Well, I'm mostly basing myself on what I have read in Dutch statistical publications on the birthrate of Turkish and Morrocan and their children in the Netherlands. Unfortunately all these reports are in Dutch, but I'll translate the relevant bits.
http://www.cbs.nl/NR/rdonlyres/CCD50...b15p096art.pdf
There are some graphs on page 106 of the report. There are other reports that say the same about the evolution of fertility in the Netherlands. I don't really see a reason why developments would be any else in most European countries.
And on Denmark
All these developments are completely logical. These immigrants come from developing countries, countries in where fertility rates are always high, regardless if they are Muslim or not. They are moving to a developed society in which birth rates (like in virtually all developed countries) is much lower. There are social and economic reasons for this drop in fertility. Why would Muslims be immune to it? Even if 'secularization' would partly explain the low birth rates, why would we assume Muslims are immune to it? Clearly, they are not, considering the high number of secularized and westernized Muslims you see everywhere.
None of your links seem to give an actual source for their claims. Besides, as far as I know there have been no European-wide studies on the fertility differences among first and second generation Muslims immigrants.Your first article is an op-ed article, which doesn't even claim that fertility is not dropping among immigrants. It is only claiming that fertility is still higher than among 'native' Europeans, which nobody is disputing.
The second article deals with Russia, which is really so much different from Western Europe. Firstly, there Muslims are indigenous and not immigrants and Russia is simply not very developed.
The third article, like the first, does not show any source and does not comment on fertility changes, but merely that they are higher currently. Which is indeed correct. Besides, these unsubstantiated claims don't seem to agree with a study like this one on West Africa.
http://www.anthrosource.net/doi/abs/...ournalCode=maq
I am not sure why the AIDS comment is in your post. How many people do you think are dying in Europe because of AIDS? :X In Holland about 100 people a year die because of AIDS. However you put it, that is simply not much at all out of a population of 16 million. AIDS is simply not a major killer in the West.
Your fourth link, the one pointing to an article from the notoriously 'Islamophobe' Daniel Pipes. These doom and gloom predictions of Muslim 'take-over' are generally based on several assumptions:
1. Muslims cannot modernize (and thus get less children or apostate)
2. Europe cannot restrict immigration
I think these assumptions are highly flawed. None of them have been substantiated by any kind of research.
Clearly Muslims can live modern life styles, they are not any different from other humans. There are generally only two groups who want to designate Muslims as 'special', Islamophobes and overly enthusiastic Muslims. Unsuprisingly, these are also the two groups that promote this idea that Islam will take over the world, the latter as a wet dream, the former to scaremonger people into action.
Clearly Europe can limit immigration if they want to, countries with strict immigration policies see huge drops after a while (look again at Denmark and Holland). Most immigration is because of import husbands/wives and family reunions. Limit that and your are halfway there.
But we are getting off-topic, we were just discussing birth rates, not immigration. This is just my opinion of course, your opinion may differ
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