I don't see anyone arguing. 

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Till @casportpony gets here can you put her into a pool or tub and add some apple cider vinegar to it? She def needs some help there. Does she have access to bathing water? Any other of your ducks like this? Trying to get some background. Do you live in the USA?
If you want to try to treat her, get some ivermectin and give it per the instructions in my post with all of the links.We are in Arizona. She lives with her male pekin. Free roam in confided fenced area, has kiddie pool that is changed every other day. I am being told it’s a mite. The other duck and chickens they also live with are all fine. After researching there is a mite that can live the entire life cycle on the duck and not go to others. 2 weeks ago she was starting to loose hair and now this is where we are at. No duck vets in my town. I might need to euthanize her.
The choice is yours to make. Other than it being strange to look at what is her quality of life? Does she otherwise act normal? Is she eating and drinking?We are in Arizona. She lives with her male pekin. Free roam in confided fenced area, has kiddie pool that is changed every other day. I am being told it’s a mite. The other duck and chickens they also live with are all fine. After researching there is a mite that can live the entire life cycle on the duck and not go to others. 2 weeks ago she was starting to loose hair and now this is where we are at. No duck vets in my town. I might need to euthanize her.
That's one of the links I posted at the beginning of the thread. Suggested treatment is ivermectin or moxidectin.That looks like mange to me. I had a dog that when I found him as a puppy he looked just like that, it was the non contagious form and is essentially small mites that got out of control, it took me months of vet visits and bathes to get him better.
No pictures, but info...
http://veterinarymedicine.dvm360.com/knemidocoptiasis-birds
She is now starting to scratch. I’m starting her on ivermectin and I continue to treat on the outside but she goes to the pool afterwards.Does she scratch this area?