Positive Feedback and System Resilience from Graphical and Finite-Difference Models: The Amazon Ecosystem—An Example

Abstract

Positive feedback has the potential to create multiple steady states that divide system space into regions of distinct behavioral modes. Graphical analysis can be used to recognize systems likely to behave in this way. For example, positive feedback created by interactions among tropical forest, regional hydrology, and climate in the Amazon basin may produce multiple steady states. As deforestation progresses, one state?the normal forest with a high leaf area index?is stable and promotes system resilience. However, deforestation can cause the system to shift toward and past a second, unstable state at moderate levels of forest cover. The latter separates forest stability in the face of stress from runaway behavior and system collapse into an alternative grassland ecology. To test this inference, a two-dimensional finite-difference model has been constructed that includes parameterizations of the functions controlling feedback. Results of the experiment indicate that human-driven deforestation may shift regions of the Amazonian ecosystem to instability after 25%?30% of the forest has been permanently cleared, within two to four decades if the current practice is maintained. Even a temporary loss of the Amazon forest or significant portions of it would negatively impact terrestrial biodiversity.