It's interesting looking at the above plot! It seems during this time period there was a fair amount of immigration happening. You can visibly see from the graph there it appears there were a few events or possibly policies that had an effect on immigration - either positively or negatively. In the late 1960's into the 1970;s the Vietnam War was in full swing which may account for the decline in immigration numbers due to a wartime conflict. It appears that around 1980 with the election of Ronald Reagan may have had a positive effect on immigration. Just prior to 1990 when the Berlin Wall fell (or was taken down) we see a large spike in immigration all around - but especially from Russia, Germany and the Ukraine. It's also very interesting that at this time China, Canada and Brazil had a spike in immigration. China can be explainable through the Tienamen Square Massacre. Really post this massacre could have been an important catalyst for chinese immigration. Some of the immigrants from other countries could have just been taking advantage of favorable immigration policies due to world events.
During the influx of immigration mentioned above. It seems that percapita GDP was on the rise - though many people from multiple countries were leaving their respective countries. This could possibly be due to the fact that economic indicators tend to lag and peak prior to a decline. Post some of these immigration time periods the percapita GDP in many of these countries drastically declined signaling that there may have been a lot of inflation - which would explain why people were immigrating at the peak percapita GDP times. More analysis would have to be completed.
It appears that many countries are in fact prospering due to the fact that the life expectancy appears to be increasing. This is good news!
Most of these countries populations seem to be on the rise. This could possibly be a reason for immigration - especially in China where the numbers are over 1 Billion people.