Target the Source: Optimal Spatiotemporal Resource Allocation for Invasive Species Control

Baker, Christopher M.

doi:10.1111/conl.12236

Cited by 58 publications

(79 citation statements)

References 32 publications

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“…Mathematical modeling and optimization play an important role in improving strategies for the control and eradication of invasive species [15,35,36], a crucial aspect in nature conservation [37].…”

Section: Symplectic-exponential Lawson Integration For the Control Ofmentioning

confidence: 99%

“…In an operator splitting perspective, to construct approximated solutions of (35), which separate diffusive and advection semiflows from reaction, a step requires the numerical integration of the reaction semiflow. For for constant value of light intensity I, the reaction semiflow is given by the autonomous and spatially homogeneous system…”

Section: Biochemical-poisson System For Modelling the Oceanic Deep Chmentioning

confidence: 99%

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Geometric Numerical Integration in Ecological Modelling

Diele

Marangi

2019

Mathematics

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A major neglected weakness of many ecological models is the numerical method used to solve the governing systems of differential equations. Indeed, the discrete dynamics described by numerical integrators can provide spurious solution of the corresponding continuous model. The approach represented by the geometric numerical integration, by preserving qualitative properties of the solution, leads to improved numerical behaviour expecially in the long-time integration. Positivity of the phase space, Poisson structure of the flows, conservation of invariants that characterize the continuous ecological models are some of the qualitative characteristics well reproduced by geometric numerical integrators. In this paper we review the benefits induced by the use of geometric numerical integrators for some ecological differential models.

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Section: Symplectic-exponential Lawson Integration For the Control Ofmentioning

confidence: 99%

Section: Biochemical-poisson System For Modelling the Oceanic Deep Chmentioning

confidence: 99%

Geometric Numerical Integration in Ecological Modelling

Diele

Marangi

2019

Mathematics

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“…Baker (2016) examines optimal management of an invasion that spreads through both local and long-distance dispersal and finds that when accounting for outlier populations having lower population spread and growth rates early on, targeting the source population is optimal, as this contributes more to slowing the spread and is more cost-effective. This finding would be further accentuated if the costs of detecting satellite populations were accounted for.…”

Section: Economics Of Invasive Species… 3343mentioning

confidence: 99%

Economics of invasive species policy and management

Epanchin‐Niell

2017

Biol Invasions

163

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This article examines the use of economic analysis to inform bioinvasion management, with particular focus on forest resources. Economics is key for understanding invasion processes, impacts, and decision-making. Biological invasions are driven by and affect economic activities at multiple scales and stages of an invasion. Bioeconomic modeling seeks to inform how resources can be optimally allocated across invasion management activities-including prevention, surveillance programs for early detection and management, and controlling invasion populations and spread-to minimize the long-term costs and damages. Economic analysis facilitates understanding of decisions by public and private decision-makers, gaps between these, and the design of policies to achieve socially desirable outcomes. Private decisionmakers may undercontrol invasions relative to socially optimal levels, because they generally account for their own costs and benefits of control but less often for broader ecosystem impacts or future spread across the landscape. Economic analysis considers approaches for increasing private invasion management and evaluates feedbacks between ecological and economic systems that can affect policy outcomes. Future research should continue evaluation and design of control strategies across the biosecurity continuum and across species to enhance cost-effectiveness, better incorporate uncertainty into policy design, increase focus on incentives and behavioral tools to influence private behaviors that affect invasion spread, and incorporate invasive species consideration within broader systems-focused science. In addition, challenges in valuing biodiversity and ecosystem service impacts and the costs and effectiveness of control measures are key data gaps. Greater collaboration between decision-makers and researchers will facilitate development and communication of usable economic research.

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“…A penalty term is added to take into account the budget constraint

E (boldx, t) \leq B

for any

(boldx, t) \in normalΩ \times [0, T]

, when the budget bound

B > 0

is fixed. As a result, we build the penalized objective function as follows (see Baker, )

J (E) = \int_{normalΩ} e^{- δ T} ν (boldx) n (x, T) d x + \int_{Ω \times [0, T]} e^{- δ t} true(c {(\frac{E (x, t)}{B})}^{2 q - 1} + {(E (boldx, t))}^{q} + ω (x, t) n true) d x d t,

where

ω

represents the cost due to the environmental damage,

ν

is a weight for the final population density,

δ \in (0, 1)

is the discount factor,

q \in boldN

q \geq 2

, and

c \geq 0

are suitable constant values. In the following, we assume

ν \in L^{\infty} (Ω)

ν (x) \geq 0

for any

boldx \in normalΩ

, and

ω \in L^{\infty} (normalΩ \times [0, T])

ω (boldx, t) > 0

over

normalΩ \times [0, T]

.…”

Section: Model Formulationmentioning

confidence: 99%

“…for any ∈ t T x ( , ) Ω × [0, ], when the budget bound B > 0 is fixed. As a result, we build the penalized objective function as follows (see Baker, 2016)…”

Section: Model Formulationmentioning

confidence: 99%

Optimal spatiotemporal effort allocation for invasive species removal incorporating a removal handling time and budget

Baker

Diele

Marangi

et al. 2018

Natural Resource Modeling

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Improving strategies for the control and eradication of invasive species is an important aspect of nature conservation, an aspect where mathematical modeling and optimization play an important role. In this paper, we introduce a reaction‐diffusion partial differential equation to model the spatiotemporal dynamics of an invasive species, and we use optimal control theory to solve for optimal management, while implementing a budget constraint. We perform an analytical study of the model properties, including the well‐posedness of the problem. We apply this to two hypothetical but realistic problems involving plant and animal invasive species. This allows us to determine the optimal space and time allocation of the efforts, as well as the final length of the removal program so as to reach the local extinction of the species.

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Target the Source: Optimal Spatiotemporal Resource Allocation for Invasive Species Control

Cited by 58 publications

References 32 publications

Geometric Numerical Integration in Ecological Modelling

Geometric Numerical Integration in Ecological Modelling

Economics of invasive species policy and management

Optimal spatiotemporal effort allocation for invasive species removal incorporating a removal handling time and budget

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