TW. I offered two definitions so you could clarify what you meant. Just because I can help with the clarification doesn't mean I was offering it up as my position.
OK: but I was merely repeating the words you offered. 
That said... the contrived wolf v. man scenario works from the perspective that it led you to agreeing that ultimately the cycle stops with the man having the last word. Because men confer rights for themselves and animals only have rights to the point where they don't conflict with our rights. In other word, only those rights we choose to confer.
Yes, I agree man will ultimatley have the last word (or, in this example, make the last killing), because he is cleverer. But as for your comments about rights, see below
If animals have natural rights as you say... then they must have been conferred on them by someone "higher" on the rightious-continuum than man... but then that entity should have made it clear to us when he/she/it conferred our rights upon us as well.
I
do say they have rights, which I concede might be better called something else. When I use the term
natural rights, I do not mean artificial rights dreamt up by man which are decided upon by courts of law and are enforced by police forces, I just mean the ability to do something. In fact, it's so obvious that animals have these abilities, it was stupid of me to mention them, and it has led to false arguments being raised about whether animals defend themselves, hunt and roam with our permission or consent, which plainly they do not.
Natural rights are not conferred by anyone, they just exist wherever any form of life exists (maybe not at the microbial level, I don't know: can microbes protect themselves?). And they don't have to be written down - for two reasons: in nature, one does not care about the natural rights of others, one merely exercises one's own; and there are many instances of even human laws being unwritten -
England & Wales have no written constitution, nor does anywhere else in the United Kingdom.
In common-law jurisdicitions such as the USA, one has to test the law to find out what it is. It's probably the same under codified legal systems too, but I don't know.
There are very few "moral codes" that have been written down (and those that have been all differ!).
Obviously we shall continue to disagree as to whether there are any innate rights that animals have.
Maybe, but we're not so far apart when it comes to legal rights: animals' legal rights are man-made and depend upon whether man decides to uphold them. The animal has no say in the matter.
This bring me back to the beginning of this thread: do, or should animals have rights: I believe man has a duty to treat all animals compassionately, and where laws have been passed to protect animals from abuse, this is a good thing and the laws should be enforced.