[Lev]

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.

I'll try again.

  fitness
  ^
  |
  |       _ max B
  |      / \
  |     /   \_
  |    /      \       _ local max A
  |  _/        \     / \
  | /           \   /   \__  __
  |              \_/       \/
  |-------B-------X--YA---------> gene pool

Suppose particular species in particular environment has this fitness function. Now, how do we get from point A to a higher fitness point B? Mutations will get some organisms to point Y which has LOWER fitness. They will have fewer offsprings than those staying at point A. Some organisms will mutate even closer to point X but according to the fitness function the closer they get to X the less likely the mutations in that direction will be passed to the next generation. With time environment may change which would cause the fitness function to change, let's say fitness at point X increases - this will allow some organisms to reach B. The fact that there are not many 'living fossils' around indicates that environment does change and species do 'improve themselves', as you say. But in some rare cases they get stuck at a nice and warm point A and don't change much for a long time. Any questions? Which part of this do you disagree with?

[gore3000]

Suppose particular species in particular environment has this fitness function.

You are supposing a lot and your explanation is all gobbledygook. Use your so called theory if you like, but answer the question: why did the coelacanth stop evolving, stop mutating for 400 million years (note also that it did not de-volve either). One thing you also need to explain about your fantastic theory is how the parameters for a particular species are measured as well as how the formulas were derived and tested.