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.
We must deal with nature by force because it lacks means of communication and negotiation. That does not mean we must deal with each other on that basis. It's self-evident that we all survive better when we avoid conflict rather than foster it, and that's what rights, laws, and dispute-resolution organizations produce. Thus we use them as conflict-reducing and eliminating devices.
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.
You need the "state" (or equivalent collectivist attitude) to perpetuate the private property meme.
You don't, actually. All you need for private property to exist is rights protection, which is easily divorced from the state.
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.
It's possible to replicate this function of government without having it in place.
You don't need one territorial monopolist to ensure no one else becomes one. It's possible to have peace without a king.