http://www.aljazeera.com/news/2015/09/million-refugees-arrive-germany-year-150914101006005.html
Since the native German TFR is the lowest in the world (1.43), it would suggest that the native German population will decrease each generation by about 25-30%. Germany has also said they are planning on taking 500,000 refugees a year for several years. Assuming that most of these refugees are Syrian (which they are not but whatever), that shows the Syrian TFR to be 2.4. However a large chunk of these refugees are from Pakistan, Bangladesh and Sub Saharan and East Africa where the TFR is considerably higher and the regions are still mostly Islamic. The TFR should be rounded up for refugees up to 3.0 if you include other ethnic groups. With an average TFR of 3.0, it results in a 25-30% increase per generation. Throw in immigration from Islamic countries and that amounts to at least a million Muslims a year. Let's assume Germany takes in a million Muslim immigrants and refugees (Germany has already promised to take 500,000) a year over say 5 years, that would amount to:
2015 - 6 million
2016 - 7 million
2017 - 8 million
2019- 9 million
2020 - 10 million
If each generation is about 30 years, extrapolating projections based on TFR gives:
2050: Non Muslim German population falls from 76 million to 53 million (with a 30% drop)
Muslim German population rises from 10 million to 13 million (with a 30% rise)
Assuming lifespans increase and TFRs drop for native Muslim population we have:
2080: Non Muslim German population falls from 53 million to 40 million (with a 25% drop)
Muslim German population rises from 13 million to 16 million (with a 25% rise)
Let's assume the overall population stays constant and Germany takes immigrants from other parts of the world, say India, China, Russia, ME and EU. As of now 20% of Germany is comprised of non ethnic Germans, and 1/8 of these legal immigrants are Muslims. Thus following the same demographic in 2080, the native born German population (born Muslim and non Muslim Germans) would be 56 million and to keep population of Germany stable at 80 million, that would require another 24 million million immigrants. If 12.5% of these 24 million native immigrants are Muslim, that's around 3 million Muslims, which would mean by 2080 the Islamic population of Germany would be 19 million and Non Muslim population will be 69 million. By mid 22nd century both populations would be equal.
We are assuming that the TFRs stay constant, which probably is wrong and will fall as is the current trend in the world. We are also assuming that Islamic religiosity stays constant, but one can argue that it could rise rather than fall. There is no shortage of poor Muslim refugees who will continue to stream into Europe for the next century, and if Germany continues to stay open it will continue to accept these Muslim refugees and thus offset the drop in native German Islamic TFR.
There is no doubt in my mind that Germany and probably Europe will have a Muslim majority in just over a 100 years, however the direction of Islamization is important. The actress who played Shae on Game of Thrones is a European Muslim, but so are the thousands of jihadists who have joined ISIS and Al Nusra.
What direction will German Islam take? What would a German state with a majority Islamic population look like?
