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Optimal design for dynamical modeling of pest populations

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  • We apply SE-optimal design methodology to investigate optimal data collection procedures as a first step in investigating information content in ecoinformatics data sets. To illustrate ideas we use a simple phenomenological citrus red mite population model for pest dynamics. First the optimal sampling distributions for a varying number of data points are determined. We then analyze these optimal distributions by comparing the standard errors of parameter estimates corresponding to each distribution. This allows us to investigate how many data are required to have confidence in model parameter estimates in order to employ dynamical modeling to infer population dynamics. Our results suggest that a field researcher should collect at least 12 data points at the optimal times. Data collected according to this procedure along with dynamical modeling will allow us to estimate population dynamics from presence/absence-based data sets through the development of a scaling relationship. These Likert-type data sets are commonly collected by agricultural pest management consultants and are increasingly being used in ecoinformatics studies. By applying mathematical modeling with the relationship scale from the new data, we can then explore important integrated pest management questions using past and future presence/absence data sets.

    Mathematics Subject Classification: 34L30, 90C30, 34A55, 65L09.


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  • Figure 1.  Traditional sensitivities for model parameters

    Figure 2.  Optimized meshes resulting from SE-optimal implementation

    Figure 3.  Relationship between sampling distribution and corresponding performance (cost)

    Figure 4.  Average standard errors (over 1000 MC trials) for each parameter, comparing optimized versus uniform grids for N = 6, 12, 18, 24, and 30

    Figure 5.  Confidence intervals for each parameter for N = 6, 12, 18, 24, and 30 on the optimized grids

    Figure 6.  Heaviside functions and Dirac delta "functions"

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      H. T. Banks , K. Bekele-Maxwell , L. Bociu , M. Noorman  and  K. Tillman , The complex-step method for sensitivity analysis of non-smooth problems arising in biology, Eurasian Journal of Mathematical and Computer Applications, 3 (2015) , 15-68. 
      H. T. Banks, A. Cintron-Arias and F. Kappel, Parameter selection methods in inverse problem formulation, CRSC-TR10-03, N. C. State University, February, 2010, Revised, November, 2010; in Mathematical Modeling and Validation in Physiology: Application to the Cardiovascular and Respiratory Systems, (J. J. Batzel, M. Bachar, and F. Kappel, eds.), 43-73, Lecture Notes in Mathematics, 2064, Springer-Verlag, Berlin 2013.
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      H. T. Banks and M. L. Joyner, Information Content in Data Sets: A Review of Methods for Interrogation and Model Comparison, CRSC-TR17-14, N. C. State University, Raleigh, NC, June, 2017. doi: 10.1515/jiip-2017-0096.
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