As much as I'd like to believe that one "bad" bacteria (desulfovibrio) is responsible for Parkinson's, I suspect the situation is more complicated than that, as this recently released study suggests;
nature.com/articles/s41467-...
Certainly the evidence is accumulating though, that a reduction in butyrate producing bacteria is a key factor, so upping the inulin and resistant starch intake is probably a good idea.