# Optimal control of an invasive using reaction diffusion model and linear programming

Mathieu Bonneau, Fred Johnson A., Brian J. Smith, Christina M Romagosa,

Julien Martin, Frank Mazzotti

► To cite this version:

Mathieu Bonneau, Fred Johnson A., Brian J. Smith, Christina M Romagosa, Julien Martin, et al. Optimal control of an invasive using reaction diffusion model and linear programming. GEER 2017, Apr 2017, Coral Springs, Florida, United States., 2017. hal-01607506

HAL Id: hal-01607506

https://hal.science/hal-01607506

Submitted on 2 Jun 2020

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Distributed under a Creative Commons Attribution - ShareAlike 4.0 International License
OPTIMAL CONTROL OF AN
INVASIVE USING REACTION
DIFFUSION MODEL AND
LINEAR PROGRAMMING

**Mathieu Bonneau**¹, Fred A. Johnson², Brian J. Smith³, Christina M. Romagosa¹, Julien Martin², and Frank J. Mazzotti³.

¹ Department of Wildlife Ecology and Conservation.
**University of Florida.**
Gainesville, Florida.

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UNIVERSITY of
FLORIDA

² Wetland and Aquatic Research Center.
**U.S. Geological Survey.**
Gainesville, Florida.

³Research and Education Center
**University of Florida.**
Ft Lauderdale, Florida.

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USGS

science for a changing world
Problem

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* Where and how much to allocate control effort?

* In an ideal world:

* **Survey:** to know where is the species.

* **Experiment:** to understand the potential harms and the population's dynamic.

* **Decide:** where and how much to control.
Problem

* Where and how much to allocate control effort?

* In an **ideal** world:

* **Survey**: to know where is the species.

* **Experiment**: to understand the **potential harms** and the **population's dynamic**.

* **Decide**: where and how much to control.

Suitability Index
Species Distribution Model
Mark Recapture

Occupancy Model
Individual Based Model

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# Reaction-Diffusion (RD) Model

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* General Pattern

* General Pattern

* Low number of parameters

* Low number of parameters

## HYPOTHESIS

* Point of first introduction.

* Population growth $\epsilon$ and diffusion $D$.

* Smooth diffusion:

* 98% of the population in the circle of radius $2\sqrt{4Dt}$
# RD model for Tegus

* Growth rate $\epsilon$ from expert elicitation

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Distribution of simulated growth rates based on a 3-point elicitation from 10 equally weighted experts.
# RD model for Tegus

* Diffusion coefficient from EDDMaps

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* EDDMaps presence only data, accessed in 2015.

* Estimation of the diffusion coefficient based on the cumulative occupied area.

* Not all the area is sampled equally.

Large Uncertainty
# Uncertainty: 25 possible population's dynamic model

* Different **growth rates**:

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* Possible **associated rates of spread**:

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Predictions: Worst Case

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Most likely out of the 25 models

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Predictions: Envelope

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Optimization

* How to minimize tegu's population with a fixed number of traps?

* Equivalently, how to maximize the number of removed tegus?
# Minimize tegus population

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Nb of traps per cell

Risk attitude

**Best – Worst**
Does best in the worst case

**Best – Average**
Does best in the average case

**Best – Best**
Does best in the best case

Concentrate traps close to the point of first introduction

Spread the traps as much as possible
# Minimize tegus population

* Current cpue = 0,035 (8,33 catch per season) and 300 traps.

* 5 traps maximal per cell (500m by 500m).

* Control starts in 2016

* No traps in Ag and urban area

Predictions (number of tegus)

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Control Strategy (number of traps)

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# Minimize tegus population

* cpue = 5 * 0,035 (41,6 catch per season) and 300 traps.

* 5 traps maximal per cell (500m by 500m).

* Control starts in 2016

* No traps in Ag and urban area

cpue increases

## Predictions (number of tegus)

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## Control Strategy (number of traps)

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# Minimize tegus population

* cpue = 5 * 0,035 (41,6 catch per season) and 500 traps.

* 5 traps maximal per cell (500m by 500m).

cpue increases

* Control starts in 2016

Number of traps increases

* No traps in Ag and urban area

<figure><img src="image_28.png" /><figcaption>Control Strategy (number of traps)</figcaption></figure>

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# Minimize tegus population

* cpue = 5 * 0,035 (41,6 catch per season) and 800 traps.

* 5 traps maximal per cell (500m by 500m).

* Control starts in 2016

* No traps in Ag and urban area

cpue increases

Number of traps increases

## Predictions (number of tegus)

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## Control Strategy (number of traps)

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No traps in Ag and urban area

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Traps everywhere

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Conclusion

➤ An optimization framework to optimize allocation of control effort under constraints

➤ Budget / Containment / Area prioritization

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➤ Important to define the objective(s) and then ask how to best allocate traps

* Even if density can decrease punctually, if there is several satellite populations, they may explode later and the situation will become out of control.

* Toward a dynamic optimization framework to increase efficacy.
Acknowledgment

* USGS Invasive Species Program.

* Greater Everglades Priority Ecosystem Science.

* University of Florida

* IFAS and Department of Wildlife Ecology and Conservation.