Exactly, natural, and that's the same way information gets into DNA.
To improve - one must *know* or *reward*. But small, random changes (like in DNA my transpose errors or knockouts) do not produce by themselves any changes in the macroscopic organism that may or may not influence progeny.
This is why slow, gradual change has been discarded as theory for the somewhat more plausible punctuated equilibrium.
I like the classic million monkeys typing for a million years example some people throw out for the usefulness of random processes....except for one problem - suppose you get to nearly the end of the complete works of Shakespeare with all but the last word spelled correctly, one letter remaining.
What stops the first monkey from changing his letter? Nothing. Because no monkey “knows” he needs to keep the letter he got lucky with.
This shows the classic problem with statistical theory with regard to randomness. That is, ALL variables are INDEPENDANT. To hold some variables static - even for a moment in time, implies *something” is holding onto that state for a reason....
There is a recent TED talk (google TED talks) about the hundreds of people wrongly convicted on DNA evidence because of a lack of understanding about what variables are independent vs Dependant - essentially there were quoting that it was “One in a Billion” that the match was not correct, when in fact, it was more like “one in one thousand”. People were convicted unjustly because reasonable doubt was destroyed.
All due to lack of understanding of just the basic “what if’s” in simple combinations of genetic markers.