If human populations were characterized by Malthusian dynamics, would we expect those local populations that have an abundance of food to be characterized by a high rate of population growth, and those locales in which people are starving to exhibit a low rate of population growth?
Over the past century, Western family sizes have declined from five to seven children (my enate grandparents had seven children, and my agnate grandfather had fourteen children, by two wives) to about two children today, and this without mandatory population control. Rostam, I've read what you've said: that one of the key drivers for large family sizes has been the concern for care and support in one's old age. Another factor about which I've read is that of the availability of birth control technology to women. A third factor that comes to mind might be women's lib, and the rise of the single-parent household.
The current population growth projection calls for world population to peak at 9 billion in 2070, and then to slowly decline. Given the extensions in the youthspan that are currently in the pipeline, that projection is probably pretty fragile, but that's the eidolon in the crystal ball right now.
Fifty years ago, we worried intensely about Malthusian pressures bringing the Four Horsemen of the Apocalypse down upon us. The world was going to run out of oil in the 1970's, and it was only a matter of time before World War III took place over the desperate conditions created by the global population explosion. (World population in 1950 was 2 billion.) There was no point in trying to feed people in third-world countries because they would simply breed that much faster. And space flight offered no hope. It would cost more to launch someone into space than it would to feed and clothe them for a lifetime. We were doomed.
Guess what? It turned out that raising the standards of living and of education led to reductions in birth rates. China, the largest country of them all, worked to reduce its birth rate. The world didn't run out of oil in the 1970's.
Another bugbear of the early 50's was differential breeding... the fact that the less intelligent were out-breeding the more intelligent. Not only would we face overpopulation... the population itself would be less intelligent than its grandparents' generation. Dunn and Dobzhansky (Genetics and the Origin of Species (1937, 3d ed. 1951)) helped lay that ghost to rest by observing that intelligence would change exceedingly slowly in a population. (This was recently reinforced by a study estimating the decline in IQ caused by differential birthrates over the period 1800 - 2000 to be less than 5 points of IQ.)
So what happened? Along came the Flynn Effect, boosting overall IQs by 3 points per decade over at least the last century. Hard on its heels is coming (I think) the ability to boost IQ chemically and/or genetically. (The most effective memory drugs right now are probably Reminyl and Memantine, although consumption of the omega-3 fatty acids--eicosapentaenoic and docosahexaenoic acids--may also be marginally helpful.) (I get my omega-3 acids by eating about 90 calories worth of canned salmon a day.)
It's my understanding that animal populations fluctuate in accordance with the Law of Malthus. However, it's my understanding that humans, given the ability to freely and effortlessly choose whether or not to reproduce, aren't necessarily subject to Malthusian rules.