Your lack of knowledge of this is very regrettable, but it's not my responsibility to give you a basic science education. Punctuated equilibrium explains stasis in the context of evolution. This theory is now quite well-established, it's almost 30 years old, and there is really no excuse to not know about it, or understand it. Again, don't rely on the creationist literature, because creationists don't understand what punctuated equilibrium is. Your question is not clear to me.
Evolution proceeds via natural selection acting on the environment.
It selects the individuals with the traits best suited to survive in a particular niche, so they live longer and reproduce more. Large populations have a large gene pool, with lots of diversity between individuals. This diversity comes about through sexual gene recombination mostly, but also mutation. I don't know why creationists only talk about mutation, as if that's all there is, when overall, mutation seems to play more of a supporting role in evolution. E.coli have a generation span of about 20 minutes.