At the same time of mass deportations of Muslims from the West, there will be a total massacre of unlucky Westerners trapped in Muslim lands.
After that, there will be a rigid partition, a quarantine, with no travel between the West and Islamic lands. Since we can never tell the Attas from the "moderate" Muslims they will ALL have to be kept out.
This "quarantine" will hurt but not destroy the Western economies, but it will prove fatal for the Muslim world, where without Western food and tech help they will starve and die by the millions.
(Of course, "evolution" might not describe what is going to happen after we invade Iraq and / or suffer a WMD attack in the USA.)