Convex Relationships in Ecosystems Containing Mixtures of Trees and Grass

The relationship between grass production andthe quantity of trees in mixed tree-grassecosystems (savannas) is convex for all or mostof its range. In other words, the grassproduction declines more steeply per unitincrease in tree quantity at low tree coverthan at high tree cover. Since much of theeconomic value in savannas is ultimatelyderived from grass, and the main mechanismcontrolling the tree-grass balance is dependenton the production of grassy fuel for fires,this non-linearity has the effect of creatingtwo savanna configurations. One has a low treedensity and supports a viable grazingenterprise, while the other has dense treecover and a frequently non-viable grazingenterprise. The non-linearity is suggested hereto have two main sources: the geometry of thespatial interaction between tree root systemand grasses, and the effect of differingphenology (the time course of leaf areaexposure) on the acquisition of water andnutrients. The existence of the non-linearityreduces the resilience of thegenerally-preferred “open” configuration, andincreases the resilience of the less-desirable“closed” configuration.