Soil fertility depletion is not a credible mechanism for population boom/bust cycles in agricultural societies
Daniel Kondor, Peter Turchin
Soil fertility depletion presents a negative feedback mechanism that could have impacted early adoptersof agriculture. In this paper, we present a formal mathematical analysis of the question whether such feedback can lead to population cycles in the context of early agriculturalists, such as the boom and bustpatterns suggested by an increasing amount of evidence for Neolithic Europe. We do this by considering candidates of second-order analytic models that capture dynamical interaction among farmers and soil fertility. Using general mathematical arguments, we show that under plausible conditions, the feedback between population growth and soil resource depletion is unlikely to lead to population cycles. This result is the consequence of two factors. First, there is an important mathematical difference between biotic (i.e. logistic) and abiotic resource replenishment; soil nutrients are better modelled by the abiotic case which leads to more stable dynamics. Second, under realistic conditions, the resource replenishment process has fast time-scales compared to attainable population growth rates, reinforcing the tendency of stable dynamics. Both of these factors play a role when considering early agricultural societies, and imply that nutrient depletion is not a credible mechanism for patterns of boom and bust cycles observed in the archaeological record.