Multiple stable states and relationship between thresholds in processes and states

Abstract

The concept of thresholds is applied broadly in ecology to both processes and states that exhibit step-like behavior. Thresholds are observed in parameters, equilibrium states, and in states over time, but presence or absence of thresholds at any of these levels does not provide information about the occurrence of thresholds at the other levels. Here we explore the relationship between thresholds and theory of multiple stable states. We present a 2-species Lotka-Volterra model of competition to illustrate that thresholds and hysteresis-like behavior are possible in linear systems. Agrazing model is presented to show that multiple stable states are possible without thresholds in the underlying processes. The concept of thresholds within the context of multiple stable states is reviewed in an attempt to resolve some of the confusion that stems from the different meanings of thresholds. © Inter-Research 2010.