# American Institute of Mathematical Sciences

August  2018, 15(4): 993-1010. doi: 10.3934/mbe.2018044

## Optimal design for dynamical modeling of pest populations

 1 Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8212, USA 2 Undergraduate Research Opportunities Center (UROC), California State University, Monterey Bay, Seaside, CA 93955, USA 3 Department of Entomology and Nematology, Center for Population Biology, University of California, Davis, CA 95616, USA

Received  July 31, 2017 Accepted  November 30, 2017 Published  March 2018

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.

Citation: H. T. Banks, R. A. Everett, Neha Murad, R. D. White, J. E. Banks, Bodil N. Cass, Jay A. Rosenheim. Optimal design for dynamical modeling of pest populations. Mathematical Biosciences & Engineering, 2018, 15 (4) : 993-1010. doi: 10.3934/mbe.2018044
##### References:

show all references

##### References:
Optimized meshes resulting from SE-optimal implementation
Relationship between sampling distribution and corresponding performance (cost)
Average standard errors (over 1000 MC trials) for each parameter, comparing optimized versus uniform grids for N = 6, 12, 18, 24, and 30
Confidence intervals for each parameter for N = 6, 12, 18, 24, and 30 on the optimized grids
Heaviside functions and Dirac delta "functions"
 [1] Luis F. Gordillo. Optimal sterile insect release for area-wide integrated pest management in a density regulated pest population. Mathematical Biosciences & Engineering, 2014, 11 (3) : 511-521. doi: 10.3934/mbe.2014.11.511 [2] Santiago Campos-Barreiro, Jesús López-Fidalgo. KL-optimal experimental design for discriminating between two growth models applied to a beef farm. Mathematical Biosciences & Engineering, 2016, 13 (1) : 67-82. doi: 10.3934/mbe.2016.13.67 [3] Bin Li, Kok Lay Teo, Cheng-Chew Lim, Guang Ren Duan. An optimal PID controller design for nonlinear constrained optimal control problems. Discrete & Continuous Dynamical Systems - B, 2011, 16 (4) : 1101-1117. doi: 10.3934/dcdsb.2011.16.1101 [4] Sanyi Tang, Lansun Chen. Modelling and analysis of integrated pest management strategy. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 759-768. doi: 10.3934/dcdsb.2004.4.759 [5] Guirong Jiang, Qishao Lu, Linping Peng. Impulsive Ecological Control Of A Stage-Structured Pest Management System. Mathematical Biosciences & Engineering, 2005, 2 (2) : 329-344. doi: 10.3934/mbe.2005.2.329 [6] Mohsen Abdolhosseinzadeh, Mir Mohammad Alipour. Design of experiment for tuning parameters of an ant colony optimization method for the constrained shortest Hamiltonian path problem in the grid networks. Numerical Algebra, Control & Optimization, 2020  doi: 10.3934/naco.2020028 [7] Benedetto Piccoli. Optimal syntheses for state constrained problems with application to optimization of cancer therapies. Mathematical Control & Related Fields, 2012, 2 (4) : 383-398. doi: 10.3934/mcrf.2012.2.383 [8] Fan Jiang, Zhongming Wu, Xingju Cai. Generalized ADMM with optimal indefinite proximal term for linearly constrained convex optimization. Journal of Industrial & Management Optimization, 2020, 16 (2) : 835-856. doi: 10.3934/jimo.2018181 [9] Faustino Maestre, Pablo Pedregal. Dynamic materials for an optimal design problem under the two-dimensional wave equation. Discrete & Continuous Dynamical Systems - A, 2009, 23 (3) : 973-990. doi: 10.3934/dcds.2009.23.973 [10] Hyeon Je Cho, Ganguk Hwang. Optimal design for dynamic spectrum access in cognitive radio networks under Rayleigh fading. Journal of Industrial & Management Optimization, 2012, 8 (4) : 821-840. doi: 10.3934/jimo.2012.8.821 [11] Junjie Peng, Ning Chen, Jiayang Dai, Weihua Gui. A goethite process modeling method by asynchronous fuzzy cognitive Network based on an improved constrained chicken swarm optimization algorithm. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020021 [12] Alexandre Bayen, Rinaldo M. Colombo, Paola Goatin, Benedetto Piccoli. Traffic modeling and management: Trends and perspectives. Discrete & Continuous Dynamical Systems - S, 2014, 7 (3) : i-ii. doi: 10.3934/dcdss.2014.7.3i [13] Marco V. Martinez, Suzanne Lenhart, K. A. Jane White. Optimal control of integrodifference equations in a pest-pathogen system. Discrete & Continuous Dynamical Systems - B, 2015, 20 (6) : 1759-1783. doi: 10.3934/dcdsb.2015.20.1759 [14] Ernesto Aranda, Pablo Pedregal. Constrained envelope for a general class of design problems. Conference Publications, 2003, 2003 (Special) : 30-41. doi: 10.3934/proc.2003.2003.30 [15] Shuhua Zhang, Xinyu Wang, Hua Li. Modeling and computation of water management by real options. Journal of Industrial & Management Optimization, 2018, 14 (1) : 81-103. doi: 10.3934/jimo.2017038 [16] Xiaodi Bai, Xiaojin Zheng, Xiaoling Sun. A survey on probabilistically constrained optimization problems. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 767-778. doi: 10.3934/naco.2012.2.767 [17] Donglei Du, Tianping Shuai. Errata to:''Optimal preemptive online scheduling to minimize $l_{p}$ norm on two processors''[Journal of Industrial and Management Optimization, 1(3) (2005), 345-351.]. Journal of Industrial & Management Optimization, 2008, 4 (2) : 339-341. doi: 10.3934/jimo.2008.4.339 [18] Andrew J. Whittle, Suzanne Lenhart, Louis J. Gross. Optimal control for management of an invasive plant species. Mathematical Biosciences & Engineering, 2007, 4 (1) : 101-112. doi: 10.3934/mbe.2007.4.101 [19] Shi'an Wang, N. U. Ahmed. Optimum management of the network of city bus routes based on a stochastic dynamic model. Journal of Industrial & Management Optimization, 2019, 15 (2) : 619-631. doi: 10.3934/jimo.2018061 [20] Shaojun Lan, Yinghui Tang, Miaomiao Yu. System capacity optimization design and optimal threshold $N^{*}$ for a $GEO/G/1$ discrete-time queue with single server vacation and under the control of Min($N, V$)-policy. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1435-1464. doi: 10.3934/jimo.2016.12.1435

2018 Impact Factor: 1.313