Abstract
It is well known from Hardin's "Tragedy of the Commons" [Hardin G (1968) Science 162:1243-1248] that, if open access is allowed, overgrazing typically results. Hardin, and most authors of the subsequent literature, adopted a static view of the underlying ecosystem. Here we extend this tragedy of the commons to consider the dynamics of the involved ecosystem as well. We consider a general model that allows for a variable carrying capacity of the pastures (due to variation in precipitation) and a stimulating effect on plant growth due to grazing. Our analysis further emphasizes the tragedy; in addition to overgrazing, the ecosystem may approach limit cycles. Thus, unless the pastoralists are able to coordinate themselves, the human capability of long-term planning will generally not stabilize the system. Although numerical optimization shows that a cooperative optimum would yield a high and stable harvest, the open-access system may produce limit cycles, in which even the peak harvest may be below the stable cooperative optimal harvest. Such fluctuations cause both losses in biomass production and utility losses. Our dynamic analysis also demonstrates that, in the absence of cooperation between herders, too much rain in an otherwise dry area might (temporally) destabilize the ecological grazing system through overstocking, subsequently leading to further overgrazing (which will be observed in, but not caused by, the typically dry conditions of landscapes where pastoralism is practiced). In short, through this study we have brought time (and temporal dynamics) into the Hardin's tragedy of the commons and show that the tragedy might be profoundly worsened.