See: Zoltan Maroti et al

"MITOMIX, an Algorithm to Reconstruct Population Admixture Histories Indicates Ancient European Ancestry of Modern Hungarians"
https://www.biorxiv.org/content/bior...47395.full.pdf

"Abstract

By making use of the increasing number of available mitogenomes we propose a novel populationgenetic distance metric, named Shared Haplogroup Distance (SHD). Unlike FST, SHD is a truemathematical distance that complies with all metric axioms, which enables our new algorithm(MITOMIX) to detect population-level admixture based on SHD minimum optimization. In order todemonstrate the effectiveness of our methodology we analyzed the relation of 62 modern and 25ancient Eurasian human populations, and compared our results with the most widely used FSTcalculation. We also sequenced and performed an in-depth analysis of 272 modern Hungarian mtDNAgenomes to shed light on the genetic composition of modern Hungarians. MITOMIX analysis showedthat in general admixture occurred between neighboring populations, but in some cases it also indicatedadmixture with migrating populations. SHD and MITOMIX analysis comply with known genetic dataand shows that in case of closely related and/or admixing populations, SHD gives more realistic resultsand provides better resolution than FST. Our results suggest that the majority of modern Hungarianmaternal lineages have Late Neolith/Bronze Age European origins (partially shared also with modernDanish, Belgian/Dutch and Basque populations), and a smaller fraction originates from surrounding(Serbian, Croatian, Slovakian, Romanian) populations. However only a minor genetic contribution(<3%) was identified from the IXth Hungarian Conquerors whom are deemed to have broughtHungarians to the Carpathian Basin. Our analysis shows that SHD and MITOMIX can augmentprevious methods by providing novel insights into past population processes."

So, male mediated and probably not very large, but enough to effectuate language change.