The syntax of the preposition epi (+ dative case) is analyzed in my comment at 1.14.6. In the context of 1.14.6, the dative case that goes with the preposition epi there involves the persona of a cult hero, Erikhthonios. In the present context, there is no involvement of a hero, though the dead at Marathon were in the course of time treated as cult heroes. That is why I apply here as well my experimental translation ‘in responsiveness to’.