Optimal Control of an Invasive Ecosystem Engineer

By

David Kling (presenter), University of California, Davis James Sanchirico, University of California, Davis Alan Hastings, University of California, Davis

Managing natural systems in the face of global anthropogenic change poses an enormous challenge. Human-mediated changes can greatly complicate resource management by rendering ecosystems unable to return to their natural condition (hysteresis) or by shifting the ecosystem to an entirely new and possibly less beneficial state (regime shift) (Beisner et al. 2003; Scheffer and Carpenter 2003). One common and pervasive example of a complex management problem is the control of invasive introduced species. It is now well-known that nonnative species can have strong negative impacts on ecosystem function and services and on native biodiversity (Chapin et al. 2000; Olson 2006). Researchers have devoted considerable effort towards understanding the economics of invasion control. Previous theoretical work has identified circumstances where the eradication of an invader is optimal (Olson and Roy 2008). Recent work has also investigated the spatial-dynamics of control and characterized how landscape features can drive optimal policies (Epanchin-Niell and Wilen 2009). A key finding from this research is that early intervention, when the population of the invader is small, is a pivotal determinant of the cost- effectiveness of eradication. Despite this progress, a persistent gap in theoretical work by economists on invasions has been left by a reliance on simple models of invader population dynamics that ignore a number of ecological processes that can accompany invasions and that may call for substantially different control strategies. Ecosystem engineers are organisms that have significant impacts on ecosystems through changing key physical characteristics of the system (Cuddington et al. 2009). Some ecosystem engineers generate valuable ecosystem services. For example, the Eastern oyster (Crassostrea virginica) improves water quality through filter feeding and builds reefs that provide habitat for commercially valuable marine life (Grabowski and Peterson 2007). Ecosystem engineers are also among the most damaging invasive species. Virtually all of the plants on the International Union for Conservation of Nature (IUCN) Invasive Species Specialist Group list of 100 worst invaders are engineers, as are some of the most costly invasive animal species. A noteworthy ecosystem engineer is cheatgrass (Bromus tectorum), an invasive weed in the western United States that has dramatically increased the frequency of range fires (Crooks 2002). Since invasive engineers can have large impacts on physical and chemical states, they often leave lasting damage that persists long after their removal. An example of this effect is seen in U.S. Pacific coast estuaries, where dense root matter left by eradicated invasive eastern smooth cordgrass (Spartina alternaflora) and its hybrids increases the local tidal elevation, threatening critical habitat for native shorebirds in the process. The impacts of harmful invasive engineers can be mitigated by a manager in two ways: removing the invader or restoring natural functions. While the former tactic can be effective at slowing or preventing the invasion, the latter is often necessary to restore previously invaded sites. In this paper, we examine the interplay between these two controls in the optimal management of an invasive ecosystem engineer using a simple but flexible bioeconomic framework. We model the manager’s problem as one of minimizing the net present value of damages from the invasion by setting controls on the density of the ecosystem engineer and on the engineered environmental state. We obtain analytical and numerical characterizations of the efficient policy in several different special cases that capture the main features of important classes of invasive engineers. For example, we show how optimal strategies for controlling an obligate engineer, or an engineer that depends on the environmental state that it changes for survival, differs from the non-obligate case. We characterize how the cost and density thresholds for optimal eradication are affected by engineering. We also examine the effect of the rate of regeneration for the environmental state, including the limiting case where hysteresis is possible even after the engineer has been eradicated. Another component of the model that we explore is the impact that different forms of damage have on the optimal policy. We present results for cases where damages flow from the density of the invader, the deviation of the environmental state from its pre-invasion equilibrium, and where damages flow from both states variables. Our results suggest that the pattern of control depends critically on the form of the linkage between the growth of the invasive engineer and the physical state. A key finding that illustrates how management of invasive ecosystem engineers diverges from non-engineers is that in many cases, the optimal policy entails prioritizing the restoration of the engineered state over driving down the engineer’s density. Our paper makes several contributions. We provide what to our knowledge are the first formal results on the optimal control of an invasive engineer. This study also provides guidance on how managing engineers differs from the control of non-engineers, which should be of considerable interest to resource managers currently grappling with established invasive species. In particular, our work suggests that relying on models that ignore an invader's capacity to change the physical environment may lead to inefficient management strategies. Additionally, we provide insights into the management of complex systems that will aid in the understanding of more general conservation problems where the need to understand economic trade-offs is beginning to be acknowledged by the conservation community (Naidoo et al. 2006). This study also adds to the theoretical foundation of ecosystem-based management, which calls for the recognition of system-component interactions and environmental factors in the formulation of renewable resource policy. Finally, our study lays the groundwork for further research on the management of both harmful and beneficial ecosystem engineers. Possible direct extensions to this study include addressing multi-species cases that mirror scenarios encountered by managers in the field. Our paper also serves as a step towards a spatial-dynamic model of invasive engineer control. This last extension could build-in Cuddington and Hasting's (2004) key finding that an invader's spread can be rapidly accelerated by engineering.

References

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