I agree with Erwin, it is easy to go back and forth between GIS and R. That is exactly what I did in two of my publications (attached - send me a message if you cannot access the full text). I created datasets of points with all variables of interest - exported the csv, which was then brought into R and analyzed with GAMs (particularly the mgcv package). If you want to map species probability, the reverse is also possible. Create a grid of points (at the scale you want your predictions) that have all of your model's covariates joined in GIS - and export as a csv/table - bring into R, and then (again, I used mgcv) in R use the 'predict' function using your final GAM model on your grid of points to predict values for. Save this predictions, along with coordinates, as a csv/table to bring back into GIS. The points to can be converted easily to a raster - to create a predicted surface.

Another option is to check out the Marine Geosptial Ecology Toolbox (MGET) created for ArcGIS - http://mgel.env.duke.edu/mget/ - it has options for species distribution models, including both GLM and GAM. I'd imagine it works regardless if your data are marine or terrestrial-oriented. I personally haven't used it but I know it is quite popular, and I have used the MGET for other tools and found them to be reliable.

Article Fine-scale movements and habitat use of juvenile southern fl...

Article Spatial and temporal shifts in suitable habitat of juvenile ...

I agree with Erwin, it is easy to go back and forth between GIS and R. That is exactly what I did in two of my publications (attached - send me a message if you cannot access the full text). I created datasets of points with all variables of interest - exported the csv, which was then brought into R and analyzed with GAMs (particularly the mgcv package). If you want to map species probability, the reverse is also possible. Create a grid of points (at the scale you want your predictions) that have all of your model's covariates joined in GIS - and export as a csv/table - bring into R, and then (again, I used mgcv) in R use the 'predict' function using your final GAM model on your grid of points to predict values for. Save this predictions, along with coordinates, as a csv/table to bring back into GIS. The points to can be converted easily to a raster - to create a predicted surface.

Another option is to check out the Marine Geosptial Ecology Toolbox (MGET) created for ArcGIS - http://mgel.env.duke.edu/mget/ - it has options for species distribution models, including both GLM and GAM. I'd imagine it works regardless if your data are marine or terrestrial-oriented. I personally haven't used it but I know it is quite popular, and I have used the MGET for other tools and found them to be reliable.

Article Fine-scale movements and habitat use of juvenile southern fl...

Article Spatial and temporal shifts in suitable habitat of juvenile ...

You should use R or other statistical software which allow you to include GIS objects (point or polygon shapefiles). 'mgcv' package is quite useful!

Best wishes

Ana

Dear all who had the interesting answers to my question and had a consequential contribution to clarify my issue. I would thanks especially to Dr. Nathan Furey for sharing his informative works and valuable recommendation and comments to my question.

I'll just add another option to Nathan Furey's post. 

If you already have raster layers for your predictor variables that are of the same geographic extent and coordinate system,  you can also import those layers into R using the raster package. (e.g., var1

Jennifer McHenry , It was shows error when I use predict function for raster stack and gam object (e.g., predict(rs_stack,gam_object,filename="file_name.tif")  ). Kindly help me what should I do exactly for the same. Thanking You.