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The Control of Invasive Species on Private Property with Neighbor-to-Neighbor Spillovers

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Abstract

Invasive pests cross property boundaries. Property managers may have private incentives to control invasive species despite not having sufficient incentive to fully internalize the external costs of their role in spreading the invasion. Each property manager has a right to future use of his own property, but his property may abut others’ properties enabling spread of an invasive species. The incentives for a foresighted property manager to control invasive species have received little attention. We consider the efforts of a foresighted property manager who has rights to future use of a property and has the ability to engage in repeated, discrete control activities. We find that higher rates of dispersal, associated with proximity to neighboring properties, reduce the private incentives for control. Controlling species at one location provides incentives to control at a neighboring location. Control at neighboring locations are strategic complements and coupled with spatial heterogeneity lead to a weaker-link public good problem, in which each property owner is unable to fully appropriate the benefits of his own control activity. Future-use rights and private costs suggest that there is scope for a series of Coase-like exchanges to internalize much of the costs associated with species invasion. Pigouvian taxes on invasive species potentially have qualitatively perverse behavioral effects. A tax with a strong income effect (e.g., failure of effective revenue recycling) can reduce the value of property assets and diminish the incentive to manage insects on one’s own property.

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Notes

  1. Attenuated spatial property rights may also have a finite time horizon.

  2. We refer to spatial property rights and not ownership because it is possible that more limited rights provide incentive for control. For example, a rancher with a grazing right to public land, and the ability to exclude other ranchers, is more likely to control an invasive weed than if the area were grazed as a commons. This is true even though the rancher does not own the range.

  3. Blunt management instruments cannot be used in a continuous way according to equimarginal principle, and many realistic land management instruments fall into this category. When pesticide is sprayed on a per area based the treatment level is not influence by the size of the pest population. Another example is engaging biosecurity measures such as fencing to protect livestock from wildlife carrying disease (Horan et al. 2008).

  4. Brazil and China have also suffered from the spread of ACP-HLB.

  5. http://usda.mannlib.cornell.edu/MannUsda/viewDocumentInfo.do?documentID=1377.

  6. Marten and Moore (2011) allows chemical and bio-control and allows for variation in intensity to assess socially optimal management (since bio-control interventions are seldom done by a single landowner). Sims et al. (2010), and Sims and Finnoff (2012) investigate control of stochastic spread of forest damaging insects.

  7. One advantage of this approach is that in principle it enables the analyst to consider the case of zero insects as a special case of the feedback rule thereby bridging localized control and localized prevention, and avoiding the need to frame the prevention-control question as one of switching regimes (Mehta et al. 2007; Polasky 2010). We do not exploit this property of this setup in the current research, and this extension is left for future work.

  8. This assumption implies that the bio-physical and economic environments have been relatively stable such that the grower has been able to converge to a long-run equilibrium.

  9. We do not consider grove biosecurity, which could affect the introduction of new insects.

  10. Morris et al. (2008) write, “some [growers] know they have greening [HLB] but rather than institute control practices, plan to take whatever profits can be made, then replant [with an alternative crop] or sell the land.”

  11. http://www.nass.usda.gov/Statistics_by_State/Florida/Publications/Citrus/aban/CitAA12.pdf.

  12. Smith et al. (2009b) use a similar setup to model the management of the depreciation of property values associated with beach erosion through beach nourishment using an approach following Hartman (1976). A critical difference between Smith et al. (2009b) and ours study is that Smith et al. (2009b) always reset the beach to the same width, while in our problem a proportion of insects are killed so the post spraying level of insects depends on the pre-spraying population.

  13. Environmental persistence of pesticide could increase the incentives for spraying. Including environmental persistence adds another state variable with nonlinear dynamics to the model. While important for considering for prescriptive purposes, residual pesticide effects likely will not affect our core insights, and would make graphical visualization challenging.

  14. While Eq. (9) can be implemented directly, rewriting the expression in terms of basis functions and employing an alternative, but smoother, function with the same roots, such as the Fischer-Burnmeister function (Sun and Qi 1999), enhances numerical convergence and reduces memory requirements. We are grateful for this recommendation from an anonymous reviewer.

  15. If growers think a cure might be available in the future they may “moth ball” their groves and cease active management, but this does not stop the groves from producing insects.

