heres some Quotes
"Collapse: How Societies Choose to Fail or Succeed" suggests five major reasons for the collapse of 41 studied cultures: environmental damage, such as deforestation and soil erosion; climate change; dependence upon long-distance trade for needed resources; increasing levels of internal and external violence, such as war or invasion; and societal responses to internal and environmental problems.
Arnold J. Toynbee in his "A Study of History" suggested that there had been a much larger number of civilizations, including a small number of arrested civilizations, and that all civilizations tended to go through the cycle identified by Mommsen. The cause of the fall of a civilization occurred when a cultural elite became a parasitic elite, leading to the rise of internal and external proletariats.
Peter Turchin in his Historical Dynamics and Andrey Korotayev et al. in their Introduction to Social Macrodynamics, Secular Cycles, and Millennial Trends suggest a number of mathematical models describing collapse of agrarian civilizations. For example, the basic logic of Turchin's "fiscal-demographic" model can be outlined as follows: during the initial phase of a sociodemographic cycle we observe relatively high levels of per capita production and consumption, which leads not only to relatively high population growth rates, but also to relatively high rates of surplus production. As a result, during this phase the population can afford to pay taxes without great problems, the taxes are quite easily collectible, and the population growth is accompanied by the growth of state revenues. During the intermediate phase, the increasing overpopulation leads to the decrease of per capita production and consumption levels, it becomes more and more difficult to collect taxes, and state revenues stop growing, whereas the state expenditures grow due to the growth of the population controlled by the state. As a result, during this phase the state starts experiencing considerable fiscal problems. During the final pre-collapse phases the overpopulation leads to further decrease of per capita production, the surplus production further decreases, state revenues shrink, but the state needs more and more resources to control the growing (though with lower and lower rates) population. Eventually this leads to famines, epidemics, state breakdown, and demographic and civilization collapse (Peter Turchin. Historical Dynamics. Princeton University Press, 2003:121–127).
(OVER POPULATION)
http://en.wikipedia.org/wiki/Civilization#The_fall_of_civilizations