2016, 13(4): 653-671. doi: 10.3934/mbe.2016013

An adaptive feedback methodology for determining information content in stable population studies

1. 

Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8212

2. 

Undergraduate Research Opportunities Center (UROC), California State University, Monterey Bay, United States

3. 

Center for Research in Scienti c Computation, North Carolina State University, Raleigh, NC 27695-8212, United States

4. 

Ecotoxicology Program, WSU Puyallup Research, Extension Center, Puyallup, WA 98371-4998, United States

Received  November 2015 Revised  February 2016 Published  May 2016

We develop statistical and mathematical based methodologies for determining (as the experiment progresses) the amount of information required to complete the estimation of stable population parameters with pre-specified levels of confidence. We do this in the context of life table models and data for growth/death for three species of Daphniids as investigated by J. Stark and J. Banks [17]. The ideas developed here also have wide application in the health and social sciences where experimental data are often expensive as well as difficult to obtain.
Citation: H. T. Banks, John E. Banks, R. A. Everett, John D. Stark. An adaptive feedback methodology for determining information content in stable population studies. Mathematical Biosciences & Engineering, 2016, 13 (4) : 653-671. doi: 10.3934/mbe.2016013
References:
[1]

K. Adoteye, H. T. Banks, K. Cross, S. Eytcheson, K. B. Flores, G. A. LeBlanc, T. Nguyen, C. Ross, E. Smith, M. Stemkovski and S. Stokely, Statistical validation of structured population models for Daphnia magna,, Mathematical Biosciences, 266 (2015), 73.  doi: 10.1016/j.mbs.2015.06.003.  Google Scholar

[2]

K. Adoteye, H. T. Banks, K. B. Flores and G. A. LeBlanc, Estimation of time-varying mortality rates using continuous models for Daphnia magna,, Applied Mathematical Letters, 44 (2015), 12.  doi: 10.1016/j.aml.2014.12.014.  Google Scholar

[3]

H. T. Banks, J. E. Banks, L. K. Dick and J. D. Stark, Estimation of dynamic rate parameters in insect populations undergoing sublethal exposure to pesticides,, Bulletin of Mathematical Biology, 69 (2007), 2139.  doi: 10.1007/s11538-007-9207-z.  Google Scholar

[4]

H. T. Banks, J. E. Banks, R. Everett and J. Stark, An Adaptive Feedback Methodology for Determining Information Content in Population Studies,, CRSC-TR15-12, (2015), 15.   Google Scholar

[5]

H. T. Banks, J. E. Banks, S. J. Joyner and J. D. Stark, Dynamic models for insect mortality due to exposure to insecticides,, Mathematical and Computer Modeling, 48 (2008), 316.  doi: 10.1016/j.mcm.2007.10.005.  Google Scholar

[6]

J. E. Banks, L. K. Dick, H. T. Banks and J. D. Stark, Time-varying vital rates in ecotoxicology: Selective pesticides and aphid population dynamics,, Ecological Modeling, 210 (2008), 155.  doi: 10.1016/j.ecolmodel.2007.07.022.  Google Scholar

[7]

H. T. Banks, S. Hu and W. C. Thompson, Modeling and Inverse Problems in the Presence of Uncertainty,, CRC Press, (2014).   Google Scholar

[8]

H. T. Banks and H. T. Tran, Mathematical and Experimental Modeling of Physical and Biological Processes,, CRC Press, (2009).   Google Scholar

[9]

J. R. Carey, Applied Demography for Biologists with Special Emphasis on Insects,, Oxford University Press, (1993).   Google Scholar

[10]

V. E. Forbes and P. Calow, Is the per capita rate of increase a good measure of population-level effects in ecotoxicology?, Environmental Toxicology and Chemistry, 18 (1999), 1544.  doi: 10.1002/etc.5620180729.  Google Scholar

[11]

V. E. Forbes and P. Calow, Extrapolation in ecological risk assessment: Balancing pragmatism and precaution in chemical controls legislation,, Bioscience, 52 (2002), 249.   Google Scholar

[12]

V. E. Forbes and P. Calow, Population growth rate as a basis for ecological risk assessment of toxic chemicals,, Philosophical Transaction of the Royal Society, 357 (2002), 1299.   Google Scholar

[13]

N. Hanson and J. D. Stark, A comparison of simple and complex population models to reduce uncertainty in ecological risk assessments of chemicals: Example with three species of Daphnia,, Ecotoxicology, 20 (2011), 1268.  doi: 10.1007/s10646-011-0675-4.  Google Scholar

[14]

N. Hanson and J. D. Stark, Utility of population models to reduce uncertainty and increase value relevance in ecological risk assessments of pesticides: An example based on acute mortality data for Daphnids,, Integrated Environmental Assessment and Management, 8 (2012), 262.  doi: 10.1002/ieam.272.  Google Scholar

[15]

