All of the names on the map are Irish, so the map suggests that Irish immigrants may take over the United States by the 1900s.
You
 may well be right about people's fears that immigrants, lots of them 
from Ireland, would overrun the country. Look up when the potato famine 
was, though. The map may be from the early 1900s, but, if so, not about 
the potato famine in Ireland.
I hope this helps.