The Global Migrant Origin Database is the main source of the data. As said on the site, it "consists of a 226x226 matrix of origin-destination stocks by country and economy". Put differently, this is a matrix showing for each pair of country X and Y "the number of persons born in a country X and now living in country Y." Globally, the map is only as good as this data is and it is quite clear, even for a non specialist like me, that obtaining accurate number on such topic is really difficult: you have to use many different sources with different counting criteria, and for some country, it would probably be better politically not to give the precise numbers. So, take the map with a grain of salt.
And perhaps an American moving to Israel is, presuming Jewish, also not counted as an immigrant, because the Law of Return says that person is already (or perhaps automatically becomes, I'm not really clear on this) an Israeli citizen?
But also, citizenship doesn't seem to be an issue here. Puerto Ricans are US citizens and are not counted in US immigration stats for that reason, but they're counted in in-migration and out-migration stats here.
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