In "The Sickly Stuarts: The Medical Downfall of a Dynasty" by Dr. Frederick Holmes, the medical case histories of the six Stuart sovereigns are examined in detail. Holmes rejects the idea that King James had porphyria, since he believes that the main symptom that manifested in James was discolored urine, "red as Alicante wine." Holmes does not believe that the environmental factors that usually cause porphyria or trigger it in those with a propensity for it were present in James's environment.
Holmes details the severe problems King James had with his kidneys. One of them was tiny and probably dysfunctional, a congenital birth defect. The other was riddled with kidney stones, which Holmes believes caused blood to mix with his urine, leading to the discoloration.
Holmes does not devote more than a brief mention to James's daughter Elizabeth, who does not seem to have suffered from kidney disease or kidney stones. However, biographies of Elizabeth and her family reveal that two of Elizabeth's sons, Rupert and Gustav, suffered from kidney stones.
Elizabeth's daughter Sophia was the mother of George I. There is no evidence that Sophia suffered from kidney problems. However, if two of her brothers suffered from them, as well as her grandfather, it seems possible that she could have passed the problem on to her descendants.
I have only recently begun reading McAlpine's book "George III and the Mad-Business", and I have yet to acquire a copy of Rohl's book, but it is my understanding that they studied only Sophia's descendants. Two of Sophia's brothers, Edward and Karl-Ludwig, left daughters whose descendants married into almost every Catholic royal family in Europe. The House of Habsburg can trace their line to Karl-Ludwig through the marriage of his great-grandson, Francis of Lorraine, to Empress Maria Theresa of Austria.
If porphyria was truly a common and hereditary problem inherited from Mary Queen of Scots, then Catholic and Protestant descendants alike would be sufferers. I hope a future study will be done that includes a random sampling of the descendants of Sophia's brothers.