A recurring argument in the global debate is that climate deterioration is likely to make social conflicts over diminishing natural resources more common in the future. The exact mechanism behind such a development has so far not been successfully characterized in the literature. In this paper, we present a general model of a community populated by farmers and herders who can either divide up land in a market economy or in autarky. The key insight from our model is that decreasing resources can make trade between the two groups collapse, which in turn makes each group's welfare independent of that of the other. Predictions from the model are then applied to the conflict in Darfur. Our analysis suggests that three decades of drought in the area can at least partially explain the observed disintegration of markets and the subsequent rise of social tensions.