I was trying to stay out of the conversation as ETH had perhaps the most coherent post on the subject in the other thread. People who do not own woodland property of any magnitude are missing the point here.
Wildlife is considered [i]res nullius[/i], the property of no one.
Here in Florida, (and I suppose every other state) the animals are placed under the "public trust" of the State. That is why, for example, one needs a state permit to hunt deer.
Since wild animals have neither the intelligence nor ability to distinguish property lines, they go anywhere. It is for this reason that state statutes give the power to it's wildlife officers to "enter upon any land or waters of the state for performance of their lawful duties...such entry shall not constitute a trespass." [FL Statute 372.07(1)] Section 2(a) of the same chapter allows FWC personnel to "Go upon all premises, posted or otherwise..." .
Additionally, sworn personnel of the FWC are "fully constituted police officers as provided under Florida Statute 372.07." This gives them the authority to enforce all laws of the state, not just those relating to resource enforcement. They are also cross-deputized to enforce federal fisheries and wildlife laws.
They also provide "general law enforcement patrol in rural, semi-wilderness, wilderness, and off-shore areas where no other law enforcement agencies routinely patrol."
There may be a case to be made at what point the FWC ceases to be a wildlife officer and becomes a law enforcement officer (in the case of the situation in the other thread). I believe that the FWC officer has to actually see the crime being committed to make an arrest.
As for a regular, local LEO - I believe the normal constitutional protections are still inforce for a property owner. So get off my property unless you are a FWC officer or have a search warrant.
I hope this answers the question once and for all.