A little later than I hoped, but here's the function I ended up using for my task related to this. It could probably be adapted to other applications.
@mdsumner was right that a high-level operation to discard non-intersects sped this up greatly. Hopefully this is useful!
library("sp")
library("rgeos")
library("plyr")
ApportionPopulation <- function(AdminBounds, poly, Admindf) { # I originally wrote this function to total the population that lies within each polygon in a SpatialPolygon object. AdminBounds is a SpatialPolygon for whatever administrative area you're working with; poly is the SpatalPolygon you want to total population (or whatever variable of your choice) across, and Admindf is a dataframe that has data for each polygon inside the AdminBounds SpatialPolygon.
# the AdminBounds have the administrative ID code as feature IDS. I set that up using spChFID()
# start by trimming out areas that don't intersect
AdminBounds.sub <- gIntersects(AdminBounds, poly, byid=TRUE) # test for areas that don't intersect
AdminBounds.sub2 <- apply(AdminBounds.sub, 2, function(x) {sum(x)}) # test across all polygons in the SpatialPolygon whether it intersects or not
AdminBounds.sub3 <- AdminBounds[AdminBounds.sub2 > 0] # keep only the ones that actually intersect
# perform the intersection. This takes a while since it also calculates area and other things, which is why we trimmed out irrelevant areas first
int <- gIntersection(AdminBounds.sub3, poly, byid=TRUE) # intersect the polygon and your administrative boundaries
intdf <- data.frame(intname=names(int)) # make a data frame for the intersected SpatialPolygon, using names from the output list from int
intdf$intname <- as.character(intdf$intname) # convert the name to character
splitid <- strsplit(intdf$intname, " ", fixed=TRUE) # split the names
splitid <- do.call("rbind", splitid) # rbind those back together
colnames(splitid) <- c("adminID", "donutshpid") # now you have the administrative area ID and the polygonID as separate variables in a dataframe that correspond to the int SpatialPolygon.
intdf <- data.frame(intdf, splitid) # make that into a dataframe
intdf$adminID <- as.character(intdf$adminID) # convert to character
intdf$donutshpid <- as.character(intdf$donutshpid) # convert to character. In my application the shape I'm using is a series of half-circles
# now you have a dataframe corresponding to the intersected SpatialPolygon object
intdf$polyarea <- sapply(int@polygons, function(x) {x@area}) # get area from the polygon SP object and put it in the df
intdf2 <- join(intdf, Admindf, by="adminID") # join together the two dataframes by the administrative ID
intdf2$popinpoly <- intdf2$pop * (intdf2$polyarea / intdf2$admin_area) # calculate the proportion of the population in the intersected area that is within the bounds of the polygon (assuming the population is evenly distributed within the administrative area)
intpop <- ddply(intdf2, .(donutshpid), summarize, popinpoly=sum(popinpoly)) # sum population lying within each polygon
# maybe do other final processing to get the output in the form you want
return(intpop) # done!
}
