Well, in my "vast" experience (all of about three weeks or so)....
My geese pretty much don't care about the ducks or the chickens - unless treats are involved, then get outta their way!!!
They ignore the ducks, the chickens they ignore mostly, unless the geese are shut into the chicken run (which I do at night for their safety) and the chickens are still in the run, too. I've gotten into the habit of putting the chickens into the coop and letting the geese have the run at night.
My gander did pick up my Dellie Roo (!!) and throw him across the run once - cause the roo got too close to his goosey girl. Otherwise, the geese don't bother the chickens to "pick at" them. But, I figure the geese (and that Dellie Roo) are happier not being in the same space.
It also makes it easier on me, because I can run the chickens inside, then leave the run door open so the geese can go in when they are ready -- no chasing or coaxing them - they'll go in at dusk happily on their own, then I just go out and shut the door. It saves me spending a lot of wasted time trying to get them into the run.
I am building a waterfowl pen, and hope to convince the geese that this is a better alternative to the chicken run for nighttime accomodations.
I would definately have two of them - one of them may decide to find a "mate" with someone (some species) who isn't interested in their attentions
Or it might just get nasty tempered because it's alone - like I said, my Vast Knowledge runs all of three weeks of owning geese - only thing I recall from my childhood is the geese were mean and chased us kids and tried to bite us all the time.
Thank goodness the two I have now are not agressive.
meri
