Due to the structure and other mechanical and chemical properties of SNPs, geneticists can actually estimate mutation rates with pretty good accuracy. With that knowledge genetic genealogists can workout when a SNP would have mutated, and so it becomes possible (given a genealogical pedigree) to piece together which ancestor (or handful of ancestors) had the initial mutation. With more people testing for a certain SNP, and more of the same SNP being identified, we can refine our results more and more until eventually we narrow it down to one ancestor. Then we can start to determine other SNPs that emerged in the subsequent generations and we can build a table of SNP belong to a certain haplogroup descended from a common ancestor. Using this methodology we can now identify members of the McCarthy Reagh clan who cannot demonstrate traditional historiographic genealogical descent. 

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The McCarthy Surname Y-DNA Study has done tremendous work to establish exactly that, and their results (current as of January 2023) can be found here: Donal Goth's descendant Haplotree. If you haven't yet seen their extensive "Scrapbook" with all the genetic genealogy be sure to visit The McCarthy Surname (Y-DNA) Study Scrapbook page. For reference, Donal Goth (spelled Donal Gott on the haplotree) is found in the R-L21 Group B, SNP R–ZS4606, chart.