It is by no means sure that Iranian Farmers mixed with steppe populations. Lazaridis modeled it only to show a three way model fitted better than a two way model and explained in the comment section of Davidski that his is not the final word.
http://eurogenes.blogspot.nl/2016/0...howComment=1466599307814#c7517378404372112535
I would think it nearly impossible that Iranian farmers migrated north of the Caucasus. First, Yamnaya and Iranian farmers have different uniparental markers. Secondly, Yamnaya was a pastoral culture whereas Iranian farmers depended greatly on cereals. Considering the fact that Ukraine mostly has Löss soils and is one the most fertile area's in the world - it still is one of the worlds bread baskets - it would be hugely strange if migrating farmers didn't use these for cereal growing on a vast scale. However, archaeological evidence points to minor cereal growing in Yamnaya culture.