At the time (last summer when I posted this) I had a grow out pen with chicks and you know how they love to fling food. That's what drew them in. It was a pair one day, four the next and pretty soon 10-15 hanging around my coop at all times. They may not be the greatest vector of disease but here in the desert they exist in larger numbers than pigeons locally. They carry all the very same diseases so my concern is the same as if they were the common pigeon.
They aren't around as much now that my young flock has merged with the main flock. My run is very big, and the one small section that is tarped scares the daylights out of my chickens when the wind comes up so I probably could not do that, but thank you for the suggestion. I'm hopeful that my cats will keep them and mice at bay. I haven't seen a mouse nor droppings in years since having them around. The fact of the matter is, my chickens were infected with lice as a result of the doves hanging around. I didn't have an infestation before they arrived, they were pacing the grow out pen wall daily and the chicks were the most heavily infested with my main flock only beginning to get infested as I had just merged them when I discovered it. Almost a month to the date when I posted this, I found lice during a routine inspection. I'm not suggesting that doves are a problem for everyone - particularly in climates where you get a nice cold winter - but they were a problem for me, and that information should be out there for anyone else that might have concern.