Meet Anza and Gnocchi. Both are male and of different (but closely-related) species. They've been pair-bonded (birdie life partners) for a year now. They feed each other, groom each other and insist on sharing a sleep cage. If one has to go away for a vet visit, both of them spend their entire time doing loud "contact calls" until they're reunited.

Now meet Clipper and Pixley. These two wild girls come from the San Francisco flock (as does Anza) and they are inseparable. Clipper had a neurological parasite that left her disabled and she relies on Pixley for a lot of her care. It's Pixley who checks out all new food, toys and perches, and she often brings tastes back to Clipper before helping her over to the food dish. Even though Pixley is the smaller bird, she never hesitates to put her body in between Clipper and any bird (or human) who might seem the least bit threatening.

Just like Anza and Gnocchi, they show all the signs of a permanent pair bond: mutual grooming, food sharing and close sleeping arrangements.
Out of 14 parrots that we've fostered, we've seen 4 pair bonds develop. Three were same-sex and the only heterosexual bond was more of a parent-child relationship between a medium-sized conure and a tiny lovebird.
Anyone who has kept a parrot flock knows this. The birds are almost oblivious to gender when it comes to pairing up for life. Since it's impossible to determine the sex of these birds by sight, I wonder how many of the observed "male/female" pairs in the wild are actually same-sex couples.
Is this what they mean by Polly-Amory?
