Introduction

Hysteresis is a possible characteristic of systems with two or more stable states. Most simply defined, hysteresis occurs when the return path between two states can be different from the outgoing path. Hysteresis reflects historical dependency in ecological dynamics, such that the order of previous events can influence current events.

There are two different ways in which alternative stable states have been conceptualized and modeled in

Starting state Forward perturbation Same reverse perturbation

Starting state Forward perturbation Same reverse perturbation

Starting state Forward perturbation Same reverse perturbation

Starting state Forward perturbation Same reverse perturbation

Figure 1 (a) Hysteresis resulting from a parameter perturbation causing landscape changes that result in the ball moving to another state. Application of an equal but opposite perturbation fails to return the community to its original state; (b) a possible analogous representation of state shifts arising from a state variable perturbation. Again, the same perturbation magnitude is insufficient to return the ball to its original state after having been moved into an alternative state. Reproduced with permission from Beisner BE, Haydon D, and Cuddington KL (2003) Alternative stable states in ecology. Frontiers in Ecology and the Environment 1: 376-382, © Ecological Society of America.

Figure 1 (a) Hysteresis resulting from a parameter perturbation causing landscape changes that result in the ball moving to another state. Application of an equal but opposite perturbation fails to return the community to its original state; (b) a possible analogous representation of state shifts arising from a state variable perturbation. Again, the same perturbation magnitude is insufficient to return the ball to its original state after having been moved into an alternative state. Reproduced with permission from Beisner BE, Haydon D, and Cuddington KL (2003) Alternative stable states in ecology. Frontiers in Ecology and the Environment 1: 376-382, © Ecological Society of America.

the ecological literature, allowing for different theoretical explanations of how hysteresis can arise. These we term the 'ecosystem' and 'community' approaches. To best understand these different conceptualizations, one can take a heuristic approach, most easily illustrated by visualizing the ecosystem or community dynamics as a ball rolling on a complex surface (Figure 1). The current state of the ecological system is represented by the position of the ball on the surface and its dynamics determined by the topography of the surface. This heuristic model can be readily applied to both views of alternative stable states, and provides the easiest means of demonstrating how the two viewpoints differ.

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