Was the fall of the Roman Empire or, as often predicted, the coming fall of the American Empire, numerically predictable?

It is, according to research led by Sergey Gavrilets, associate director for scientific activities at the National Institute for Mathematical and Biological Synthesis and a professor at the University of Tennessee-Knoxville published in Cliodynamics: The Journal of Theoretical and Mathematical History.

Yes, that's a journal dedicated to theoretical history and mathematics, though obviously on a science site we will note they are using theoretical colloquially and mean hypothetical or even speculative.   Bet you are not laughing at our proposals for degrees in Quantum Paleontology and Theoretical Phys Ed now, are you?

The numerical model in the paper focuses on size and complexity of emerging "polities" or states as well as their longevity and settlement patterns as a result of warfare.   A number of factors were measured but in their model the largest effect on the results was due to just two factors – the scaling of a state's power to the probability of winning a conflict and a leader's average time in power.

According to the simulation, the stability of large, complex polities is strongly promoted if the outcomes of conflicts are mostly determined by the polities' wealth or power, if there exist well-defined and accepted means of succession, and if control mechanisms within polities are internally specialized. The results also showed that polities experience what the authors call "chiefly cycles" or rapid cycles of growth and collapse due to warfare.

A hexagonal array of initially autonomous local communities or villages, which is part of a polity. Polities grow, decrease in size, or disappear as a result of conquest with the winner absorbing all of part of the loser. Credit: Gavrilets S, Anderson D, Turchin P.

The wealthiest of polities does not necessarily win a conflict, there are many other factors besides wealth that can affect the outcome of a conflict, the authors write. The model also suggests that the rapid collapse of a polity can also occur without environmental disturbances, such as drought or overpopulation.

By using a mathematical model, the researchers claim they were able to capture the dynamical processes that cause chiefdoms, states and empires to emerge, persist and collapse at the scale of decades to centuries. 

"In the last several decades, mathematical models have been traditionally important in the physical, life and economic sciences, but now they are also becoming important for explaining historical data," said Gavrilets. "Our model provides theoretical support for the view that cultural, demographic and ecological conditions can predict the emergence and dynamics of complex societies."