This discussion seems handy as an excercise but as poor in vitamins as a mother-in-law's kiss.
We're making some assumptions here, the worst of which is we are not part of the animal kingdom; that we can stand outside the system and make dicisions of "right" based on our exclusion.
I view the planet as an organism and the different subsytems as interdependent. We, along with the rest of the animal kingdom, are one of the subsystems, dependent on the others to survive. Other subsytems; plants, for example, are dependent on us as well as other subsystems to survive.
We have the same rights as the other animals in the subsystem; the right to claw our way to an age when we can reproduce. If something happens to us before we reach that age, we lost that right. Just as I have the right to eat one of the other animals, they have the same right if I'm not smart enough or quick enough or both to prevent being consumed. Just as I have the right to kill some crackhead for kicking in my front door and threatening my kids with a gun, so a mother grizzly has the right to tear me to shreds if I get between her and her cubs.
Just because we ascended to a point where we have power over the entire planet doen't mean we have the "right" to excercise that power and destroy the planet.
We tend to think that whatever we decide is right is a "Right". The inalienable rights and our dominion over the animals are "Divine Rights". ...whatever...
I think the folks who lived here long before Columbus talked Isabella into hockin' her jewels had it "right". They lived with nature, as part of the subsytem.
Mark