According to the 'ecosystem approach', state shifts occur as a result of slow changes to the parameters in a model that defines the ecological system under study. Examples of model parameters can include characteristics of the interacting components in the ecosystem or community such as rates of growth, death, feeding, migration, or flow of resources and energy. Changes to model parameters are analogous to altering the surface topography of our visualization. These changes in topography around the ball allow for alternative basins of attraction to form through time. The depth (the strength of attraction) of the basin in which a ball resides can be eroded by the perturbation to model parameters, even while another basin is forming elsewhere on the landscape. Once the 'high-ground' between the basins has eroded sufficiently, the ball will roll to the alternate basin representing a change in the system state (Figure 1a). Stochastic perturbations can include environmental variability in abiotic factors, or demographic stochasticity in small populations -features not explicitly included in the model.
The slow change in a parameter is the same as a perturbation that changes the equilibrium point of the community or ecosystem. As the ball begins to move with the shifting basin of attraction, it traces a trajectory across the surface (Figure 2). Hysteresis is revealed when the perturbation is relaxed and parameters return to their original values, as reflected by a surface that re-assumes its original configuration. Hysteresis can be said to have occurred if the return trajectory of the equilibrium point (or ball) 'differs' to that adopted during its 'outward' journey (Figures 1a and 2). For this 'ecosystem' view of hysteresis, there must be multiple possible equilibrium points for some (but not necessarily all) values of the perturbed parameters.
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