Today myself and another student were asked by a Geshe (presumably a Gelug Geshe in what took a very Zen interview turn that I had so far never experienced in Tibetan Buddhism) what the specific karma was for human rebirth and precious human rebirth and by extension asura rebirth and deva rebirth?
I answered that human rebirth was the result of pure morality (I actually meant pure virtue) from past lives - so saving beings' lives or keeping pure morality. And that precious human rebirth was more a result of pure morality.
The Geshe posed the question several times and the translator apologized because he wasn't really able to translate the nuances that the Geshe was trying to communicate but the Geshe basically said that human rebirth is the result of any kind of virtue actually.
We briefly touched on the obscurantism leading to rebirth in the lower realms but did not go into this in detail.
I will review what I have on the subject (mostly from Sakya sources) and see what they say. Shakyamuni taught on this very subject in detail and his teaching can be subtle (the Dog Duty Ascetic Sutta for example).
Does anyone have other sources (Gampopa for example has to go into this in the Jewel Ornament)?