That being said it also seems that there is an immediate correlation between suddenly higher income and a individual family unit also increasing (i.e. when a family gets a sudden, large increase in income they will generally also increase their family size at that time).
So, with all of that being said, since in the words of the Gates this is a "bet", we could also potentially bet that by increasing the number of middle class individuals within a given population we will also see an overall increase in birthrate among those populations.
[1]: http://en.wikipedia.org/wiki/Demographic-economic_paradox
I remain a perpetual technological optimist, we'll solve this problem as well.
Btw, it's very hard not to read your comment like "wouldn't it be better for everyone if all these poor people just died off...?"
The correlation doesn't seem to hold at the high end, and much of the data in the western world confounds population growth due to fertility (still low) with population growth due to immigration (which has upticked across the board in recent years). As far as I know, though, the effect is still strong in the delta range that the Gates foundation is targeting.
Furthermore, depletion of resources is not a simple numbers game: a rich person produces several orders more CO2 than a poor person to name just one example. If Africa becomes wealthy enough to come anywhere close to Americans for meat consumption there is going to be a huge issue.
Population control of some kind is so much easier now than if we wait 20 years and Chinese-like draconian measures become necessary.
1. http://www.newscientist.com/article/mg22329882.800-global-po...
"These new predictions are drawing criticism. "Raftery's projections are too high for Africa, because they don't include the fact that female education is the key driver of fertility decline," says Wolfgang Lutz of the International Institute for Applied Systems Analysis in Laxenburg, Austria."
This is great, obviously, but overpopulation is a huge problem and regrettably that problem will now get worse. The predictions for the maximum population expected at mid-century have recently been adjusted upwards. Resources will be depleted ever more quickly if poor people get as rich as Bill predicts.
I have no answer. Surely we cannot withhold medecine from poor people to prevent overpopulation. But two decades from now overpopulation will be the major worry on everybody's mind if this trend continues.
Edit: The assumption of negative growth once countries hit a certain level of development/stability/richness has recently stopped being true [1], I probably should have mentioned that in my first comment
1. http://en.wikipedia.org/wiki/Projections_of_population_growt...