THE YEAR IN ECOLOGY AND CONSERVATION BIOLOGY, 2009 Long-Term Population Cycles in Human Societies Peter Turchin Department of Ecology and Evolutionary Biology, University of Connecticut, Storrs, Connecticut, USA Human population dynamics are usually conceptualized as either boundless growth or growth to an equilibrium. The implicit assumption underlying these paradigms is that any feedback processes regulating population density, if they exist, operate on a fast-time-scale, and therefore we do not expect to observe population oscillations in human population numbers. This review asks, are population processes in historical and prehistorical human populations characterized by second-order feedback loops, that is, regulation involving lags? If yes, then the implications for forecasting future population change are obvious—what may appear as inexplicable, exogenously driven reverses in population trends may actually be a result of feedbacks operating with substantial time lags. This survey of a variety of historical and archeological data indicates that slow oscillations in population numbers, with periods of roughly two to three centuries, are observed in a number of world regions and historical periods. Next, a potential explanation for this pattern, the demographic-structural theory, is discussed. Finally, the implications of these results for global population forecasts is discussed. Key words: human; population; cycles; history; dynamics; global Introduction would be as pronounced in Western Europe, except for a masking effect of immigration), the Long-term human population dynamics are discussion in the popular press shifted to the op- often portrayed as an almost inexorable expo- posite tack. Now predictions are equally dire, nential growth. During the 1960s, it even ap- but instead of fearing population explosion, we peared that global population was growing at are supposed to worry about how to support a faster-than-exponential rate, leading to pre- increasing numbers of retirees on a shrinking dictions of “Doomsday” that was to occur on base of the working population. Some of the Friday, November 13, 2026 (Von Foerster et al. current numerical predictions are as extreme 1960, Berryman and Valenti 1994). During the as previous doomsday warnings. For example, 1990s, when a noticeable decline in global pop- the popular press in Russia routinely publishes ulation growth rate took place (due largely to predictions that the population of that country precipitous drops in birth rates of populous will be halved by 2050. developing countries, primarily China and In- Although many media reports have a sensa- dia), it became clear that erstwhile predictions tionalist, and even hysterical quality, the main of doom (Ehrlich 1968) were unsustainable. question as to what will happen to popula- In fact, with most European countries experi- tions of different countries, as well as the to- encing population declines (which is especially tal population of the Earth, is very impor- noticeable in Eastern European countries, but tant. The numbers and structure of human populations have an enormous impact on the well-being of individuals, societies, and the Address for correspondence: Peter Turchin, Department of Ecology and Evolutionary Biology, University of Connecticut, Storrs, CT 06269. biosphere. Yet, I would argue, the majority [email protected] of forecasts are based on models of human The Year in Ecology and Conservation Biology, 2009: Ann. N.Y. Acad. Sci. 1162: 1–17 (2009). doi: 10.1111/j.1749-6632.2009.04447.x c 2009 New York Academy of Sciences. 1 2 Annals of the New York Academy of Sciences population dynamics that are fundamentally to begin increasing, there is no immediate ef- flawed. The simplest forecasting devices are fect on the prey’s population growth rate. This deterministic extrapolations of current trends. happens because it takes time for the predator These approaches may employ the exponential numbers to increase to the level where they be- model, or even faster-than-exponential growth, gin affecting prey numbers. Furthermore, once as in the Doomsday model. A somewhat more there are many predators, and the prey popu- sophisticated approach is to allow for change lation has started collapsing, the predators con- in demographic rates (birth, death, migration), tinue to drive prey numbers down. Even though but still to assume that these processes are therearefewprey,andmostpredatorsare driven by exogenous influences (which can be starving, it takes time for predators to die out. modeled either stochastically, or by assuming As a result, second-order population feedbacks a deterministic trend). Note that these stan- act with a substantial lag and tend to induce dard approaches to forecasting human popula- oscillations. tion are essentially zero-order models, because As I have argued in Complex Population Dy- they do not take into account potential feed- namics (Turchin 2003a), such second-order pro- backs from population density to demographic cesses as interactions between predators and rates. Zero-order dynamics are nonequilibrial; prey, hosts and parasitoids or parasites, and depending on parameters, the population num- plants and herbivores (generally known as bers either increase to infinity or decline to trophic interactions) are very important drivers zero (Turchin 2003a, p. 37). Including den- of population fluctuations. The great majority sity dependence in population-growth models of population cycles in nature are driven by (the canonical model in population ecology is trophic mechanisms (Turchin 2003a, p. 384). the logistic) leads to first-order dynamical pro- In contrast, human demographers, as far as I cesses, characterized by a convergence to an know, do not consider second-order processes equilibrium (often called the carrying capacity). when modeling and forecasting human popula- Demographers of the human population be- tion dynamics. There has been some discussion gan seriously entertaining density-dependent of demographic cycles, for example, oscillations models much later than population ecolo- in the population age structure with the period gists working with nonhuman animals (Lee roughly equal to one human generation (ca. 1987). 25 years). Another kind of cycle is character- First-order feedbacks act on a fast-time-scale. ized by an alternation of high fecundity–low For example, in a territorial mammal, as soon fecundity generations, with an overall period of as population has increased to the point where roughly 50 years (Easterlin 1980; Wachter and all available territories are occupied, any sur- Lee 1989). In population ecology, such oscil- plus animals become nonterritorial “floaters” lations are often called generation cycles and with poor survival rates and zero reproductive first-order cycles, respectively (Turchin 2003a, prospects. Thus, as soon as population num- 25). As we shall see in the following sections, bers reach the carrying capacity determined second-order cycles should be characterized by by the total number of territories, population much longer periods. growth rate is reduced to zero without any This review asks, are population processes in time lag. Some regulatory processes, however, historical and prehistorical human populations act on a slow-time-scale (these are second- characterized by second-order feedback loops? order feedbacks). The paradigmatic example If yes, then the implications for forecasting of a second-order dynamical process in animal future population change are obvious—what ecology is the interaction between predators may appear as inexplicable, exogenously driven and prey. When a population of prey reaches a reverses in population trends may actually be high enough density for a predator population a result of feedbacks operating with substantial Turchin: Long-Term Population Cycles in Human Societies 3 its mean (average age of female at birth) is around 25–30 years (Wrigley et al. 1997). There is a large amount of variation in these mea- sures of generation length for humans, depend- ing on biological (nutrition, mortality sched- ules) and social (marriage age) characteristics of the population. It is clear, though, that for most historical human populations, generation time should lie in the interval between 20 and 30 years. This is, therefore, the time step at which, ideally,population trajectories should be measured. Figure 1. Global population numbers over the last four millennia (McEvedy and Jones 1978). Another, and longer, timescale is the ex- pected period of second-order cycles, if such exist. Population theory based on discrete mod- time lags. Furthermore, once we have under- els suggests that second-order cycles are char- stood the specific mechanisms driving second- acterized by periods ranging from 6 to 12–15 order dynamics, we may learn to anticipate generations (there is, actually, no upper limit such changes in demographic regimes. on the period, but longer periods become pro- gressively rarer in the parameter space). Us- ing the extreme values of 20 and 30 years for A Survey of Population Trajectories human generation time suggests that second- in Historical Agrarian Societies order cycles in humans should have periods ranging from 120 to 450 years, with the most Even a casual look at population history of likely region being 200–300 years. Another way humans over the last several millenia suggests to evaluate the magnitude of period for pos- that global population growth was not quite as sible second-order cycles, this time using the