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The demographic transition & continuation of the Dreamtime* is not a guarantee; the future may be African: "World population stabilization unlikely this century", Gerland et al 2014 (https://dl.dropboxusercontent.com/u/5317066/2014-gerland.pdf); excerpts:

"The United Nations recently released population projections based on data until 2012 and a Bayesian probabilistic methodology. Analysis of these data reveals that, contrary to previous literature, world population is unlikely to stop growing this century. There is an 80% probability that world population, now 7.2 billion, will increase to between 9.6 and 12.3 billion in 2100. This uncertainty is much smaller than the range from the traditional UN high and low variants. Much of the increase is expected to happen in Africa, in part due to higher fertility and a recent slowdown in the pace of fertility decline. Also, the ratio of working age people to older people is likely to decline substantially in all countries, even those that currently have young populations.

The United Nations (UN) is the leading agency that projects world population into the future on a regular basis (1). Every two years it publishes revised data of the populations of all countries by age and sex, as well as fertility, mortality and migration rates, in a biennial publication called the World Population Prospects (WPP) (2). In July 2014, probabilistic projections for individual countries to 2100 were released. Unlike previous projections, they allow us to quantify our confidence in projected future trends using established methods of statistical inference. They are based on recent data, including the results of the 2010 round of censuses and recent surveys until 2012, as well as the most recent data on incidence, prevalence and treatment for the countries most affected by the HIV/AIDS epidemic (3), which had not been included previously.

- 1. W. Lutz, S. K C, "Dimensions of global population projections: What do we know about future population trends and structures?" http://storage.globalcitizen.net/data/topic/knowledge/uploads/20120209152732705.pdf , Philos. Trans. R. Soc. London Ser. B 365, 2779–2791 (2010). Medline doi:10.1098/rstb.2010.0133
- 2. United Nations, World Population Prospects: The 2012 Revision http://esa.un.org/wpp/ (Population Division, Dept. of Economic and Social Affairs, United Nations, New York, 2013).
- 3. UNAIDS, Global Report: UNAIDS Report on the Global AIDS Epidemic 2013 http://www.unaids.org/en/media/unaids/contentassets/documents/epidemiology/2013/gr2013/UNAIDS_Global_Report_2013_en.pdf (UNAIDS, Geneva, Switzerland, 2013).

In a methodological innovation aimed at overcoming this limitation, we derived new probabilistic projections based on probabilistic Bayesian hierarchical models for major components of demographic change, namely fertility (6–8) and life expectancy (9, 10). These models incorporated available data and take advantage of data from other countries when making projections for a given country. They also incorporated external information through Bayesian prior distributions, including an upper bound of 1.3 years per decade on the asymptotic rate of increase of life expectancy, based on historic data on life expectancy in leading countries (11) and on changes in the maximum age at death (12). They included the assumption that the total fertility rate for a country will ultimately fluctuate around a country-specific long-term average which is estimated from the data; these long-term averages are between 1.5 and 2 children per woman for most countries with high probability (7).

- 6. L. Alkema, A. E. Raftery, P. Gerland, S. J. Clark, F. Pelletier, T. Buettner, G. K. Heilig, "Probabilistic projections of the total fertility rate for all countries" http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3367999/. Demography 48, 815–839 (2011). Medline doi:10.1007/s13524-011-0040-5 - 7. A. E. Raftery, L. Alkema, P. Gerland, "Bayesian population projections for the United Nations" http://arxiv.org/pdf/1405.4708 . Stat. Sci. 29, 58–68 (2014). doi:10.1214/13-STS419
- 8. B. K. Fosdick, A. E. Raftery, "Regional probabilistic fertility forecasting by modeling between-country correlations" http://arxiv.org/pdf/1212.0462 . Demogr. Res. 30, 1011–1034 (2014). doi:10.4054/DemRes.2014.30.35
- 9. A. E. Raftery, J. L. Chunn, P. Gerland, H. Sevčíková, "Bayesian probabilistic projections of life expectancy for all countries" http://researchonline.jcu.edu.au/28347/1/RafteryChunnEtAl_LifeExp.pdf . Demography 50, 777–801 (2013). Medline doi:10.1007/s13524-012-0193-x
- 10. A. E. Raftery, N. Lalic, P. Gerland, N. Li, G. Heilig, "Joint probabilistic projection of female and male life expectancy" http://esa.un.org/unpd/ppp/pdf/Raftery-Lalic_2012_Joint%20Probabilistic%20Projection%20of%20Female%20and%20Male%20Life%20Expectancy.pdf . Demogr. Res. 30, 795–822 (2014). doi:10.4054/DemRes.2014.30.27
- 11. J. Oeppen, J. W. Vaupel, "Broken limits to life expectancy" http://jeffreydachmd.com/wp-content/uploads/2013/07/Life_expectancy_scienceMay2002.pdf . Science 296, 1029–1031 (2002). Medline doi:10.1126/science.1069675
- 12. J. R. Wilmoth, L. J. Deegan, H. Lundström, S. Horiuchi, "Increase of maximum life-span in Sweden, 1861–1999" http://hanson.gmu.edu/EC496/Sources/MAXLIFE.PDF . Science 289, 2366–2368 (2000). Medline doi:10.1126/science.289.5488.2366

Since 1950, fertility has declined rapidly in Asia and Latin America, and has also started to decline in Africa. Demographers had projected that fertility in African countries would decline at a rate similar to what has been observed in Asia and Latin America. However, while fertility has been declining in Africa over the past decade, it has been doing so at only about one-quarter of the rate at which it did in Asia and Latin America in the 1970s, when they were at a comparable stage of the fertility transition (16). Indeed, in some African countries, the decline seems to have stalled (18).
Bongaarts and Casterline (16) suggest two reasons for the slower fertility decline in Sub-Saharan Africa. First, they note that despite declines in fertility desires in Africa, the most recent levels of ideal family size are still high, with a median of 4.6 children per woman. This is in line with prevailing family norms (19), and the fact that total fertility before fertility started to decline was higher in Africa (6.5) than in the other regions (5.8) (20, 21). Second, the unmet need for contraception (the difference between the demand for contraception and its use) has remained substantial at about 25%, with no systematic decline over the past 20 years (22).
A stall in the decline in the past decade is apparent from the past and projected levels of TFR for Nigeria, the most populous country in Africa (Fig. 2A). The UN’s projection continues to project a decline, but the uncertainty bands are wide, indicating that the stall could continue for a considerable time. This continued high fertility for total population: would result in a projected increase of more than five-fold by 2100, from the current 160 to 914 million (Fig. 2B). There is considerable uncertainty about this, but there is still a 90% probability that Nigeria’s population in 2100 will exceed 532 million, a more than three-fold increase."

* http://www.overcomingbias.com/2009/09/this-is-the-dream-time.html
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