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People in the easier areas of science and in the area of humanities often create vocabulary in order to obscure their subject. As a mathematician, this baffles me, because my vocabulary is an endless search for intuitive terms.

What was it that baffled you? Maximum parsimony? You understand parsimony, right? Well, a maximum parsimony tree is a tree that requires the minimum number of changes to connect all the elements on the tree.

I had no idea a mathematician would have such difficulty with common English words.

So, in general, it would be impossible to conduct an efficient algorithm for what you ask. Although approximation would be possible, any attempt to create a maximum tree would just be ad hoc.

It's odd it's impossible, since we've been doing it for at least 20 years. The scaling of the problem is irrelevant if you're talking about small numbers of organisms and relatively short sequences, and the method is intuitive.

But if you are in the habit of giving your students monkey-work, maybe they are able to get the measure of your field.

I hope you don't teach, because it appears you have a propensity for talking out of the wrong orifice about subjects you don't understand.

"ribosomal protein" and "s7" are particular terms and "widely separated" and "maximum parsimony tree" are, in an of themselves are also particular terms with particular meanings that cannot be immediately deciphered from the individual words. If you think they can, note that the term "maximum parsimony tree" is, in fact, defined as a minimum of some function. To the uninitiated, it isn't clear what function you are optimizing, let alone that it is a minimum.

The scaling of the problem is irrelevant if you're talking about small numbers of organisms

That's what makes it monkey-work. It's just an algorithm. Grab the handle. Turn the crank. There's your answer. The real questions are: Can you prove that the algorithm always gives a maximum parsimony tree? That's "proof" now. Not proof-by-example. What is the average-time performance? What conditions on the sequences will fail to produce average-time performance? Can they be considered "unnatural"? Can you construct a tree in polynomial time such that the number of changes to connect all elements on the tree is always at most (1+epsilon)M where M is the minimum and epsilon is a fixed positive constant.

Now if you present a proof in class that the algorithm always terminates and always produces the MPT, then that would be a good start.