Typical gobledygook. Trying to sound profound when all you are doing is being unintelligible.
You have not answered my question as to why these species have not been mutating for 400 million years.
If you don't know what it is how can you say it's gobledygook? Ok, I'll explain. An example of local maximum would be a tv, a remote and a beer. You could get to a 'higher' point on a fitness landscape by going to your next door neighbor if he had a bigger tv - a small change in gene pool. To get to a higher point you would need to get a job, earn some money and buy a bigger tv. But that would be too big a change - evolution doesn't work in such large steps, it's 'blind', it does not see the payoff after several 'low fitness' steps. That's why some species don't change for 400 million years - in a stable environment the paths to better fitness are TOO LONG.
You have not answered my question as to why these species have not been mutating for 400 million years. There are always improvements possible regardless of how limiting the environment may be. In fact, if punk-eek is to be true for example, the species in the limited environment must overcome the limiting environment in order to spread itself past its boundaries. I also see no particular limitation to the coelacanth's environment. The oceans are huge and there is no reason why the species could not have improved itself. Unless of course the demi-god Darwin ordered them to stop mutating, to stop adapting, to stop evolving.