tk, you certainly accept that property is a category which doesn't exist outside human society. Even further, there have been societies without any form of property. Without getting into too much detail here, it would be important to define exactly what type of property we are talking about: there is conceptually a big difference between your private CD collection and the computer you use at work. The only one that plays a role in thie economic context is the second, which is a means of production.

Thus, if property exists, it is a form of our (social) existence, which is entirely the result of our own (human) evolution. This is the same evolution that shaped our (human) nature.
I'm unable to coin the term 'natural' in this context, you make it sound a bit metaphysical.