I am new to the chicken thing and wonder about two of my chickens. They are missing a bunch of feathers on their rump. There is a bare patch about the size of a fist. First I freaked out and thought they were being picked, but now I am not sure. Their skin is intact, no blood spots, no tears, just no feathers. They both seem a bit broody--they are usually on eggs and peck at me when I take the eggs away--so now I wonder, are they pulling out their own feathers to make nests? None of the other birds look like this, should I worry?