A range of data sources as e.g. the Swiss Census and the World Value Surveys showed the reproductive potential of various religious communities. Vegard Skirbekk, Anne Goujon and Eric Kaufmann did another study in religious demography at the Vienna Institute of Demography, based on post-millennia General Social Surveys in the USA. Their findings are fully congruent: Most religious communities are showing higher fertility rates than the religiously non-Affiliated, whose birth rates are far below replacement level.
Please note that fundamentalist Protestants do have more children (on average) than moderate and liberal ones. An interesting case is US-Judaism: While Swiss Jews performed near the top of the Swiss birth table -together with the highest portions of academics, leading professionals and urban dwellers-, Jews come out below the non-Affiliated in the USA. The reason is: regional religious history. While there are strong conservative, orthodox and some ultra-orthodox (Haredim) communities among the Swiss Jews, most US-American Jews are (yet) liberal, although the Orthodox share is growing quickly - most importantly due to its higher fertility.
Another interesting set of data explored the transition rates between the various religious groups.
The results seem to be pretty conclusive. There IS secularization: From 7.3% of former Catholic Hispanics to 19.7% of former Hindus and Buddhists, almost all religious groups are losing members to the category of the Non-affiliated (which includes various ranges of individual religiosity and spirituality). But then, nearly half (44.1%) of those raised without religious affiliation chosed to join one later - according to the study, especially women.
Together with the low birth rates of seculars, these data sets explain how waves of secularization and religious revivals progress simultaneously. Neither secularization nor religion may win entire populations - especially among the free and educated, there will be ups and downs driven by demography and culture.
The reproductive advantage of religiosity, which was -according to my knowledge- at first assumed by nobel laureate Friedrich August von Hayek, is observable in the USA, too. Religious communities don't need State funding to raise the average reproductive success of their adherents. And Twin-studies are strongly supporting the - expectable - assumption of partial, genetic heritability. As this wonderful video-clip from Tuebingen University is showing: Darwin rocks! Religiosity and religions are part of the great, evolutionary story.