FOR a Turkish woman ready to start a household, Weseler Strasse in Duisburg is a one-stop shop. There, in the shadow of an enormous steel works, are dozens of stores selling wedding dresses and glitzy tuxedos; jewellery and home furnishings. What this stretch of Weseler Strasse does not contain is a baby shop. In the early 1980s women with foreign passports in Duisburg had a birth rate much higher than native Germans (see chart). Most of the foreigners were Turks, who had settled in this Ruhr Valley city for its industrial jobs and brought their big-family culture with them. But then came an astonishing drop. Today foreigners are actually slightly less fertile than natives. That is saying something: German women in Duisburg, and in Germany as a whole, do not have nearly enough babies to keep the population ticking over naturally.

Xenophobes and xenophiles share a belief in the fecundity of newcomers. “Immigrants are more fertile,” explained Jeb Bush, an erstwhile American presidential candidate (and xenophile) in 2013. “They love families and they have more intact families, and they bring a younger population.” That is still just about true in America, but the gap is vanishing.

Between 2006 and 2013 the fertility rate among Mexicans in America fell by 35%, compared with a drop of 3% among non-Hispanic whites. In the Netherlands, the immigrant fertility rate is now almost exactly the same as the native one. Even in Britain, where a quarter of births are to immigrants, statisticians reckon that immigration has raised overall fertility by a mere 0.08 children per woman.

The fertile immigrant is partly an illusion. Women tend not to move country with babies in tow, explains Gunnar Andersson of Stockholm University: they travel first and then have a child quickly. That makes them seem keener on babies than they really are. Partly, too, the countries that send migrants to the rich world have changed, points out Michael Teitelbaum, a demographer at Harvard Law School. Fertility rates have plunged in both Mexico and Turkey, from more than six children per woman in 1960 to less than three today. Grandma in Oaxaca is probably no longer pushing her emigrant daughter to have a third.

But the big reason immigrants’ birth rates are falling is that they tend to adopt the ways of the host communities. This happens fast: some studies suggest that a girl who migrates before her teens behaves much like a native. Acculturation is so powerful that it can boost birth rates as well as cut them. In England, migrants from high-fertility countries like Nigeria and Somalia have fewer babies than compatriots who stay put. Those from low-fertility countries such as Lithuania and Poland have more.

Christine Bleks, who runs a children’s charity near Weseler Strasse, points to the front gardens of houses around Duisburg’s large mosque. They are small and orderly, with neat hedges and kitsch ornaments. The style is stereotypically German, she says. But the owners are mostly Turkish. As with gardens, so with families: immigrants have gone native.