According to this study, fertility in much of the Ummah--the worldwide community of followers of Islam--has fallen in the past 20 years to levels comparable to the United States. If that isn't amazing enough, the data indicate that increased use of birth control and socioeconomic development have had little to do with it. (And the article doesn't even mention abortion as an explanation. Correct me if I'm wrong, but abortion is illegal and rare in many Muslim countries.)
By contrast, the correlation between desired and actual family size is extremely high in these countries. According to the author, the revolutionary change has been due to changes in individual family size preferences. He doesn't use the world culture, but that's what I would call it when people's preferences change collectively.
This dramatic worldwide decline should reduce immigration numbers and ease the assimilation problems in the developed world.