It is alleged that selection from a range of such mutations gives rise to complexity, but to state categorically that selection of mutations over a long time period is the origin of complexity is pushing it too far, since this is very difficult to demonstrate scientifically. For example, much is made of the ability of bacteria and viruses to 'adapt' to pathogens, but in every case this is a result of reduction in the organism's complexity, as pointed out by Michael Behe in 'The Edge of Evolution'.
Uh... fail?
Bacteria, in some case, GAIN abilities, such as the biological
tools required to process nylon.
Digesting nylon required a specific enzyme that these bacteria
did not have before the invention of nylon in 1935.
Now they do.
What would you call that, if not an "increase in complexity"?
[inkling]