"Understanding the PD" per se is an arbitrary requirement. Recognition of an animal's ethical worth should depend on a less parochial standard, like whether they act on gratefulness / reciprocity / Golden Rule / subjunctive consequences. I would consider it close enough that e.g. the animal does good things for you as a result of you having done good things for it.
I don't know about birds, but domestic cats and dogs definitely meet that standard.
I'm not so much concerned about an animal's "ethical worth", I just don't want anybody force-feeding me in order to eat my liver.
Foie gras, the delicacy made from the liver of a very fat goose (or sometimes duck), is believed to be unethical and is therefore frequently banned. For a long time, it was believed that the only way to properly fatten a goose is to continually force-feed it through a tube over several weeks, which is probably a highly unpleasant experience, although it's difficult to tell. Recently, Spanish farmer Eduardo Sousa revealed that under highly specific conditions, you can get geese to fatten themselves voluntarily.
Geese will instinctively gorge themselves when winter is coming on. Eat a goose right after it's fattened itself up for the winter, and you get a delicious treat that died happy. The problem is that geese will only do this if they believe food may become scarce during the winter (or their instinct to gorge only kicks in when the environment is such that that would be a reasonable inference; it's not clear whether it's the goose or evolution doing the analysis). If they realize that food will remain available during the winter, they eat normally. And there are quite a few possible clues--farmers trying to replicate Sousa's setup have discovered that cheating on any part leads to unfatted livers.