An alt-right web site, "Red Ice" (apparently belonging to Henrik Palmgren), proposes that there's a nearly worldwide decrease in IQ due to immigration. The Red Ice piece apparently originated from unz.com so clearly this story was more widely circulated in the alt-right circles, circa 2016. (It was listed on the first page of results on my google search for IQ and immigration.) The author of the piece is Anatoly Karlin, whose science-related qualifications are unclear (to me), unlike his political views.
The average IQ score cannot really drop due to the way it's calculated (as discussed at Is global IQ dropping over time?), but what the Karlin piece seems to be talking about is a decrease in PISA scores:
The author's interpretation is (for instance) that:
Western Europe is a complete disaster zone, getting a harder cognitive hit even though the immigrant share of their population is considerably smaller than the US, where they constitute almost a quarter of the PISA-taking population. The German national average takes an astounding 2.4 IQ point hit due to immigrants. [...]
The situation in the US is actually considerably better than in Europe – the low-IQ Central Americans, who are not sending their best, are counterbalanced by the millions of talented East Asians, Indians, and other intelligent and highly motivated people who still want to make America their home. Thanks to that the world’s biggest immigrant nation only loses 1.3 IQ points due to all the newcomers.
So is there any truth to (1) the raw PISA data has decreased; (2) does it really correspond to an "IQ" (let's say raw IQ score) decrease; and (3) does it really imply anything about the effects of immigration?