In general terms, to get the design of the map you refer to and presuming the GPS point data contains the breeding attributes of one species, and the grid is a polygonized fabric with one point max per cell:
1. do a spatial join with the polygons as target and the points as the join table in ArcMAP (points to Polygons and select option to add all attributes) 2. The resulting output polygons shapefile with have an automatic field call "distance": Select from the new polygon shapefile those polygons with "0" distance (means they fell within) and export this selection to a new shapefile (this step is just to eliminate the grid cells with no points) 3. add 2 fields to the new join polygon shapefile and use Field Calculator to create the X and Y coordinates of the Centroid of the polygon. 4. export this shapefile to a table (dbf etc.) 5. Using the Add XY Data (or the Arc 10 equivalent Display XY ..) create a point file using the new XY coordinates of the centroids 6. symbolize the points using the breeding characteristics as Unique Categories (or create buffers) with nothing appearing for the 7. overlay this on a map of the area with or without the grid polygons
Each of those steps assumes a bit of how - to familiarity with Attribute Table operations (right click menus and table Options), but all basic and easily found in the help files as you proceed. No doubt there may be more elegant ways of doing this in Arc10, but I think this will work for what you want. Post again if you have questions specific to any step or find something better.
If you have more than one point per cell you should use the "JOIN_ONE_TO_MANY" option in the ArcToolbox > Analysis Tools > Overlay > Spatial Join instead of the simple join in the TOC layers right click menu. With this tool you need to uncheck the "keep all target features" option as shown in the clip of the tool dialog box. (With the TOC layer join you'll only get the first instance of a join.)
From there you will have multiple overlapping polygons to create centroids points from and may have to manually shift the points to display them in the cells the way you were wanting to. Presumably these are the exceptions and the manual work will be minimal, or you might have to consider a smaller cell size.
In looking at the proposed, and implemented, methodology the result is sound. However, please take the result with a grain of salt. There is a big difference in what you produced and a species distribution estimate. The result of a species distribution model (SDM) is representative of the niche (potentially occupied habitat) of a species. What you have produced are the "observed" breeding locations. Because it does not represent the species environmental "space", this is a very constrained picture of the species breeding habitat. I would also imagine that this data has not been corrected for probability of detection, which is a critical step in accounting for bias in field observation. I would highly recommend reading some of the primary literature related to niche and species distribution modeling.