This paper has at least two massive flaws, namely assuming that Muslim emigrant fertility rates are fixed at a 'snapshot' high rate by looking at fertility in their native countries, and not taking into account the trend of lower fertility of 2nd and further generation immigrants in the host country.
They justify this by referencing the
Pew writeup, which states,
Note that the Pew projection is just talking about new immigrants, and furthermore it also fails to take into account the dynamic nature of fertility in origin countries - in fact looking at a snapshot of Pakistani and
Bangladeshi fertility rates shows a clear and ongoing decline over the past 20 years.
View attachment 71447
Now apart from this, the original paper also assumes that fertility rates of immigrants in host countries will remain equivalent to their native countries, without providing any evidence for this assumption.
In fact, there is
good evidence that 2nd and further generation immigrants tend to converge closer to the average fertility rate (likely due to better education rates, lower levels of poverty and child mortality).
Even assuming some cultural aspects remain within further generations which favour larger families, the initial assumption of a fixed fertility rate is still wrong.
This is even explicitly stated by the Pew paper (below), but somehow the authors of the previous paper completely ignored it:
The wavelet analysis is also entirely irrelevant here when they're working off of such poor assumptions.