As migration flow data are often incomplete and not comparable across nations, we estimate the number of movements by linking changes in migrant stock data over time. Using statistical missing data methods, we estimate the five-year migrant flows that are required to meet differences in migrant stock totals. For example, if the number of foreign-born in the United States increases between two time periods, we estimate the minimum migrant flows between the US and all other countries in the world that are required to meet this increase.
For each country of birth, we estimate the minimum number of migrant flows required to match differences in stocks by assuming that people are more likely to stay than to move. This estimation procedure is replicated simultaneously for all 196 countries to estimate birthplace specific flow tables, resulting in a comparable set of global migration flows. Alterations are made to the migrant stock counts to control for births and deaths during the period. This allows our country-specific net migration flows to closely match the net migration estimates published by the United Nations.
This is obviously complex! and so you need to study their instructions for interpreting the graphic. In addition, they provide the data that they have put together, so you can see the numbers behind the visualization. I appreciate this, in particular, because I am currently trying to do something similar, albeit on a much smaller scale, for a paper that I will be presenting in April at the annual meetings of the Association of American Geographers in Tampa.