Malthusian catastrophe
Malthusian catastrophe, sometimes known as a Malthusian check, Malthusian crisis, Malthusian dilemma, Malthusian disaster, Malthusian trap, or Malthusian limit is a return to subsistence-level conditions as a result of agricultural (or, in later formulations, economic) production being eventually outstripped by growth in population. Theories of Malthusian catastrophe are very similar to the subsistence theory of wages. The main difference is that the Malthusian theories predict over several generations or centuries whereas the subsistence theory of wages predicts over years and decades.

# Traditional views
In 1798 Thomas Malthus published An Essay on the Principle of Population, describing his theory of quantitative development of human populations:
I think I may fairly make two postulata. First, That food is necessary to the existence of man. Secondly, That the passion between the sexes is necessary and will remain nearly in its present state. These two laws, ever since we have had any knowledge of mankind, appear to have been fixed laws of our nature, and, as we have not hitherto seen any alteration in them, we have no right to conclude that they will ever cease to be what they now are, without an immediate act of power in that Being who first arranged the system of the universe, and for the advantage of his creatures, still executes, according to fixed laws, all its various operations....Assuming then my postulata as granted, I say, that the power of population is indefinitely greater than the power in the earth to produce subsistence for man. Population, when unchecked, increases in a geometrical ratio.
A series that is increasing in geometric progression is defined by the fact that the ratio of any two successive members of the sequence is a constant. For example, a population with an average annual growth rate of, say, 2% will grow by a ratio of 1.02 per year. In other words, the ratio of each year's population to the previous year's population will be 1.02. In modern terminology, a population that is increasing in geometric progression is said to be experiencing exponential growth.
In contrast, Malthus assumed that the growth of agrarian economics is in arithmetic progression, meaning that any two successive members of the sequence have a constant difference. In modern terminology, this is called linear growth.
If unchecked over a sufficient period of time, and if the ratio between successive sequence members is larger than 1.0, then exponential growth will always outrun linear growth. From this fact Malthus concluded that the growth of human populations will be naturally checked by misery, vice or the like in its natural development. Every phase of unchecked exponential growth (as might occur when inhabiting new habitats or colonies, e.g. the American continent at Malthus' time, or when recovering from wars and epidemic plagues) will be followed by a catastrophe or misery, and thus unlimited growth may even directly cause misery and vice (Malthus 1798, chapter 7: A Probable Cause of Epidemics).

