Well there's your problem.
You do realize that chimpanzees are genetically much closer to us than any aliens could possibly be, don't you?
Except by some amazing (read: impossible) fluke, you could substitute any known life form for "chimpanzees" in the above sentence.
There was no war...
I think you mean: "We have always been at war with East Asia"
an external population with which to mediate the process.
Mediate how exactly? They still can't contribute to the "gene pool" since there is no pool. Asexual reproduction involves no transferral of genes within a generation, only from parent to child.
would the group go through a smaller or greater number of mutations?
On average, for the same number of generations, they would go through the same number of mutations. (This is of course disregarding things that would directly damage DNA ("free radicals")). The only effect that having them "inbred" (you really need to see this), in a lab is that the researchers can monitor and control the whole process.
There was also no theoretical reason for monopoles _to_ exist.
I think the point the GP was making was that there was no reason that they couldn't exist...
Long computations which yield zero are probably all for naught.