The paper is not out, but since the data has been uploaded they posted the abstract for the world to see, Project: PRJEB44430:
Horse domestication fundamentally transformed long-range mobility and warfare. However, modern domesticates do not descend from the earliest domestic horse lineage associated with archaeological evidence of bridling, milking and corralling at Botai, Central Asia ~3,500 BCE (Before Common Era). Other long-standing candidate regions for horse domestication, such as Iberia and Anatolia, were also recently challenged. Therefore, the genetic, geographic and temporal origins of modern domestic horses remained unknown. Here, we pinpoint the Western Eurasian steppes, especially the lower Volga-Don region, as the homeland of modern domestic horses. Furthermore, we map the population changes accompanying domestication from 273 ancient horse genomes. This reveals that modern domestic horses ultimately replaced almost all other local populations as they rapidly expanded across Eurasia from ~2,000 BCE, synchronously with equestrian material culture, including Sintashta spoke-wheeled chariots. We find that equestrianism involved strong selection for critical locomotor and behavioral adaptations at the GSDMC and ZFPM1 genes. Our results reject the commonly held association between horseback riding and the massive expansion of Yamnaya steppe pastoralists into Europe ~3,000 BCE driving the spread of Indo-European languages. This contrasts with the situation in Asia where Indo-Iranian languages, chariots and horses spread together, following the early second millennium BCE Sintashta culture.
If you ever inspect the domestic horse lineages you will note that they’re a monophyletic clade. They are recently descended from a common ancestor. Additionally, there is a massive skew in stallion lineages toward a few breeders. Ancient DNA has now solved the question of which prehistoric horse population the modern domestic breeds descend from: the horses from the eastern edge of the post-Yamnaya cultural zone.