Good news for Islam. This is exactly how the Muslims overtook, once Christian, North Africa.
Initially they outbred the local population, then when their numbers had grown that they became significant as a group, they conquered the remaining Christians by the sword.
America there is your future. I am sure that what is presently happening in Europe will eventually happen here. Congress and administration are you listening??!! (Oh what the hell, I am wasting my breath. They can only think as far ahead as the next election.)