U. Hommen, J. M. Baveco, N. Galic and P. J. van den Brink, Potential application of ecological models in the European environmental risk assessment of chemicals I: review of protection goals in EU directives and regulations,, Integrated Environmental Assessment and Management, 6 (2010), 325.  doi: 10.1002/ieam.69.  Google Scholar

[16]

M. Kot, Elements of Mathematical Ecology,, Cambridge University Press, (2001).  doi: 10.1017/CBO9780511608520.  Google Scholar

[17]

J. D. Stark and J. E. Banks, Developing Demographic Toxicity Data: Optimizing Effort for Predicting Population Outcomes,, PeerJ, (2015).   Google Scholar

show all references

References:
[1]

K. Adoteye, H. T. Banks, K. Cross, S. Eytcheson, K. B. Flores, G. A. LeBlanc, T. Nguyen, C. Ross, E. Smith, M. Stemkovski and S. Stokely, Statistical validation of structured population models for Daphnia magna,, Mathematical Biosciences, 266 (2015), 73.  doi: 10.1016/j.mbs.2015.06.003.  Google Scholar

[2]

K. Adoteye, H. T. Banks, K. B. Flores and G. A. LeBlanc, Estimation of time-varying mortality rates using continuous models for Daphnia magna,, Applied Mathematical Letters, 44 (2015), 12.  doi: 10.1016/j.aml.2014.12.014.  Google Scholar

[3]

H. T. Banks, J. E. Banks, L. K. Dick and J. D. Stark, Estimation of dynamic rate parameters in insect populations undergoing sublethal exposure to pesticides,, Bulletin of Mathematical Biology, 69 (2007), 2139.  doi: 10.1007/s11538-007-9207-z.  Google Scholar

[4]

H. T. Banks, J. E. Banks, R. Everett and J. Stark, An Adaptive Feedback Methodology for Determining Information Content in Population Studies,, CRSC-TR15-12, (2015), 15.   Google Scholar

[5]

H. T. Banks, J. E. Banks, S. J. Joyner and J. D. Stark, Dynamic models for insect mortality due to exposure to insecticides,, Mathematical and Computer Modeling, 48 (2008), 316.  doi: 10.1016/j.mcm.2007.10.005.  Google Scholar

[6]

J. E. Banks, L. K. Dick, H. T. Banks and J. D. Stark, Time-varying vital rates in ecotoxicology: Selective pesticides and aphid population dynamics,, Ecological Modeling, 210 (2008), 155.  doi: 10.1016/j.ecolmodel.2007.07.022.  Google Scholar

[7]

H. T. Banks, S. Hu and W. C. Thompson, Modeling and Inverse Problems in the Presence of Uncertainty,, CRC Press, (2014).   Google Scholar

[8]

H. T. Banks and H. T. Tran, Mathematical and Experimental Modeling of Physical and Biological Processes,, CRC Press, (2009).   Google Scholar

[9]

J. R. Carey, Applied Demography for Biologists with Special Emphasis on Insects,, Oxford University Press, (1993).   Google Scholar

[10]

V. E. Forbes and P. Calow, Is the per capita rate of increase a good measure of population-level effects in ecotoxicology?, Environmental Toxicology and Chemistry, 18 (1999), 1544.  doi: 10.1002/etc.5620180729.  Google Scholar

[11]

V. E. Forbes and P. Calow, Extrapolation in ecological risk assessment: Balancing pragmatism and precaution in chemical controls legislation,, Bioscience, 52 (2002), 249.   Google Scholar

[12]

V. E. Forbes and P. Calow, Population growth rate as a basis for ecological risk assessment of toxic chemicals,, Philosophical Transaction of the Royal Society, 357 (2002), 1299.   Google Scholar

[13]

N. Hanson and J. D. Stark, A comparison of simple and complex population models to reduce uncertainty in ecological risk assessments of chemicals: Example with three species of Daphnia,, Ecotoxicology, 20 (2011), 1268.  doi: 10.1007/s10646-011-0675-4.  Google Scholar

[14]

N. Hanson and J. D. Stark, Utility of population models to reduce uncertainty and increase value relevance in ecological risk assessments of pesticides: An example based on acute mortality data for Daphnids,, Integrated Environmental Assessment and Management, 8 (2012), 262.  doi: 10.1002/ieam.272.  Google Scholar

[15]

U. Hommen, J. M. Baveco, N. Galic and P. J. van den Brink, Potential application of ecological models in the European environmental risk assessment of chemicals I: review of protection goals in EU directives and regulations,, Integrated Environmental Assessment and Management, 6 (2010), 325.  doi: 10.1002/ieam.69.  Google Scholar

[16]

M. Kot, Elements of Mathematical Ecology,, Cambridge University Press, (2001).  doi: 10.1017/CBO9780511608520.  Google Scholar

[17]

J. D. Stark and J. E. Banks, Developing Demographic Toxicity Data: Optimizing Effort for Predicting Population Outcomes,, PeerJ, (2015).   Google Scholar

[1]

