I think he refers to crackpot theories about low birthrates in europe and how the original europeans are "dying out" and are "being replaced by reproduction happy immigrants" (it has actually been demonstrated that birthrates of immigrants match those of the host population in few years after immigrating, being apparently linked to socioeconomic factors). Therefore its not really founded by anything, but it sounds scary!!! Some far right parties in europe capitalize on that. Europe might reduce population density in the next 200 years (it is overpopulated anyway and reliant on raw materials from other parts of the world), but dying out is not even an issue. Its situation is more comparable to that of Japan. Europe will have to accept that there are immigrants, due to economical needs and develop a similar narrative to it like Canada und the US did over 100 years ago: "Give me your tired, your poor, Your huddled masses yearning to breathe free, The wretched refuse of your teeming shore. Send these, the homeless, tempest-tost to me, I lift my lamp beside the golden door!"