Why are populations that are more diverse usually more stable?
It is going to depend on what you consider stability.
The pirah are not very diverse at all in their population and are extremely stable. [ They also have a frustratingly complicated language and no concept of numbers which keeps foreign influence out for the most part.
A diverse population would be more resistant to disease because of simple biology. The more sources for possible resistance
the better the heterogeneous pool will be at resisting disease. You also have to take in to consideration things like the availability of modern medicine and the ability to be isolated during illness.
Predation? I would need you to clarify what you mean.
Invasion is a tricky one and the answer is going to depend on what school of thought you take on the subject. Personally I think it has to do with the fact that many of the worlds more diverse population centers are also many of the worlds largest population centers which make them less prone to invasion on that basis alone. ]
There are no new answers.