Yanfei Lu, Qingfei Yin, Hongyi Li, Hongli Sun, Yunlei Yang, Muzhou Hou. Solving higher order nonlinear ordinary differential equations with least squares support vector machines. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-22. doi: 10.3934/jimo.2019012

[2]

Zhou Sheng, Gonglin Yuan, Zengru Cui, Xiabin Duan, Xiaoliang Wang. An adaptive trust region algorithm for large-residual nonsmooth least squares problems. Journal of Industrial & Management Optimization, 2018, 14 (2) : 707-718. doi: 10.3934/jimo.2017070

[3]

Mahendra Piraveenan, Mikhail Prokopenko, Albert Y. Zomaya. On congruity of nodes and assortative information content in complex networks. Networks & Heterogeneous Media, 2012, 7 (3) : 441-461. doi: 10.3934/nhm.2012.7.441

[4]

C. Bonanno. The algorithmic information content for randomly perturbed systems. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 921-934. doi: 10.3934/dcdsb.2004.4.921

[5]

Yunhai Xiao, Soon-Yi Wu, Bing-Sheng He. A proximal alternating direction method for $\ell_{2,1}$-norm least squares problem in multi-task feature learning. Journal of Industrial & Management Optimization, 2012, 8 (4) : 1057-1069. doi: 10.3934/jimo.2012.8.1057

[6]

Pedro Caro. On an inverse problem in electromagnetism with local data: stability and uniqueness. Inverse Problems & Imaging, 2011, 5 (2) : 297-322. doi: 10.3934/ipi.2011.5.297

[7]

Victor Isakov. On uniqueness in the inverse conductivity problem with local data. Inverse Problems & Imaging, 2007, 1 (1) : 95-105. doi: 10.3934/ipi.2007.1.95

[8]

Ya-Xiang Yuan. Recent advances in numerical methods for nonlinear equations and nonlinear least squares. Numerical Algebra, Control & Optimization, 2011, 1 (1) : 15-34. doi: 10.3934/naco.2011.1.15

[9]

Mila Nikolova. Analytical bounds on the minimizers of (nonconvex) regularized least-squares. Inverse Problems & Imaging, 2008, 2 (1) : 133-149. doi: 10.3934/ipi.2008.2.133

[10]

Hassan Mohammad, Mohammed Yusuf Waziri, Sandra Augusta Santos. A brief survey of methods for solving nonlinear least-squares problems. Numerical Algebra, Control & Optimization, 2019, 9 (1) : 1-13. doi: 10.3934/naco.2019001

[11]

Subrata Dasgupta. Disentangling data, information and knowledge. Big Data & Information Analytics, 2016, 1 (4) : 377-389. doi: 10.3934/bdia.2016016

[12]

Francis J. Chung. Partial data for the Neumann-Dirichlet magnetic Schrödinger inverse problem. Inverse Problems & Imaging, 2014, 8 (4) : 959-989. doi: 10.3934/ipi.2014.8.959

[13]

Valter Pohjola. An inverse problem for the magnetic Schrödinger operator on a half space with partial data. Inverse Problems & Imaging, 2014, 8 (4) : 1169-1189. doi: 10.3934/ipi.2014.8.1169

[14]

Li Liang. Increasing stability for the inverse problem of the Schrödinger equation with the partial Cauchy data. Inverse Problems & Imaging, 2015, 9 (2) : 469-478. doi: 10.3934/ipi.2015.9.469

[15]

Suman Kumar Sahoo, Manmohan Vashisth. A partial data inverse problem for the convection-diffusion equation. Inverse Problems & Imaging, 2020, 14 (1) : 53-75. doi: 10.3934/ipi.2019063

[16]

Yun Chen, Jiasheng Huang, Si Li, Yao Lu, Yuesheng Xu. A content-adaptive unstructured grid based integral equation method with the TV regularization for SPECT reconstruction. Inverse Problems & Imaging, 2020, 14 (1) : 27-52. doi: 10.3934/ipi.2019062

[17]

JaEun Ku. Maximum norm error estimates for Div least-squares method for Darcy flows. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1305-1318. doi: 10.3934/dcds.2010.26.1305

[18]

Yun Cai, Song Li. Convergence and stability of iteratively reweighted least squares for low-rank matrix recovery. Inverse Problems & Imaging, 2017, 11 (4) : 643-661. doi: 10.3934/ipi.2017030

[19]

Runchang Lin, Huiqing Zhu. A discontinuous Galerkin least-squares finite element method for solving Fisher's equation. Conference Publications, 2013, 2013 (special) : 489-497. doi: 10.3934/proc.2013.2013.489

[20]

H. D. Scolnik, N. E. Echebest, M. T. Guardarucci. Extensions of incomplete oblique projections method for solving rank-deficient least-squares problems. Journal of Industrial & Management Optimization, 2009, 5 (2) : 175-191. doi: 10.3934/jimo.2009.5.175

2018 Impact Factor: 1.313

Metrics

  • PDF downloads (11)
  • HTML views (0)
  • Cited by (0)

[Back to Top]