  16. A 10 % increase in \(\beta \) did not have an observable influence on the boundary given the density of collocation nodes. Figure 3 presents a doubling of \(\beta \) for illustrative purposes.

  17. Moving grower \(j\) farther from grower \(i\), which is essentially what biosecurity measures do, enhances the value of grower \(i\)’s capital, but investments in biosecurity may have different properties than investments in onsite control. Biosecurity may also transfer or shift the externality to neighbors.

  18. This simplifies the problem by eliminating the problem of the optimal time to pay. The La Chatelier principle suggests that if it is optimal for grower \(i\) to make a payment at the appointed time, then freeing the time of the payment can make grower \(i \)no worse off. For the payment to be moved voluntarily to another time, the payment can also not make grower \(j\) worse off. Therefore, a more flexible program would only enhance the likelihood that a payment system is welfare enhancing.

  19. Biosecurity investments that prevent transmission between groves could be a strategic substitute that leads to free-riding. Other research on invasive species prevention and control suggests that actions to prevent invasion may shift risk to others (Warziniack et al. 2011), but spraying abates damages rather than shifting them.

  20. Such an equilibrium is almost certainly unstable when perturbed with heterogeneous local information.

  21. Given the very high levels of ACPs per citrus tree reported in the literature, marginal reductions in citrus stock are likely to have little effect on the ACP stock. Therefore, marginal reductions in citrus stock in response to a tax are highly unlikely.

  22. Antidotal evidence from Florida suggests livestock grazing under abandoned citrus tress is one potential alternative land use.

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Acknowledgments

The funding support for the paper is: We thank David Finnoff and two anonymous reviewers for their helpful comments. This publication was made possible by Grant Number 1R01GM100471-01 from the National Institute of General Medical Sciences (NIGMS) at the National Institutes of Health, by the United States Department of Agriculture, Specialty Crop Research Initiative (USDA-SCRI) Award Number 2010-51181-21246, an award from the Saguaro high performance computing center at Arizona State University, and support from Yale’s high performance computing services. Its contents are solely the responsibility of the authors and do not represent the official views of NIGMS or USDA.

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Authors and Affiliations

  1. Yale School of Forestry and Environmental Studies, New Haven, CT, 06511, USA

    Eli P. Fenichel

  2. Morrison School of Agribusiness and Resource Management, Arizona State University, Mesa, AZ, 85212, USA

    Timothy J. Richards

  3. School of Life Sciences, Arizona State University, Tempe, AZ, 85287, USA

    David W. Shanafelt

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  1. Eli P. Fenichel
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Correspondence to Eli P. Fenichel.

Appendix

Appendix

The choice of \(\beta \) is dependent on the extent to which HLB is present, which can be highly variable even within infected regions (Gottwald 2010). Our choice of \(\beta \) reflects a limited amount of HLB (Halbert and Manjunath 2004) and is within the range implied by Chiyaka et al. (2012). The net growth rate of ACP is highly variable and dependent on environmental conditions. Our choice falls within the range from the literature (Lui and Tsai 2000; Tsai and Liu 2000). The rate is lower than the average growth rate used by Chiyaka et al. (2012), but their growth model enables the net growth rate to change seasonally. This is why their model enables a longer persistence of citrus trees. Our growth rate is also reduced relative to the estimate provided by Richards et al. (in press), but still seems to give realistic results. The carrying capacity conversion coefficient, \(b\), was chosen to be realistic but conservative by envisioning 10,000 ACP per tree as a maximal density, which is substantially lower than values reported in the literature, and a square grove with approximately 31 trees on a side.

The profitability parameter \(q\) was chosen so that growers were not too profitable, but that in the absence of ACP and HLB operations are a rational enterprise. Data from the University of California extension office suggests that citrus operations are at best marginally profitable (O’Connell et al. 2009). Spraying costs are often computed on a per acre bases and can be highly variable (Aubert 1987; Catling 1970; Cocco and Hoy 2008). Therefore, our choice of \(c\) is chosen to match in a realistic way with the choice of \(q\), though our parameter is likely on the low side of costs. The technical spraying parameter \(\alpha \) comes from (Setamou et al. 2010).

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Fenichel, E.P., Richards, T.J. & Shanafelt, D.W. The Control of Invasive Species on Private Property with Neighbor-to-Neighbor Spillovers. Environ Resource Econ 59, 231–255 (2014). https://doi.org/10.1007/s10640-013-9726-z

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