Article Contents
Article Contents

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

• 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.
Mathematics Subject Classification: 34A55, 65L09, 62G05.

 Citation:

•  [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), 73-84.doi: 10.1016/j.mbs.2015.06.003. [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), 12-16.doi: 10.1016/j.aml.2014.12.014. [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), 2139-2180.doi: 10.1007/s11538-007-9207-z. [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, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, November, 2015. [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), 316-332.doi: 10.1016/j.mcm.2007.10.005. [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), 155-160.doi: 10.1016/j.ecolmodel.2007.07.022. [7] H. T. Banks, S. Hu and W. C. Thompson, Modeling and Inverse Problems in the Presence of Uncertainty, CRC Press, New York, 2014. [8] H. T. Banks and H. T. Tran, Mathematical and Experimental Modeling of Physical and Biological Processes, CRC Press, New York, 2009. [9] J. R. Carey, Applied Demography for Biologists with Special Emphasis on Insects, Oxford University Press, Oxford, 1993. [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), 1544-1556.doi: 10.1002/etc.5620180729. [11] V. E. Forbes and P. Calow, Extrapolation in ecological risk assessment: Balancing pragmatism and precaution in chemical controls legislation, Bioscience, 52 (2002), 249-257. [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, London, B: Biological Sciences, 357 (2002), 1299-1306. [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), 1268-1276.doi: 10.1007/s10646-011-0675-4. [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), 262-270.doi: 10.1002/ieam.272. [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), 325-337.doi: 10.1002/ieam.69. [16] M. Kot, Elements of Mathematical Ecology, Cambridge University Press, Cambridge, 2001.doi: 10.1017/CBO9780511608520. [17] J. D. Stark and J. E. Banks, Developing Demographic Toxicity Data: Optimizing Effort for Predicting Population Outcomes, PeerJ, submitted, 2015.