A great blog post written by Maurice Gleeson almost a year ago calling for the term 'NPE' (Non-paternity Event or Not Parent Expected) to be referred to as Surname or DNA Switch, 'SDS'. The blog is great at explaining the possibilities and probabilities of this occurring.
For a Doherty tester born in 1950 there is 31 – 52.5% of a SDS occurring in their patriline across 37 generations to what is believed to be the surname progenitor or common ancestor of 850 – 900 AD. (continue reading for the math involved).
His probability calculations on this occurring is based on several conservative estimates from various studies of 1 – 2% per generation. Note that he calculated this incorrectly with a correction in the comments.
For Ó Dochartaigh if we are to assume that Group 1 testers descend from the progenitor of the first man to earn the title "Dochartaig" then the testers are estimated to converge at around 850-900 AD.
If we have a male Doherty (or variant spelling) tester born around 1950 then, on average assuming 30 years per generation, there would be approximately 1,100 years to this progenitor or ~37 generations.
So, the calculation for a 1% per generation would be:
0.99 ^ 37 = 0.6894
which is stating there is a 68.9% chance this Doherty tester DID NOT HAVE AN SDS on his line, or, in other terms, there is a 31% chance this tester's patriline experienced an SDS.
Same calculation for 2% would be:
0.98 ^ 37 = 0.4735 or 47.4% of no SDS, in other terms 52.6% probability of a SDS occurring across 37 generations.
So, a male tester born in 1950 would have a 31 – 52.5% chance of a Surname or DNA Switch on their patriline across 37 generations or approximately back to 850 AD when Group 1 Dohertys converge on a common ancestor. Please keep in mind regardless of this happening on one's patriline it should not diminish your identity as a Doherty. If you are born a Doherty then you are a Doherty, plain and simple.