# Neo-Malthusian theory
Neo-Malthusian theory argues that unless at or below subsistence level, 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
will eventually come to resemble
regardless of how large the constant a is or how small the constant 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 neo-Malthusian 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 fertility genes (except much faster because of greater diversity). According to neo-Malthusians, this increase in fertility will lead to hyperexponential population growth that will eventually outstrip growth in economic production. This appears to make any sort of voluntary fertility control futile, in the long run. Neo-Malthusians argue 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. Neo-Malthusians argue that hyperexponential population growth has begun or will begin soon in developed countries.
To this can be added that, unknown to Malthus, farmland deteriorates with use. Some areas where there was intensive agriculture in classic times (i.e., the feudal era) had already declined in population because their farmland was worn out, long before he wrote.
At the time Malthus wrote, and for 150 years thereafter, most societies had populations at or beyond their agricultural limits. After World War I, the growth rate of the world's population accelerated rapidly, resulting in predictions by Paul R. Ehrlich and many others of an imminent Malthusian catastrophe. However, the so-called Green Revolution produced a contemporaneous exponential increase in the world's food supply, and the date of the predicted Malthusian collapse had been temporarily forestalled, until the peaking of agricultural production began to occur in the 1990s in several world regions.
Pimentel and Nielsen, working independently, found that the human population has passed the numerical point where all can live in comfort, and that we have entered a stage where many of the world's citizens and future generations are trapped in misery. There is evidence that a catastrophe is underway as of at least the 1990s; for example, by the year 2000, children in developing countries were dying at the rate of approximately 11,000,000 per annum from strictly preventable diseases. This data suggests that by the standard of misery, the catastrophe is underway. The term 'misery' can generally be construed as: high infant mortality, low standards of sanitation, malnutrition, inadequate drinking water, new and widespread diseases (e.g. HIV), war, political unrest.
Regarding famines, data demonstrates the world's food production has peaked in some of the very regions where food is needed the most. For example in South Asia, approximately half of the land has been degraded such that it no longer has the capacity for food production. In China there has been a 27% irreversible loss of land for agriculture, and continues to lose arable land at the rate of 2,500 square kilometres per year. In Madagascar, at least 30% of the land previously regarded as arable is irreversibly barren. On the other hand, recent data shows the number of overweight people in the world now outnumbers the number of malnourished, and the rising tide of obesity continues to expand in both rich and poor countries.
Many technologically developed countries have by 2006 passed through the demographic transition, a complex social development in which total fertility rates drop in response to lower infant mortality, more education of women, increased urbanization, and a wider availability of effective birth control causing the demographic-economic paradox. By the end of the 21st century, these countries could avoid population declines by permitting large-scale immigration. On the assumption that the demographic transition is now spreading to less developed countries, the United Nations Population Fund estimates that human population may peak in the late 21st century rather than continue to grow until it exhausted available resources. Some have expressed doubt about the validity of the UN projections, claiming that they are below the projections by others. The most important point is that none of the projections show the population growth beginning to decline before 2050. Indeed, the UN "high" estimate does not decline at all, even out to 2300, indicating the potential for a Malthusian catastrophe.
The actual growth curve of the human population is another issue. In the latter part of the 20th century many argued that it followed exponential growth; however, a more recent view is that the growth in the last millennium has been faster, at a rate termed hyperbolic or hyperexponential. Alternatively, the apparently exponential portion of the human population growth curve may actually fit the lower limb of a logistic curve, or a section of a Lotka-Volterra cycle.
Historians have estimated the total human population on earth back to 10,000 BCE. The figure on the right shows the trend of total population from the year 500 CE to 2005, and from there in three projections out to 2150 (low, medium, and high). If population growth were exactly exponential, then the trend would be a straight line on this semilog graph. The fact that it has been curving upwards indicates faster-than-exponential growth over the last 1500 years of history. However, the United Nations population projections out to 2150 (the red, orange, and green lines) show a possible end to this phenomenon occurring as early as 2050 in the most optimistic scenario, and by 2075 in the "medium" scenario.
The graph of annual growth rates (below) also does not appear exactly as one would expect for long-term exponential growth. For exponential growth it should be a straight line at constant height, whereas in fact the graph from 1800 to 2005 is dominated by an enormous hump that began about 1920, peaked in the mid-1960s, and has been steadily eroding away for the last 40 years. The sharp fluctuation between 1959 and 1960 was due to the combined effects of the Great Leap Forward and a natural disaster in China. Also visible on this graph are the effects of the Great Depression, the two world wars, and possibly also the 1918 influenza pandemic.
Though short-term trends, even on the scale of decades or centuries, cannot prove or disprove the existence of mechanisms promoting a Malthusian catastrophe over longer periods, the prosperity of a small fraction of the human population at the beginning of the 21st century, and the debatability of ecological collapse made by Paul R. Ehrlich in the 1960s and 1970s, has led some people, such as economist Julian L. Simon, to question its inevitability.
A 2004 study by a group of prominent economists and ecologists, including Kenneth Arrow and Paul Ehrlich suggests that the central concerns regarding sustainability have shifted from population growth to the consumption/savings ratio, due to shifts in population growth rates since the 1970s. Empirical estimates show that public policy (taxes or the establishment of more complete property rights) can promote more efficient consumption and investment that are sustainable in an ecological sense; that is, given the current (relatively low) population growth rate, the Malthusian catastrophe can be avoided by either a shift in consumer preferences or public policy that induces a similar shift.
However, some contend that the Malthusian catastrophe is not imminent. A 2002 study by the UN Food and Agriculture Organization predicts that world food production will be in excess of the needs of the human population by the year 2030, even though that source states that hundreds of millions will remain hungry (presumably due to economic realities and distribution issues).

# Application to energy/resource consumption
Another way of applying the Malthusian theory is to substitute other resources, such as sources of energy for food, and energy consumption for population. (Since modern food production is energy and resource intensive, this is not a big jump. Most of the criteria for applying the theory are still satisfied.) Since energy consumption is increasing much faster than population and most energy comes from polluting and non-renewable sources, the catastrophe appears more imminent, though perhaps not as certain, than when considering food and population continue to behave in a manner contradicting Malthus's assumptions.
Retired physics professor Albert Bartlett, a modern-day Malthusian, has lectured on "Arithmetic, Population and Energy" over 1,500 times. He published an article entitled Thoughts on Long-Term Energy Supplies: Scientists and the Silent Lie in Physics Today (July 2004). For a response to Bartlett's argument, see two articles on energy and population in Physics Today, November 2004, and following letters to the editor.
A further way of analyzing resource limitation is the dwindling area for storage of soil contaminants and water pollution. The high rate of increase in toxic chemicals in the environment (especially persistent organic chemicals and endocrine altering chemicals) is creating a circumstance of resource limitation (e.g. safe potable water and safe arable land).