# Climate Smart Pest Management

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The General Conceptual Framework

#### 2.2. The Specific Case

**Proposition 1.**

## 3. Empirical Analyses

#### 3.1. Objective Function

#### 3.2. State Equations

#### 3.3. Data and Model Parameters

## 4. Results

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Proof of Equation (3)

## Appendix B. Proof of Equation (7)

## Appendix C. Proof of Equation (13)

## Appendix D. Proof of Equation (15)

## Appendix E. Proof of Equation (19)

## Appendix F. Proof of Proposition 1

**Proof.**

Par. | Value (Unit) | Source | Description |
---|---|---|---|

${\sigma}^{A}$ | 0.351 | Regression Analysis | Standard deviation of aphid diffusion |

${\sigma}^{\theta}$ | 0.121 | Regression Analysis | Standard deviation of weather diffusion |

${\mu}^{A}$ | 0.30 | Regression Analysis | Growth rate of aphid |

${\mu}^{Y}$ | 0.137 | Regression Analysis | Growth rate of crop |

$\rho $ | 0 | Regression Analysis | Correlation coefficient between weather |

and aphid variation (${\rho}^{\tilde{A}\tilde{\theta}}$) | |||

T | 14 weeks | Oplinger et al. (1990) [48] | A full growing season |

$\alpha $ | 0.25 | Regression Analysis | Marginal weather effect on aphid growth |

$\beta $ | 0.85 | Elbakidze et al. (2011) [15] | Pesticide efficiency |

$\gamma $ | −0.074 | Regression Analysis | Marginal weather effect on biomass growth |

r | 0.0035 | Marsh et al. (2000) [16] | Discount rate |

P | 0.295 $/lb | Painter (2011) [49] | Per pound lentil price |

W | 4.84 $/Acre | Painter (2011) [49] | Per acre pesticide cost |

A(0) | 1 | Assumed | Initial number of aphids |

${A}_{max}$ | $1.8\times {10}^{7}$ | Oplinger et al. (1990) [48] | Carrying capacity of aphid per acre |

${\mu}^{\theta}$ | 0.08 | Regression Analysis | Growth rate of weather index |

SUR Formulation (31) | Equation (32) | ||
---|---|---|---|

VARIABLES | $ln\mathbf{\theta}$ | $ln\mathbf{A}$ | $ln\mathbf{Y}$ |

$\mathrm{T}$ | 0.0372607 *** | 0.0101419 *** | |

(0.0043546) | (0.0013303) | ||

$ln\theta $ | 0.2549528 | −0.0742 | |

(0.2343415) | (0.235) | ||

A | −0.0568 * | ||

(0.0316) | |||

Constant | −2.493412 | 1.999086 | 7.751 *** |

(1.999086) | (0.1346805) | (1.764) | |

Observations | 137 | 137 | 23 |

R-squared | 0.4678 | 0.2979 | 0.16 |

Baseline Model | Climate Change Model | |||||
---|---|---|---|---|---|---|

Week | Usage w/o | Usage with | t-Test: | Usage w/o | Usage with | t-Test: |

info: ${\mathbf{Eu}}^{\mathbf{0}}$ | $\mathbf{\rho}$info:${\mathbf{Eu}}^{\mathbf{1}}$ | ${\mathbf{u}}^{\mathbf{0}}={\mathbf{u}}^{\mathbf{1}}$ | info: ${\mathbf{Eu}}^{\mathbf{2}}$ | $\mathbf{\rho}$info:${\mathbf{Eu}}^{\mathbf{3}}$ | ${\mathbf{u}}^{\mathbf{2}}={\mathbf{u}}^{\mathbf{3}}$ | |

($\mathbf{\rho}=\mathbf{0}.\mathbf{5})$ | ($\mathbf{\rho}=\mathbf{0}.\mathbf{5}$) | |||||

1 | 0 | 0.001 | 0.316 | 0 | 0.001 | 0.874 |

2 | 0.001 | 0.001 | 1 | 0 | 0.002 | 0.900 |

3 | 0.004 | 0.009 | 0.166 | 0.006 | 0.004 | 0.766 |

4 | 0.018 | 0.018 | 1 | 0.017 | 0.015 | 0.974 |

5 | 0.04 | 0.044 | 0.655 | 0.044 | 0.032 | 0.433 |

6 | 0.067 | 0.082 | 0.2 | 0.095 | 0.079 | 0.250 |

7 | 0.158 | 0.15 | 0.627 | 0.137 | 0.148 | 0.588 |

8 | 0.194 | 0.208 | 0.438 | 0.191 | 0.223 | 0.047 ** |

9 | 0.273 | 0.263 | 0.621 | 0.277 | 0.252 | 0.095 * |

10 | 0.346 | 0.33 | 0.456 | 0.313 | 0.357 | 0.022 ** |

11 | 0.401 | 0.4 | 0.965 | 0.39 | 0.406 | 0.873 |

12 | 0.431 | 0.476 | 0.04 ** | 0.443 | 0.469 | 0.065 * |

Expected | 113.24 | 122.103 | 0.000 *** | 94.25 | 106.49 | 0.008 *** |

Net Return |

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**MDPI and ACS Style**

Du, X.; Elbakidze, L.; Lu, L.; Taylor, R.G.
Climate Smart Pest Management. *Sustainability* **2022**, *14*, 9832.
https://doi.org/10.3390/su14169832

**AMA Style**

Du X, Elbakidze L, Lu L, Taylor RG.
Climate Smart Pest Management. *Sustainability*. 2022; 14(16):9832.
https://doi.org/10.3390/su14169832

**Chicago/Turabian Style**

Du, Xiaoxue, Levan Elbakidze, Liang Lu, and R. Garth Taylor.
2022. "Climate Smart Pest Management" *Sustainability* 14, no. 16: 9832.
https://doi.org/10.3390/su14169832