Identifying overlapping polygons

Hi.  I am relatively new to Spatial-R.  I have two objects that are both
SpatialPolygonsDataFrame classes.  One is comprised of polygons from a
section of a segmented image and the other is essentially circular polygons
representing the potential areas that the crowns of known tree locations
might cover.  I would like to identify every polygon from the first object
(image segmentation polys) that completely are even partially (hopefully I
can control the "partial" threshold) falls within any given polygon from the
second object (crown areas).  In ArcGIS this can be accomplished using the
Identity application under ArcToolbox.  I was hoping to accomplish the same
feats in R.  Any help would be greatly appreciated!!

Andrew Niccolai
Doctoral Candidate
Yale School of Forestry