Cost-effective management of invasive species using linear-quadratic control

Blackwood, Julie C.; Hastings, Alan; Costello, Christopher

doi:10.1016/j.ecolecon.2009.08.029

Cited by 78 publications

(63 citation statements)

References 24 publications

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“…Many programmes adopt a passive approach to restoring invaded systems and simply aim to remove the existing invaders and limit or prevent their regeneration. This approach often fails to achieve the desired outcome of a functional ecosystem dominated by native species (D'Antonio & Meyerson, 2002;Hulme, 2006;Reid et al, 2009;Blackwood et al, 2010). Practical problems that prevent the achievement of goals include 'secondary invasions' -the rapid replacement of the removed invasive species by others that capitalize on disturbance caused by the control operations.…”

Section: Introductionmentioning

confidence: 99%

Impacts of invasive Australian acacias: implications for management and restoration

Maitre¹,

Gaertner

Marchante

et al. 2011

Diversity and Distributions

339

293

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Aim The biophysical impacts of invasive Australian acacias and their effects on ecosystem services are explored and used to develop a framework for improved restoration practices.Location South Africa, Portugal and Chile.Methods A conceptual model of ecosystem responses to the increasing severity (density and duration) of invasions was developed from the literature and our knowledge of how these impacts affect options for restoration. Case studies are used to identify similarities and differences between three regions severely affected by invasions of Australian acacias: Acacia dealbata in Chile, Acacia longifolia in Portugal and Acacia saligna in South Africa.Results Australian acacias have a wide range of impacts on ecosystems that increase with time and disturbance, transform ecosystems and alter and reduce ecosystem service delivery. A shared trait is the accumulation of massive seed banks, which enables them to become dominant after disturbances. Ecosystem trajectories and recovery potential suggest that there are important thresholds in ecosystem state and resilience. When these are crossed, options for restoration are radically altered; in many cases, autogenic (self-driven and self-sustaining) recovery to a pre-invasion condition is inhibited, necessitating active intervention to restore composition and function.Main conclusions The conceptual model demonstrates the degree, nature and reversibility of ecosystem degradation and identifies key actions needed to restore ecosystems to desired states. Control and restoration operations, particularly active restoration, require substantial short-to medium-term investments, which can reduce losses of biodiversity and ecosystem services, and the costs to society in the long term. Increasing restoration effectiveness will require further research into linkages between impacts and restoration. This research should involve scientists, practitioners and managers engaged in invasive plant control and restoration programmes, together with society as both the investors in, and beneficiaries of, more effective restoration.

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Section: Introductionmentioning

confidence: 99%

Impacts of invasive Australian acacias: implications for management and restoration

Maitre¹,

Gaertner

Marchante

et al. 2011

Diversity and Distributions

339

293

View full text Add to dashboard Cite

show abstract

“…For example, Albers et al (2010) and Sanchirico et al (2010b) identify equilibrium control solutions for a complex model of invasion spread and reproduction dynamics in a two-patch model allowing for multiple types of control. Blackwood et al (2010) take the closest to our approach by accounting for large-scale explicit space, but solve for optimal spatial-dynamic control policies over a finite horizon with no transversality condition. They model a pest that exhibits exponential growth over time and quadratic control costs, assumptions that allow them to cast the problem as a linear-quadratic control problem.…”

Section: Related Literaturementioning

confidence: 99%

Optimal Control of Spatial-Dynamic Processes: The Case of Biological Invasions

Epanchin‐Niell

Wilen

2011

SSRN Journal

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This study examines the spatial nature of optimal bioinvasion control. We develop a spatially explicit two-dimensional model of species spread that allows for differential control across space and time, and we solve for optimal spatial-dynamic control strategies. We find that the optimal strategies depend in interesting ways on the shape of the landscape and the location, shape, and contiguity of the invasion. For example, changing the shape of the invasion or using landscape features to reduce the extent of exposed invasion edge can be an optimal strategy because it reduces long-term containment costs. We also show that strategies should be targeted to slow or prevent the spread of an invasion in the direction of greatest potential long-term damages. These spatially explicit characterizations of optimal policies contribute to the largely nonspatial literature on controlling invasions and our general understanding of how to control spatial-dynamic processes.

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“…Increasing the complexity and realism of a model makes it harder to analyze and interpret mathematically, so it is reasonable to use a model which is just complex enough to be able to answer the question at hand. One of the most common simplifications to make is to only consider the temporal aspect of a problem (Courchamp et al 2003, Hastings et al 2006, Zhang et al 2006, Hauser et al 2007, Kern et al 2007, Baxter et al 2008, Blackwood et al 2010, Rout et al 2013, or only its spatial aspect (Neubert 2003, Hauser and McCarthy 2009, Baker and Bode 2013. However, invasive species control problems are inherently spatiotemporal, since the abundance of an invasive population, and the implementation of a management project, change in both space and time.…”

Section: Introductionmentioning

confidence: 99%