They are as distinct genetically from the settled Irish as the Germans are from Italians or the English are from the Spanish, and there is some genetic substructure with at least two distinct populations and possibly three or four, that correspond fairly closely to linguistic differences.
Each of these sub-populations diverged from settled Irish populations genetically before the Great Famine in the mid-19th century. While other Irish populations have experienced exponential growth, Irish Travelers have suffered sustained demographic decline. The body of the paper says this about the divergence date between the settled Irish and the Irish Travellers.
The dating of the origin of the Irish Travellers is of considerable interest, but this is distinct from the origins of each population. We have estimated the point of divergence between the Traveller and the settled Irish population using two different methods. Our LD-based (TF) method estimates a split 40 (±2 std.err) generations ago, or 1200 (±60 – std.err) years ago (assuming a generation time of 30 years). Our IBD-based method (TIBD) estimates 12 (8–14) generations, or 360 (240–420) years ago. However both estimates suggest that the Irish Travellers split from the settled population at least 200 years ago. The Irish Great Famine (1845–1852) is often proposed as a/the source of the Irish Traveller population, but results presented here are not supportive of this particular interpretation.The IBD based date is more reliable in this context as it controls better for issues related to having a small relatively genetically isolated population. So, that puts the divergence date around 1650 CE.
The paper's abstract and the citation for it are as follows:
Edmund Gilbert, et al., "Genomic insights into the population structure and history of the Irish Travellers" 7 Scientific Reports 42187 (February 9 2017).The Irish Travellers are a population with a history of nomadism; consanguineous unions are common and they are socially isolated from the surrounding, ‘settled’ Irish people. Low-resolution genetic analysis suggests a common Irish origin between the settled and the Traveller populations. What is not known, however, is the extent of population structure within the Irish Travellers, the time of divergence from the general Irish population, or the extent of autozygosity. Using a sample of 50 Irish Travellers, 143 European Roma, 2232 settled Irish, 2039 British and 6255 European or world-wide individuals, we demonstrate evidence for population substructure within the Irish Traveller population, and estimate a time of divergence before the Great Famine of 1845–1852. We quantify the high levels of autozygosity, which are comparable to levels previously described in Orcadian 1st/2nd cousin offspring, and finally show the Irish Traveller population has no particular genetic links to the European Roma. The levels of autozygosity and distinct Irish origins have implications for disease mapping within Ireland, while the population structure and divergence inform on social history.