Was it likes waves of conversion to Christianity and Islam in small time frames or a gradual linear process? During the Muslim conquests were there more Christians or Jews? Were Christians, Jews, or other groups more liked to convert to Islam? When was each religion dominant? What about immigration, did a lot of Muslims immigrate there? When and from where?
You might need to narrow the timeframe. There were many periods where "native" people were expelled or converted in the area. There's the biblical account of the conquest under Joshua, the conquest of the northern kingdom, the conquest of the southern kingdom, the return from Babylon, the conquest by the Romans, the Crusades, and probably a lot more. There's a whole lot of very different circumstances where your question might apply.