All fine, all generally anecdotal. Where there may be some mathematical modelling concerning populations, it does not address the specific question of how you know evolution is not a uniform process? So far all you've answered is why one might think it is not uniform.
If you can't answer simple direct questions you ought not get all huffy, coyoteman. Science isn't telling stories. My mind is made up about that, yes.
The reason why it is not uniform is because the conditions change.
Uniform response of an organism to uniform conditions would give a uniform rate of change. Even if there is a uniform response by the organism or population to its environment, nonuniform conditions would give a non-uniform rate of change.
Hope this helps. Do you have calculus behind you? It would help if you did. You don't need to really grasp fluxions and such, but I would explain it differently if you didn't.