Dynamic modeling of environmental amenity-driven migration with ecological feedbacks.

Environmental amenity-driven migration presents a double-edged sword to policy makers concerned with both economic and ecological sustainability. Clearly the protection of environmental amenities is important, but what is the right balance between ecosystem protection and regional economic processes that simultaneously respond to and degrade ecological resources? We consider this question in the context of households that are attracted to a region by urban and lake amenities and a lake ecosystem that becomes degraded by land development. An analytical expression for the time evolution of population is derived from households' and firms' optimizing behaviors. Numerical methods with phase plane diagrams are used to study the steady state and transient dynamics of the resulting population-phosphorus coupled system. The system is found to be bi-stable under a range of parameter values with one attractor corresponding to a desired "balanced" economy-ecology state and the other to a very small population base with fully restored ecology. We examine the dynamics and quantify the resilience of the system in and away from the balanced steady state using phase plane diagrams that demarcate the two domains of attraction. Economic-ecological interactions fundamentally alter regional economic dynamics and influence the resilience of the balanced domain of attraction. For example, a one percent increase in the loadings coefficient associated with residential land development generates a three percent decline in the resilience of the balanced state. We find that economic feedbacks often increase system resilience. Initial increases in the attraction of urban amenities spur greater population growth that increases the resilience of the balanced state. In addition, price feedbacks that arise from capitalized (dis)amenities increase the resilience of the system to bad ecological shocks.

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