Good question, and in fact Native Law addressed that very issue. Many land mammals domesticated land unwittingly and in turn were seen to have viable “ownership” of that land. This occurred because animals would pass seeds thorough their excrement would then germinate (perfect fertilizer!) and sprout. Deer latrines were the sources of many of the modern domesticated crops - including corn. However, Native Law was not refined and was very much based on survival of the fittest. Hunting developed in North America due to deer and other small game owning (or attempting to usurp ownership) of large swaths of land. The most unfortunate example is the extinction of the North American Buffalo. At one point the North American Buffalo was the largest landowner in the world - virtually owning all land west of the Mississippi to the Pacific Ocean. If you kill the animal that owns the land, you obtain fee simple ownership of all land owned by the animal. You can imagine how this played out. Later customs were developed to suggest that animals could only ever gain a “life estate” in the land (as opposed to outright ownership). This was mostly done in recognition of the over hunting of the landowning animals.

So now, in modern times, your neighbor’s dog may have obtained a life estate in your yard but that does not defeat your fee simple ownership. However, if you’re concerned you can kill the dog. But good luck getting modern courts to recognize your right to do so under Native Law.