Response to Oscillations in Population Sizes – From Ecology to History

Peter Turchin
Structure and Dynamics January 5, 2005 Journal Link PDF


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.
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