The mixture of highly differentiated populations is a recurrent process in our history. - David E. Reich

Ancient DNA available from this time in Anatolia shows no evidence of steppe ancestry similar to that in the Yamnaya (although the evidence here is circumstantial as no ancient DNA from the Hittites themselves has yet been published). This suggests to me that the most likely location of the population that first spoke an Indo-European language was south of the Caucasus Mountains, perhaps in present-day Iran or Armenia, because ancient DNA from people who lived there matches what we would expect for a source population both for the Yamnaya and for ancient Anatolians. If this scenario is right the population sent one branch up into the steppe-mixing with steppe hunter-gatherers in a one-to-one ratio to become the Yamnaya as described earlier- and another to Anatolia to found the ancestors of people there who spoke languages such as Hittite.

We warn that models in population genetics should be treated with caution. Although they provide an important framework for testing historical hypotheses, they are oversimplifications. For example, the true ancestral populations of India were probably not homogeneous as we assume in our model, but instead were probably formed by clusters of related groups that mixed at different times. (Reich et al. 2009: 492)

People often think that Europeans are homogeneous group that arrived in a simple way there maybe 40 or 50 thousand years ago maybe based on the archaeology and just kind of sat there until they became the Europeans they are today, but that's probably not true: the Europeans today are a replacement population who came in much more recently and replaced the people who were there originally 40 thousand years ago.