I have a similar issue. I have a wild Muscovy duck and her eggs are gone but she is staying on the empty nest. I'm hopeful that she will soon leave but she is persistent. I don't want to scare her off as she has always come to our yard for food and she's laid eggs previously with success.I have a wild Muscovy duck that started laying eggs in April in my flowerbed. She laid about 18 eggs. She is still sitting on them 3 months later. I feel bad for her and don’t know what to do.