Coupled economic-ecological systems with slow and fast dynamics
Ecosystems are often complex adaptive systems with components that can exhibit non-linear dynamics. These nonlinearities can lead to alternative ecosystem states, which often results in dramatic shifts in the resources and services that those ecosystems can provide to people. Alternative states generally occur when there are positive feedbacks in the system, particularly those that influence “slow” variables. These slow variables typically change on time scales that are largely different in magnitude from other ecosystem components. Thus, once slow variables shift enough to flip the system into an alternative state, it can be extremely difficult to reverse, except over very long time scales. Considering the consequences of changes in these slow variables is important, because the values of the goods and services associated with the ecosystem are generally very different depending on what state the system is in. Therefore, if managers want to preserve the value of specific services, they need to consider the system trajectory, particularly if an important slow variable is near a bifurcation point where it would lead the system to switch into the alternative, potentially less desirable state.
To demonstrate a tractable method to determine economic outcomes associated with different management strategies for a system that exhibits alternative states, Crepin et al. (2011) use a “slow-fast” modeling approach (which turns the slow variable into a static parameter in the model for the fast ecosystem components) to model insect pest control. They compare management strategies that use direct pest control methods (e.g. pesticides, harvesting) vs. protecting bird diversity, which naturally reduce pest abundance. In their model, the slow variable was the bird abundance, which changes much more slowly than the density (of the insect pests (which can go through multiple generations and exhibit exponential growth in a single growing season). Bird abundance does not depend on pests because they eat other food unless the pests are highly abundant, and thus, bird populations are driven by external factors to the system. The number of bird species is a function of the proportion of land that is not cultivated, and species richness of birds affects the efficiency of pest removal. In this system, the pest can either be in the high abundance outbreak state, or in the low abundance state, depending on the bird diversity slow variable, and the state the system was in previously if the slow variable was in the region between the two thresholds between the alternative states.
They also incorporated two contrasting resource users, one type who consume goods that depend on the land that the pests affect (e.g. farmers), and others who benefit from the goods and services of the birds in the system (e.g. bird-watchers). The authors compared two different resource exploitation models, one for the resource exploiters deciding on strategies, and another where a social planner decides on the resource with consideration of the needs of both users in mind. They found that the optimal level of pesticide use was very low for both farmers and social planners, and controlling the proportion of cultivated habitat to protect bird diversity use was the optimal strategy for both, although farmers tended to use more land than social planners did. When they incorporated a tax or a subsidy as incentives that the social planner could use to achieve their objective of finding an optimal land management and pest control strategy for both user groups, the authors found that the model was so sensitive to the parameter values that there was not one generally best price instrument. Thus, a great deal of system-specific knowledge is required for managing complex human-ecological systems, particularly ones that exhibit alternative states.
Crépin, A.-S., Norberg, J. & Mäler, K.-G. Coupled economic-ecological systems with slow and fast dynamics: Modelling and analysis method. Ecological Economics 70, 1448–1458 (2011).