Soil fertility depletion is not a credible mechanism for population boom/bust cycles in agricultural societies

Soil fertility depletion presents a negative feedback mechanism that could have impacted early adopters of agriculture. We consider whether such feedback can lead to population cycles among early agriculturalists, such as the boom-and-bust patterns suggested by an increasing amount of evidence for Neolithic Europe. Using general mathematical arguments, we show that this is unlikely, due to the interplay of two factors. First, there is an important mathematical difference between biotic (i.e., logistic) and abiotic resource replenishment; soil nutrients are better modeled by the abiotic case, which leads to more stable dynamics. Second, under realistic conditions, the resource replenishment process operates on fast time scales compared to attainable population growth rates, reinforcing the tendency towards stable dynamics. Both these factors are relevant for early agricultural societies and imply that nutrient depletion is likely not the main contributing factor to boom-and-bust cycles observed in the archaeological record.