Do all descendants of your great-grandfather all have similar Jewish DNA markers?  If they are only seen in one of his children's line it suggests differing parentage.

Every child inherits 50% of DNA from each parent, but each is a random assortment of the parent's DNA. So you and a sibling only share 25%. That is why organ transplant Dr. look at parents or children first for a good match.

So all descendants of a great-grandparent will not have the same Jewish DNA markers. There are a lot of markers checked, so DNA testing will probably find some, but not all the same.

Sally Bruckheimer
Molecular Biologist who knew this in high school
Princeton, NJ

Your regions of ancestral origins are statistical estimates, based on the company’s database. Your Ethnicity Estimates are updated by the ancestry company, as more people get tested. Ancestry has a database of approximately 15 million, MyHeritage 4 million. My first estimates, with Ancestry.com, showed that I was 95% European Jewish, next 99%.  The last update, shows that I’m 100% European Jewish. According to MyHeritage, I'm 94% Ashkenazi Jewish and 6% Sephardic Jewish. 

Do all descendants of your great-grandfather all have similar Jewish DNA markers?  If they are only seen in one of his children's line it suggests differing parentage.   Is your father not DNA related to a known descendant?  
Paul

I am not familiar with MorleyDNA, and so I can't comment on how it is predicting your father's haplogroup based on his autosomal data. But I would be very wary about taking MyHeritageDNA's ethnicity analysis at face value, even with a couple of non-randomly-selected Jewish DNA matches as "corroboration."

My ethnicity as MHDNA estimates it is 88% Ashkenazi Jewish, 7% Finnish, and 5% "West Asian - Mizrahi Jewish." The same data run through AncestryDNA, which has a much larger user base to draw on for its reference samples, comes out as 100% "European Jewish."

My late grandfather's DNA test has even bigger discrepancies: per AncestryDNA, he is 99% European Jewish and 1% non-Jewish Eastern European. per MHDNA, he is...75% Ashkenazi, 15% "Italian", 1% Baltic, and 8% Sephardic Jewish. It makes very little sense to me how my grandfather could supposedly have 23% Southern European ancestry, yet my own DNA actually ended up with zero of whatever markers are supposedly typical of these ethnic groups. Much more likely to me is that MHDNA's ethnicity analysis isn't worth the pixels it's printed on, and whatever reference samples they are using to power this feature of the product are probably small enough that lots of customers' results end up with quite a bit of nonsense.

Keep in mind that all admixture reports from all companies are still at the level of "for entertainment value only" -- and MyHeritage is the absolute clown of the bunch. They predict ancestry that is ridiculously false for basically everyone. (For me, it's Swedish; for my cousin, it's British Isles. Both of us actually have all of our ancestors squarely in the Carpathian Basin.)

Ashkenazi genetics is endogamous enough that it's pretty confidently identifiable, even by MyHeritage, but the percentages they report can be wildly different from other companies. When it comes to something like "West Asian", all bets are off: neither the reference populations nor the customer base have even remotely enough representatives from this area to come to any definitive conclusions.

What it comes down to is that despite what all the DNA companies would have you believe, geography is not genetic.

Julia
./\ /\
.>*.*<

A note about DNA results... Two Jewish great grandparents may yield results similar to one Jewish grandparent, in terms of percentages of Jewish ancestry. (Ditto for four great great grandparents, etc.)

This may not be of any direct assistance but I wanted to offer a parallel example of Jew's melding into Irish Catholic society. While working in San Francisco I was introduced to a woman whose name is Yvonne O'Connor. She had 12 siblings and fell right in the middle by age. After a number of years of close friendship she told me a story about her last trip home to Dublin. To her great surprise she found an old photo in the coal shed of her grandfather. He was known as "Altman the Salt man". After some cajoling with her extended family some things became clearer to her. There were certain burial traditions that the extended family followed that clearly were not Catholic. There was one older member of thee family that would not eat pork. A member or two would not travel on the sabbath.

Eventually she was reconciled to the fact that she was Jewish. Please keep in mind that this was a Catholic girl that had to dig deep into Irish history and eventually found family names in Synagogue records. She imparted to me that "Altman the Salt man" was a character in one of James Joyce's novel "Ulysses". She is now the director of the Jewish Museum in Dublin. She speaks many languages, is well traveled and knows much about Jewish history on the "Isle". If you are inclined she might have something to offer.

There is a significant Jewish world in Scotland and it is not uncommon for people to adopt culture and unintentionally lose some family history. Good Luck!