Looks like the steppe theory of Indo-European origins is winning out over the Anatolian theory, unless the earlier middle eastern farmers that spread into Europe were also Indo-European.
Thanks to natural climate cycles, there's been a pulse of ingress into neighboring areas from Central Asia, followed by a population crash, ingress into Central Asia as the world warmed back up, a population spike, then mass exit when the temperature crashes again. The various cultures managed to carve out new realms in China, India, the Middle East, Anatolia, and Europe.