Easter Islanders: Just to be clear Easter Island residents were never an empire. This was a subsistence culture for the most part. Not much more advanced than stone age hunter / gatherers.
Cliff Dwelling Cultures of SW Unitied States: Neither were these. Also, a subsistence culture for the most part. Not much more advanced than stone age hunter / gatherers.
But, I will accept the idea that the Mayans, Incans, or Summerians. Or, egyptian, greek, roman, ottoman or such.
Incans fell due to invasion (and small pox) brought by the Spanish Conquistadors.
Mayans: I thought the same was true for the Mayans. I'd love an explanation about how this is an environmental collapse. But, I will accept if folks say there were climate changes that occurred as well.
Sumerians: It sounds like this was environmental in some form.