Gaps also appear because evolution is not a smooth process, and once in a while a large number of mutations are selected for. We see the same type of pattern even in vitro. Moreover, mutations are not always well described by gaussian processes: the rate of mutation can be seen as having a fat tailed distribution.
Mutations has to be incremental because most mutations are not viable or doesn't provide any reproductive gain. Having multiple functional mutations all at once happening in a very short amount of time and being naturally selected in big enough number of infections is very very improbable.
> mutations are not always well described by gaussian processes: the rate of mutation can be seen as having a fat tailed distribution
I'm sorry if I have to be blunt, but you have no idea of what you are talking about.
