As with most forms of dementia, Parkinsons might be caused by excessive insulin production. Insulin is effectively a growth hormone and excess insulin causes growth where you don't want it. If so, then a keto diet should reverse it and, indeed, anecdotal observations confirm that it does.

Of course, Big Pharma will never instigate a proper trial of this theory because there's zero profit to be made. Instead, they promote expensive "treatments" that mitigate the problem, but don't cure it.

Alternatively: Parkinson's disease may be triggered by gut microbes, according to a California Institute of Technology (Caltech) study that points to probiotics as a potential therapy for the disease.

Findings point to the gut as the origin of Parkinson's disease, not only in the brain as previously thought.

Gastrointestinal problems such as constipation often precede the decline in motor skills seen in patients with Parkinson's.

(From my own research.)

Also: http://whale.to/w/parkinsons.htm