In 1761 Robert Wallace published “Various Prospects of Mankind”. In the tract he argued that progress would eventually undo itself by overstocking the world with people. Thirty-seven years later, Thomas Malthus published his now famous Essay on the Principle of Population. In it, he predicted that population growth would eventually outrun food supply. This prediction was based on the idea that population, if unchecked, increases at an geometric rate, whereas the food supply could only grow at an arithmetic rate. Mathematically, any increasing geometric sequence (e.g. 1, 3, 9, 27, 81) will eventually overtake all arithmetic sequences (e.g. 10, 20, 30, 40, 50). The resulting decrease in food per person will eventually lead to subsistence level conditions. According to Malthus, the Catastrophe can only be prevented by self-restraint or vice – which for him included contraception, abortion and homosexuality.
Malthus did not give a time frame for his catastrophe. Thus far, population growth has been essentially geometric as Malthus predicted. The Malthusian catastrophe, however, has not occurred, principally because food supply growth has also been roughly geometric, not arithmetic. Furthermore, the widespread use of contraception and abortion (Malthusian vices) have, as Malthus said they could, restrained population growth significantly. In fact currently food supply per person is several times higher than when Malthus wrote his essay.
Neomalthusian theory argues that unless at or below subsistence, a population's fertility will tend to move upwards. Assume for example that a country has 10 breeding groups. Over time this country's fertility will approach that of its fastest growing group in the same way that f(x) = a*1.01^t + b*1.02^t will eventually come to resemble the g(x) = b*1.02 regardless of how small a is or how large b is . Under subsistence conditions the fastest growing group is likely to be that group progressing most rapidly in agricultural technology. However in above subsistence conditions the fastest growing group is likely to be the one with the highest fertility. Therefore the fertility of the country will approach that of its most fertile group. This however is only part of the problem.
In any group some individuals will be more pro-fertility in their beliefs and practices than others. According to neomalthusian theory, these pro-fertility individuals will not only have more children, but also pass their pro-fertility on to their children, meaning a constant selection for pro-fertility similar to the constant evolutionary selection for beneficial genes (except much faster because of greater diversity). According to neomalthusians, this increase in fertility will lead to hyperexponential population growth that will eventually outstrip growth in economic production. Neomalthusians point out that although adult immigrants (who, at the very least, arrive with human capital) contribute to economic production, there is little or no increase in economic production from increased natural growth and fertility. Neomalthusians argue that hyperexponential population growth has begun or will begin soon in developed countries.