broken feathers, scaly balding patch and poop around vent

We have 6 Dominiques just over a year old-- 5 hens and one rooster. Over the last couple of weeks we've noticed a patch on the back of one of the hens that looked like she might have become a target for feather-picking, though frequent observation of the chickens showed none of this behavior (so at least they aren't doing it when we're watching?). Today, we noticed that this same hen now has a lot of poop around her vent. It isn't dried, so it's likely a recent thing, I guess, and it looks the usual color/consistency (of the runnier, brownish cecal variety of droppings), but there is a lot of it there. We took a closer look at the bald patch on her back (~4"x4") and while most of the spot has broken-off-looking feather shafts so that the contours of the feathers there lay flat, we see that on both sides of that spot she has a completely bald, scaly red patch. We aren't sure whether the bald spots are outside of the feather tract or not. Other than those symptoms, her behavior & appearance seem normal & healthy, and none of the other chickens are showing any signs of the same.

Other information that may or may not be helpful, just to make sure I've covered as much as I can:
-We are in south Louisiana
-They are in a ~10'x4' coop, with a ~20'x8' run.
-They get Purina Layena layer rations and occasional treats (fruits & veggies mostly) and water, of course!
-There hasn't been a drop or change in egg production (still averaging 4 per day from the 5 hens).
-Recent changes-- we usually feed the pellet food, but at the last trip to the feed store, there was only the granule food available (so same product, but different texture). We also recently changed the orientation of the run (dimensions pretty much the same), but we're pretty sure the feather issue started before that.

I hope that covers it. Any ideas about what might be going on and ways to handle it would be most appreciated!

 

Thanks for the links, Miss Lydia!

We'll take a look in the coop with a flashlight to check for mites, but as we haven't noticed any drop in egg production or appetite, and none of the other hens have any feather problems two or three weeks after this first showed up with her, I'm inclined to go with the "popular with the rooster" theory. Also, we're pretty good about dusting the coop & run now & then with DE, so I'd hope that would have done its job in preventing mites.

A follow-up question-- a saddle seems like the way to go, but do we need to be concerned about the heat if she's wearing one of those? I'm not fully up to speed on how chickens regulate body temperature, but does it not cover enough of her to cause a problem with overheating? We're already getting pretty warm down here, and it's quickly getting hotter.