The key to understanding the apparent differences between the community and ecosystem approaches, and the consequent interpretation of how hysteresis arises, depends ultimately on model formulation and whether a quantity in a model is treated as a parameter or a variable. In practice, we examine the quantities involved in a dynamical process and include and identify as state variables all those quantities (usually population sizes) that change in response to feedback from other components of the system. Parameters are those quantities that are either independent of, or subject only to very slow feedback from state variables within the model. The community and ecosystem approaches to understanding hysteresis will differ in terms of which feedback processes are explicitly included in the model formulation.
For example, returning to the harvesting of fish populations - this problem can be modeled using either approach. Humans often harvest fish at a rate independent of fish population size. If fishing pressure is considered to be largely independent of, and free from, feedback from fish stocks, then fishing pressure may be considered as a slowly increasing death rate parameter as fishing technology advances, and under this assumption the fishery dynamics should be examined from an ecosystem perspective. Hysteresis would therefore arise along a slowly changing gradient of harvesting pressure (as along the TP gradient in the ecosystem approach' example above). Changing the harvesting parameter can drive the fish stocks from one stable state to another in a process analogous to that discussed for lake algae: stocks start initially at higher levels where harvesting is low, but following slow increases in fishing pressure, a crash eventually occurs. A subsequent reduction in fishing pressure to the same level just before the crash, however, is no guarantee of reinstatement of the high stable equilibrium fish densities, because other components of the ecosystem (such as competition from other species that have grown to replace the harvested species for example) may prevent the population of interest from regrowth. Thus hysteresis may be observed (and can often be a surprising phenomenon to managers), because there are other factors which are not explicitly modeled, that prevent a simple return of the ecosystem to its former state.
If fishing pressure by humans is dependent on the fish stock size (i.e., there is a type of predator-prey interaction between fish and humans), and the feedback occurs with little time-lag, then the change in fishing pressure is best directly modeled by incorporating a predation equation with a harvesting function dependent on stock density. Thus, there would be fixed basins of attraction in the dynamical landscape, reflective of the available alternative stable states. This situation is modeled using the 'community approach'. In this conceptualization, this fish-human system could be moved from one state to another through perturbations to state variables such as a large increase in fishing effort (e.g., resulting from migration of fishing armadas from one location of the sea to another in search of larger catches per unit effort). Hysteresis could be said to occur in such a case only when the effort required to reverse a change to population densities in one direction is different from what it would be in the other direction. Thus, if hysteresis is present, the simple reduction of fishing effort after their perturbation might not lead to a re-establishment of the same population size of fish without some further effort to supplement population sizes. Again, hysteresis in this case may arise through competition with other fish species which prevent the harvested population from increasing once it has been reduced below some threshold level.
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