Recent Historical Genetic Evidence

Map showing the distribution of mitochondrial Haplogroup H among modern populations which is the main marker for Neolithic farmer migrations.
Map showing the distribution of mitochondrial Haplogroup H among modern populations which is the main marker for Neolithic farmer migrations. This genetic mutation originated in modern day Syria around 23,000 BCE. Not well shown on the map is that the Basques in Spain have a high percentage (28%) of this haplogroup meaning that their unique language should have more Akkadian than other European languages.
from Wikipedia Commons via Alvarez and all (2009) at: https://commons.wikimedia.org/wiki/File:Spatial_frequency_distribution_of_different_sub-lineages_of_mtDNA_haplogroup_H.png
Mitochondrial genealogy of the main haplogroups.
Mitochondrial genealogy of the main haplogroups. Since language would have been mostly transmitted to the next generation by the mothers, this haplogroup genealogy is also likely the genealogy of ancient language. from Wikipedia at: https://en.wikipedia.org/wiki/Haplogroup_H_(mtDNA)
This video by GeoNomad introduces the Y-DNA of the people who built Stonehenge. They suddenly disappear after 3000 BC. The video also introduces the Y-DNA of the people who supposedly exterminated them. It also maps the geographic features of the British Isles from the Ice Age to 6000 BC.

Neolithic Farmer Genetics

(August 20, 2022) The main genetic marker for the Neolithic farmers is the female side mitochondrial DNA haplogroup H. A mitochondria is an organelle in the cell body which generates energy for the cell. Thus it only exists in the egg and from there it is transmitted to future offspring only by the mother.

Haplogroup H had frequency of 19% among Neolithic Early European Farmers and is  virtually absent among Mesolithic European hunter gatherers. (Brotherton and all 2013)

Haplogroup H was also present in the Cucuteni–Trypillia culture. Nikitin and all (2017)

The clade has been observed among ancient Egyptian mummies excavated at the Abusir el-Meleq archaeological site in Middle Egypt, which date from the pre-Ptolemaic/late New Kingdom and Ptolemaic periods. Schuenemann and all (2017)

Additionally, haplogroup H has been found among specimens at the mainland cemetery in Kulubnarti, Sudan, which date from the Early Christian period (AD 550–800). Sirak (2016)  

References

Álvarez-Iglesias V, Mosquera-Miguel A, Cerezo M, Quintáns B, Zarrabeitia MT, Cuscó I, et al. (2009) New Population and Phylogenetic Features of the Internal Variation within Mitochondrial DNA Macro-Haplogroup R0. PLoS ONE 4(4): e5112. doi:10.1371/journal.pone.0005112 http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0005112
Brotherton P, Haak W, Templeton J, Brandt G, Soubrier J, Jane Adler C, et al. (2013). "Neolithic mitochondrial haplogroup H genomes and the genetic origins of Europeans". Nature Communications. 4: 1764. Bibcode:2013NatCo...4.1764.. doi:10.1038/ncomms2656. PMC 3978205. PMID 23612305.
Nikitin AG, Potekhina I, Rohland N, Mallick S, Reich D, Lillie M (2017). "Mitochondrial DNA analysis of eneolithic trypillians from Ukraine reveals neolithic farming genetic roots". PLOS ONE. 12 (2): e0172952. Bibcode:2017PLoSO..1272952N. doi:10.1371/journal.pone.0172952. PMC 5325568. PMID 28235025.
Schuenemann VJ, Peltzer A, Welte B, van Pelt WP, Molak M, Wang CC, et al. (May 2017). "Ancient Egyptian mummy genomes suggest an increase of Sub-Saharan African ancestry in post-Roman periods". Nature Communications. 8: 15694. Bibcode:2017NatCo...815694S. doi:10.1038/ncomms15694. PMC 5459999. PMID 28556824.
Sirak K, Frenandes D, Novak M, Van Gerven D, Pinhasi R (2016). "Abstract Book of the IUAES Inter-Congress 2016 – A community divided? Revealing the community genome(s) of Medieval Kulubnarti using next- generation sequencing". Abstract Book of the Iuaes Inter-Congress 2016. IUAES: 115.
Wikipedia (2022) at: https://en.wikipedia.org/wiki/Haplogroup_H_(mtDNA)

The Migration of Farmers into Europe

Great video by David Reich on historical genetics on the migration patterns into Europe. He is one of the leading researchers in the field.

Interaction Between Indo-Europeans and Neolithic Farmers in West Europe

Historical genetic resolution is still increasing as as more genetic research is done. This recent report from geneticists led by David Reich and Iosif Lazaridis of Harvard University presents the results of sampling DNA from more than 700 individuals who lived and died in the Near East and Eastern Europe over a span of 10,000 years. 
The Akkadian speaking Neolithic farmers of Anatolia who entered Europe were a mixture of two earlier sources dating between 10,000 to 6,500 BCE. One source came from today’s Iraq and Syria while the other source came from the Levant. 
The Indo-European invaders also came in two waves. The first group arrived in Anatolia starting about 5,000 BCE. They were followed around 3,000 BCE by the Yamnaya from the steppes north of the Black Sea. The Yamnaya added to the genetic picture without really changing the percentages of Indo-European genetics.
Image from Iosif Lazaridis. Online at: https://twitter.com/iosif_lazaridis/status/1562867952692899840/photo/1

Dr. David W. Anthony: “How ancient DNA revived ancient migrations in archaeology” (2021)

(Jan 7, 2023) One of the leading experts on the Indo-European invasion gives his insight into the process in light of the new genetic evidence. I was not aware that the Indo-Europeans also seem to have been carriers for an early version of what would later be called the Black Death. This may have killed off many of the Neolithic farmers without warfare.

While he still claims the horse and cart were the main cause of their population increase I am skeptical. While they were important to their new more intensive way of farming they were just one component of this new more intensive farming culture, a culture to which most Neolithic farmers did not adopt.

Most European Indo-European Culture Originated with the Yamnaya People

(June 20, 2023) This video is a good introduction to Indo-European cultural origins. My only complaint is that the Indo-Europeans need to be considered as semi-nomads and not pure nomads. They had farming settlements along their rivers and their genetics is 18% Anatolian farmer. The Indo-Europeans had integrated nomadism with by settled farming making both more productive and mutually supportive. Metalworking technology requires permanent settlements with established trade routes.

When the Indo-Europeans entered Europe they found lots of vacant fields already cleared of trees and free for the taking. Neolithic farming culture away from marshes and rivers practiced slash and burn agriculture. When the fertility of their fields faltered they simply moved on. 

References

Anthony, David (2019) Archaeology, Genetics, and Language in the Steppes: A Comment on Bomhard. Journal of Indo-European Studies. Online at: https://www.academia.edu/39985565/Archaeology_Genetics_and_Language_in_the_Steppes_A_Comment_on_Bomhard