It's not biological evolution but social evolution that'll happen. Right now you have immigrants coming from a family with 7 siblings. They move to a Western country. The second generation immigrant will be at the same 1.x reproduction number as the rest of that country. It's the environment, the social arrangement.
It means that the countries supporting of children in the long term will survive and pressure cooker ones with very child unfriendly traditions and policies will slowly fade away.