If you are looking for a study done on parrots and all the benefits of calcium, you might not find it because, for all we know, there might not even be one as scientists hardly ever use parrots for any study. And, when they do, it's usually about intelligence or speech. Parrots are very long-lived and, when you talk about health issues, the study usually needs to be long-termed (and sometimes it requires more than one generation) but the 'term' is relative to the animal's average lifespan and no scientist is going to do a study that is going to require his own lifetime.
But there are studies on calcium all over the place which tell us why it's needed, where it's found, how it's absorbed, what functions it serves, etc. and all the results (with the exception of actual amounts) can be extrapolated to any animal but more so to the oviparous as they also need it to produce the eggshells.




