How to model migration and events from a single point?

In my current world setup, there's a singular point of creation of the sapient race/s (not sure on that detail yet) on a mountain-island at the centre of the world, from which there are waves of migration out into the other continents.

My question is how to model the history of such a world? In terms of history to reference, documented migrations have always had local populations to come into contact/conflict with. With no native populations to hit, how do you give texture to the history of such a setup?

So far, I've come up with the idea of waves of migration from the home mountain, with the time passing creating cultural change both among each migrant wave and the settled population. Any more ideas on how to give a realistic model or point of reference for how this kind of migration/expansion could work?