Mark Steyn was recently interviewed by Danish TV when he was in Denmark to receive the Sappho Award from the Free Press Society.
In this interview he brings up several points I agree with: the fact that Europeans constantly degrade their own culture and are afraid of nationalism and patriotism, but then expect immigrants to assimilate into this self-hating culture, for example.
His demographic calculations, though, are extremely simplistic. He gives as an example a country with 10% Muslim population. For starters, there is no such country, yet.. but let's assume an hypothetical country, with 100 residents, and 10% Muslims. The most simple calculation gives us the following:
Non-Muslims (1.4 children): 90 -> 126 -> 176.4 (59%)
Muslims (3.5 children): 10 -> 35 -> 122.5 (41%)
Not exactly 'catching up', but a very big minority nonetheless.
Of course, since we live longer nowadays, we should try not to kill the grandparents:
Total Non Muslims: 90 +126 + 176.4 = 392.4 (70%)
Total Muslims: 10 + 35 + 122.5 = 167.5 (30%)
The simple calculation doesn't take into account that women make up just 50% of the population:
Non-Muslims (1.4 children): 90 -> (90/2*1.4) 63 -> (63/2*1.4) 44.1 (59%)
Muslims (3.5 children): 10 -> (10/2*3.5) 17.5 -> (17.5/2*3.5) 30.6 (41%)
Apparently, just the same as our previous calculation. But if we don't kill off the grandparents:
Total Non-Muslims: 90 + 63 + 44.1 = 197.1 (77%)
Total Muslims: 10 + 17.5 + 30.6 = 58.1 (23%)
A somewhat smaller minority. And that's assuming all women marry and have the average number of children.
Talking about Muslims taking over Europe by births alone disregards the fact that without the constant inflow of immigration, the Muslim population would not be growing so much, and the number of births would drop dramatically.
It also doesn't take into account the variability of life. There are already reports of a Muslim emigration movement from some countries. In some cases, they move to other European countries (more specifically, the UK), in others, they go back to their homelands (Turks leaving Germany). As life becomes more difficult, and as people realize that they're not being accepted as locals as long as they don't assimilate, they will (and do) face an identity crisis.
Finally, as Mark Steyn points out, immigration is not the reason Europeans are having less children, and it won't 'save them' from that fate. In our hypothetical country, those 90 people who only had 41 grandchildren will continue to dwindle down.