Capitalism and Socialism is Collectivism. It's the same Bullshit. Private property is always sub-property, which is guaranteed by the state, because with this private sub-property, the tax payer is able to generate taxed surpluses. Without a state, there is no such thing as a private property.
This has never been true and is an example one of the great falsities the leftist-anarchs believe. Not only does property exist without the state, animals act as if they own things, themselves, their herds of female, and territories even. There've been done some interesting studies on property ownership in the animal kingdom.
Some primitive tribes do live collectively, but in that case they live as if the tribe owns everything, not as if there were no property at all, which belies your point, since they are stateless.
Functionally it's impossible to live without property as a concept. Because if you can't be the exclusive owner of a thing, then you cannot even live. For to dispose of a bit of food and water is to sequester it away for your exclusive use, which is to own.
Those railing against property have completely missed the mark, and it's a shame that all of leftist anarchism and socialism is focused on doing away with private ownership of property.
It was never property that was the problem. Property is the solution! The problem is government itself interfering. The socialists then allied with government and became the very thing the left-anarchs had railed against.
You are correct in looking to nature for a solution, I too look to nature for the solutions, but what I see reveals the non aggressive principal is not part of properly in nature.
All the territory or herd property, that exists in nature is defended by strength. Your property is challenged all the time, regardless of species. It can be claimed by whoever wants it, there is never a non aggressive principal to allow an imbalance to exist to the detriment of the majority in nature.
Challenges to the territory in question are almost always called off before life threatening injuries, and never allow an imbalance of natural recourses to accumulate in one territory unchallenged.