I looked at the paper (already kindly linked by bartonfink, but here it is again: <a href="http://arxiv.org/abs/1012.1375" rel="nofollow">http://arxiv.org/abs/1012.1375</a>). I think there's considerably less to it than meets the eye.<p>The authors have a very simple model of the dynamics of religious adherence, which amounts to saying: people convert from one (ir)religious position to another in numbers proportional to some function of (1) the fraction of the population currently adhering to each position and (2) some measure of how attractive each position is. They assume that #2 is constant over time. They choose a particular (reasonably plausible) form for the dependency on #1. They have a couple of free parameters, which they adjust to make their predictions fit reality as well as possible. They plot a few graphs, which show their predictions fitting tolerably well.<p>They observe, quite rightly, that their analysis implies that on not-terribly-long timescales whichever position is more attractive will dominate completely. They fail to observe that since at present neither religion (any, or all collectively) nor irreligion is completely dominant anywhere, the attractivenesses must in fact be varying over time, and that future changes to that parameter make an enormous difference to their model’s predictions. They fail to consider the possibility that their model (even if generally adequate) may break down badly for small-minority positions. (If so, its predictions about extinction of any position could be very wrong.) They fail to consider that differences in personality, experiences, etc., may render (ir)religion differently attractive to different people, which could entirely change their model’s predictions near the edges. (That is, once it starts predicting that either religion or irreligion will go extinct or nearly so. That is, exactly the situation the headline describes.)<p>They do (and frankly this is the only interesting bit) consider the effect of clustering effects: a person’s conversion probability may depend not on the <i>overall</i> popularity of the "old" and "new" positions but on their local popularity: people are affected more by their friends, family, neighbours, colleagues, etc. They find that provided people aren’t completely isolated this doesn’t make a huge difference to the overall prediction of the model.<p>I don't think the paper gives much more reason to anticipate the extinction of religion than we already had. (Opinions vary as to how much that is...)