Are the current levels of immigration into Western countries very high in global historical terms? What other periods in history have had similarly high rates, and what happened? Did most of the migrants assimilate peacefully? Or did they displace the native population? Or end up being expelled/ethnically cleansed? Are there patterns in what happens historically?
Sorry, we don't allow "example seeking" questions. It's not that your question was bad; it's that these kinds of questions tend to produce threads that are collections of disjointed, partial, inadequate responses. If you have a question about a specific historical event, period, or person, feel free to rewrite your question and submit it again. If you don't want to rewrite it, you might try submitting it to /r/history, /r/askhistory, or /r/tellmeafact.
For further explanation of the rule, feel free to consult this META thread.