Grid vs. Polygon Overlay in R gives different results than in QGIS

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I have a shapefile of range polygons. Each colored set of polygons represents a different group of species/genera/whatever.



I next overlay a 5x5 grid onto this map. And then use join attributes by location to find the number of grids that intersect each polygon



The final output gives me a column in the attribute table COUNT that indicates the number of grids intersected by the polygons.

################## NEXT PHASEI want to duplicate this same process entirely within R. First I load the same shapefile of range polygons into R using the rgdal package.

RangeShape
 
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