Let's say we have a small, genetically limited population due to bottleneck/founder effect - is there a way for such a population to increase it's genetic diversity other than by introducing new DNA from the outside? I am talking about small, genetically limited populations like the Amish. 

You’re still going to have mutations.

@CharonY Anything to say here?

9 hours ago, Otto Kretschmer said:

Let's say we have a small, genetically limited population due to bottleneck/founder effect - is there a way for such a population to increase it's genetic diversity other than by introducing new DNA from the outside? I am talking about small, genetically limited populations like the Amish. 

Depends on the species.  Franklin's 50/500 rule is often cited for humans (I just wrote on this on another thread but can't find atm) and that top number is seen as what is needed for longterm viability and sufficient genetic diversity.  Lower numbers and a species can wither.  Too much inbreeding, losses of useful genetic variants to genetic drift, etc.  Most mutations are deleterious, about 75-80% of single nucleotide variants, so the lucky dice roll of a positive mutation (roughly 1-2%) that adds useful diversity is going to be rare in too small of a population.  I've seen debate on the number, but there seems to be some agreement that 500-600 is enough for humans.  I know NASA has funded some studies on this, with a longterm view to understanding what are viable populations for establishing colonies on other worlds.