I recently posted that I was concerned about fish oil because it had DHA. It seems that was only 1 or 2 studies and the bulk of the evidence is strongly in favor of fish oil and DHA. For comparison, there is almost no evidence for coconut oil. There is a good chance fish oil is the most important of the basic nutrients for PD, ahead of things like magnesium, vitamin E, and vitamin D.
Mediterranean populations seem to have genes that are associated with increased risk of PD, and yet they have less incidence of Parkinson's, possibly due to consumption of olive and fish oils.