World population in 2050 : new revision but what about accuracy?

United Nations has released this month the 2012 revision of their demographic forecast :
the world population of 7.2 billion in mid-2013 is projected to increase by almost one billion people within the next twelve years, reaching 8.1 billion in 2025, and to further increase to 9.6 billion in 2050 and 10.9 billion by 2100. These results are based on the medium-variant projection.

Source : United Nations, Department of Economic and Social Affairs, Population Division (2013). World Population Prospects: The 2012 Revision, Key Findings and Advance Tables.

The "constant fertility" scenario assumes the current fertility rate in the different countries remains unchanged in the future. This rate is the most critical parameter in the U.N. projections, whereas there are many others important parameters.

This global trend is putting even further pressure on natural ressources, as described in our previous articles about the Global Ecological Crisis (MAP1MAP2).

But we would like here to challenge these U.N. projections. The authors speak about Medium (Median (50%) prediction interval), High (Higher 95% prediction interval) and Low (Lower 95% prediction interval) fertility scenarii but do not propose, define or estimate accuracy for each of them. We have first think to compare current data with past projections. We can observe in the figure that the different scenarii produce significant separate results 20 to 30 years in the future. What about comparing currently measured population sizes with U.N. projections made in the 70's ?

Well, this job has already been done, with much greater details I would have hope. In 2000, the Panel on Population Projections published "Beyond Six Billion: Forecasting the World's Population", a detailed scientific study to examine official population projections: to assess their assumptions, estimate their accuracy and uncertainty (past U.N. projections did not precise the prediction interval), and evaluate the implications of current demographic research for projection procedures. This study is freely available.
The results are in short: 

Using the ex post approach and an appropriate statistical model developed after analysis of errors in international forecasts, we estimated prediction intervals for the current U.N. forecast. These intervals are constructed on the assumption that errors in current projections resemble those in past projections made after 1970. Our results suggest that the uncertainty in country projections is quite variable and is dramatically greater than suggested by U.N. high-low scenarios, with a typical 95-percent range more than twice as wide as the U.N. high-low intervals.
Regional 95-percent intervals are similarly variable but generally much narrower than country intervals. For developing regions, however, they are still consistently wider than U.N. high-low intervals. Across regions, the median 95-percent interval in 50-year projections was 40 per-cent wider than the U.N.’s high-low interval. However, prediction intervals are proportionally narrower for industrial regions and for the world as a whole. In these cases, our estimated prediction intervals are narrower than the intervals defined by the U.N. high-low scenarios. The world prediction interval also suggests a greater possibility of a downside than an upside error, making sustained population decline appear quite unlikely during the next 50 years.