January 19, 2011
Co-authors are David G.
Anderson, professor of anthropology at the University of
Tennessee-Knoxville and Peter Turchin, professor of ecology and
evolutionary biology and mathematics at the University of
The National Institute for Mathematical and Biological Synthesis (NIMBioS)
brings together researchers from around the world to collaborate
across disciplinary boundaries to investigate solutions to basic and
applied problems in the life sciences.
NIMBioS is sponsored by the
National Science Foundation, the U.S. Department of Homeland
Security, and the U.S. Department of Agriculture with additional
support from The University of Tennessee, Knoxville.
The instability of large, complex societies is a predictable
phenomenon, according to a new mathematical model that explores the
emergence of early human societies via warfare.
Capturing hundreds of years of human
history, the model reveals the dynamical nature of societies, which
can be difficult to uncover in archaeological data.
The research, led 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, is published in the first issue of the new
Cliodynamics: The Journal of Theoretical and
Mathematical History, the first academic journal
dedicated to research from the emerging science of theoretical
history and mathematics.
The numerical model focuses on both 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
unexpectedly, 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 model, 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.
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 occur even without environmental disturbances, such as drought
By using a mathematical model, the researchers 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
“Our model provides theoretical
support for the view that cultural, demographic and ecological
conditions can predict the emergence and dynamics of complex
Gavrilets S, Anderson D, Turchin
P. 2010. Cycling in the complexity of early societies.
Cliodynamics: The Journal of Theoretical and Mathematical
1. Karl Kaiser January 19, 2011
It is a bit of a dogmatic stretch to
say that this model “explains” how societies evolve. When does a
model go from simply modeling or mimicking reality to
“explaining” it to actually revealing exactly all of it’s hidden
Scientists (and thinking people in
general) have a dogmatic and neurotic tendency to prematurely
declare that they have “explained” reality just because their
models coincide with what we are able to observe of it.