Exchange is widespread in biological systems, where (for example) trees trade nutrients via mycorrhizal networks, and bacterial communities swap metabolites via crossfeeding. Exchange is also central in social systems, for example as a means to mitigate variable and uncertain environments in ancestral and modern societies. While food exchange as a general strategy is well-established, quantifying the precise structure of exchange–who gives to whom, how much, and why–continues to occupy the attention of anthropologists, economic historians, and human behavioral ecologists. However, it does seem clear that there are consistent patterns in the ways that humans have exchanged food, and this consistency raises the question of whether specific networks of food exchange exhibit features that allow them to persist in the longer term. We address this question using a new approach based on the analysis of population stability—i.e. we ask whether some networks lead to population dynamics that are more likely to be stable. To develop this analysis, we draw from and adapt recent work on stability criteria in ecological consumer-resource systems.
Results/Conclusions
We develop a range of models based on the consumption and depletion of a natural resource by multiple groups in different locations, drawing from existing consumer-resource models in ecology, and with clear parallels to models of commodity exchange in economic systems. We first draw from both climate reconstruction and modern agricultural data to establish what might be considered plausible variability in the food production possible on a given landscape. We then show the result that essentially any network of exchange can buffer this kind of environmental variability. Importantly, this spreading of risk doesn't just reduce the variation in the total population size, but guarantees reduced population variation at each individual site. On the other hand, we can't expect exchange to buffer variability in cases of system-wide reductions in productivity, for example during an extended drought. During this kind of event we'd likely expect all population sizes to be reduced. However, our analysis of population stability demonstrates that system-wide scarcity can also lead to instability, and potentially complete depopulation at one or more locations. We prove that only a handful of networks, which we term stabilizing modes of exchange, guarantee stable population sizes in our models. This result suggests that population stability may be an important filter for any given system of food exchange to persist.