Correctly modeling plant-insect-herbivore-pesticide interactions as aggregate data

H. T. Banks; John E. Banks; Jared Catenacci; Michele Joyner; John Stark; H. T. Banks; John E. Banks; Jared Catenacci; Michele Joyner; John Stark

doi:10.3934/mbe.2020091

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 2: 1743-1756. doi: 10.3934/mbe.2020091

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Correctly modeling plant-insect-herbivore-pesticide interactions as aggregate data

1.
Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, 27695, USA
2.
Undergraduate Research Opportunities Center (UROC), California State University, Monterey Bay, Seaside, CA 93955, USA
3.
The Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, USA
4.
Department of Mathematics & Statistics, East Tennessee State University, Johnson City, TN 37614, USA
5.
Department of Entomology, Washington State University, Puyallup, WA 98371, USA

Received: 31 July 2019 Accepted: 19 November 2019 Published: 13 December 2019

We consider a population dynamics model in investigating data from controlled experiments with aphids in broccoli patches surrounded by different margin types (bare or weedy ground) and three levels of insecticide spray (no, light, or heavy spray). The experimental data is clearly aggregate in nature. In previous efforts ^[1], the aggregate nature of the data was ignored. In this paper, we embrace this aspect of the experiment and correctly model the data as aggregate data, comparing the results to the previous approach. We discuss cases in which the approach may provide similar results as well as cases in which there is a clear difference in the resulting fit to the data.
- plant-insect interactions,
- inverse problems,
- hypothesis testing and standard errors in dynamical models,
- aggregate data,
- Prohorov metric
Citation: H. T. Banks, John E. Banks, Jared Catenacci, Michele Joyner, John Stark. Correctly modeling plant-insect-herbivore-pesticide interactions as aggregate data[J]. Mathematical Biosciences and Engineering, 2020, 17(2): 1743-1756. doi: 10.3934/mbe.2020091

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Abstract

We consider a population dynamics model in investigating data from controlled experiments with aphids in broccoli patches surrounded by different margin types (bare or weedy ground) and three levels of insecticide spray (no, light, or heavy spray). The experimental data is clearly aggregate in nature. In previous efforts ^[1], the aggregate nature of the data was ignored. In this paper, we embrace this aspect of the experiment and correctly model the data as aggregate data, comparing the results to the previous approach. We discuss cases in which the approach may provide similar results as well as cases in which there is a clear difference in the resulting fit to the data.

References

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[23]	P. Billingsley, Convergence of Probability Measures, Wiley, New York,1968.

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