Peak global population may not be as unsupportable as we thought

There was an interesting article is the today's paper about immigration, and how Canada is poised to deal better with peak population and declining birth-rates because of its relatively open policy on immigration. What particularly struck me, though, were some of the statistics on global population and fertility.
The UN sees the world's population continuing to increase until about the end of his century, increasing from about 7 billion today to about 11 billion in 2100, after which it is expected to start falling, although very gradually. That is the model I am familiar with. However, there are a growing number of other comparing models that predict a much earlier and lower peak in global numbers: the International Institute for Applied System Analysis (IIASA) sees the world's population peaking at just over 9 billion some time around the middle of this century, and a Deutsche Bank reports has it peaking at less than 9 billion, also mid-century.
It's all to do with fertility rates and the replacement rate. Many richer countries that do not have much immigration (e.g. Japan, Kofea, Spain, Italy, and much of Eastern Europe) are already shrinking. But, more importantly, fertility rates are plummeting in some of the largest developing countries. China's fertility rate (i.e. the number of live births per woman) is actually very similar to that of Canada, USA and UK, all of which are well below the 2.1 rate of replacement. But, unlike those countries, China does not supplement its population with immigrants, so within a few years it will start losing population. The same is true of Brazil, and even India's population is only just above the replacement rate and falling, so soon it too will start to lose population.
The decrease in global fertility statistics is partly because of increasing urbanization (families in cities do not need children to help work the land; in fact, children in the city are a liability and a drain on resources). But also, as women move to cities, they acquire education and start to exercise more autonomy and to take control of their bodies, often leading to fewer children. Africa is the main exception to this trend, and it remains largely poor and rural, although even there there is some hope, as women start to demand more autonomy in countries like Kenya and Rwanda, and even countries like Nigeria has reduced it fertility rate from seven to about five in just a few decades.
So, it seems that there is a good chance that the global population may not actually be much more than it is currently, which is still going to put a lot of strain on the environment, especially if global warming continues to stress it as expected. But it may not be completely unsupportable in a Malthusian sense.