Commentary on my article in Structure and Dynamics

Most preindustrial states experienced recurrent waves of political collapse and internal warfare. One possible explanation of this pattern, the demographic-structural theory, suggests that population growth leads to state instability and breakdown, which in turn causes population decline. Mathematical models incorporating this mechanism predict sustained oscillations in demographic and political dynamics. Here I test these theoretical predictions with time-series data on population dynamics and sociopolitical instability in early modern England, the Han and Tang China, and the Roman Empire. Results suggest that population and instability are dynamically interrelated as predicted by the theory.

I wish to thank Natalia Komarova for bringing up a very important issue in modeling dynamical phenomena—what mathematical framework to use. Komarova argues that a delayed logistic model provides a better framework for modeling historical dynamics than the ordinary differential equations used in my paper. Before addressing the main point of Komarova’s critique, however, I need to clarify one other aspect of my paper—the role of internal warfare in the theory of secular cycles. Komarova wonders how “warfare ... can become an independent entity, take a life of its own and exert prey-like pressure” on population. First, I want to stress that my model of interaction between population dynamics and socio-political instability in no way is based on an analogy between secular cycles and predator-prey cycles. These are phenomena from completely different disciplines, and I find any cross-parallels between them completely unhelpful, and even potentially misleading (which is probably the source of my critic’s puzzlement) . True, mathematical models are somewhat similar, but that’s the power of mathematics—that formally the same equations can be applied to completely different fields of science by interpreting the variables in appropriate ways. A model for a planet hurtling around the Sun is another example of the same mathematical approach applied to substantively very different phenomena.