Distribution and Demographics of Dusty Young Stellar Objects
  We analyze the spatial distribution of dusty young stellar objects (YSOs)
identified in the Spitzer Survey of the Orion Molecular clouds, augmenting
these data with Chandra X-ray observations to correct for incompleteness in
dense clustered regions. We also devise a scheme to correct for spatially
varying incompleteness when X-ray data are not available. The local surface
densities of the YSOs range from 1 pc$^{-2}$ to over 10,000 pc$^{-2}$, with
protostars tending to be in higher density regions. This range of densities is
similar to other surveyed molecular clouds with clusters, but broader than
clouds without clusters. By identifying clusters and groups as continuous
regions with surface densities $\ge10$ pc$^{-2}$, we find that 59% of the YSOs
are in the largest cluster, the Orion Nebular Cluster (ONC), while 13% of the
YSOs are found in a distributed population. A lower fraction of protostars in
the distributed population is evidence that it is somewhat older than the
groups and clusters. An examination of the structural properties of the
clusters and groups show that the peak surface densities of the clusters
increase approximately linearly with the number of members. Furthermore, all
clusters with more than 70 members exhibit asymmetric and/or highly elongated
structures. The ONC becomes azimuthally symmetric in the inner 0.1 pc,
suggesting that the cluster is only $\sim 2$ Myr in age. We find the star
formation efficiency (SFE) of the Orion B cloud is unusually low, and that the
SFEs of individual groups and clusters are an order of magnitude higher than
those of the clouds. Finally, we discuss the relationship between the young low
mass stars in the Orion clouds and the Orion OB 1 association, and we determine
upper limits to the fraction of disks that may be affected by UV radiation from
OB stars or by dynamical interactions in dense, clustered regions.
