STABLE AND UNSTABLE STATES IN A SYSTEM CONTROLLED BY POSITIVE FEEDBACK, IMPLICATIONS FOR THE TROPICAL RAINFOREST ECOSYSTEM

If positive feedback controlling system behavior results from couplings defined by independent mathematical relationships, the system may contain both stable and unstable steady states. For example, if the system has two steady states, one will be stable and the other unstable. Under normal conditions any long-lived system would reside at or near the stable steady state. However, continuous external forcing can cause the system to shift toward the second steady state that separates regions of relative stability and possible return to initial conditions from instability and runaway behavior. Once the unstable steady state is reached, additional forcing will cause system-collapse.

Feedback between tropical rainforest and climate may create such a system. Couplings relate precipitation (P) to deforestation through the equations ET_i (evapo-transpiration)=P_i - R_i (runoff) and P_i+1=Ext (water from external sources) + ET_i. Ext is nearly constant, fixed at levels of R prior to deforestation. Deforestation reduces ET and increases R as a per cent of P. This loss of water in the system leads to a reduction in future P. P affects the health of the forest and, by implication, ET. The geologic record suggests that this feedback has created a stable ecosystem in areas like the Amazon Basin, however, current deforestation may be forcing the system toward collapse.

To test this hypothesis, a two-dimensional finite-difference model was constructed that treats both the effect of deforestation on ET and R and the effect of P on forest regrowth as non-linear equations. Model results indicate that the current stable ecosystem is threatened by deforestation and resultant climatic change. If model parameters are accurate, the ecosystem may enter instability with as little as 20% of the basin deforested. This could cause a permanent ecosystem shift from forest to grassland or a temporary collapse of the forest followed by slow recovery. Either scenario predicts a serious loss in global biodiversity.