Phosphine Mortality Estimation for Simulation of Controlling Pest of Stored Grain: Lesser Grain Borer (Rhyzopertha dominica)

Authors: Mingren Shi, Michael Renton

Abstract:

There is a world-wide need for the development of sustainable management strategies to control pest infestation and the development of phosphine (PH3) resistance in lesser grain borer (Rhyzopertha dominica). Computer simulation models can provide a relatively fast, safe and inexpensive way to weigh the merits of various management options. However, the usefulness of simulation models relies on the accurate estimation of important model parameters, such as mortality. Concentration and time of exposure are both important in determining mortality in response to a toxic agent. Recent research indicated the existence of two resistance phenotypes in R. dominica in Australia, weak and strong, and revealed that the presence of resistance alleles at two loci confers strong resistance, thus motivating the construction of a two-locus model of resistance. Experimental data sets on purified pest strains, each corresponding to a single genotype of our two-locus model, were also available. Hence it became possible to explicitly include mortalities of the different genotypes in the model. In this paper we described how we used two generalized linear models (GLM), probit and logistic models, to fit the available experimental data sets. We used a direct algebraic approach generalized inverse matrix technique, rather than the traditional maximum likelihood estimation, to estimate the model parameters. The results show that both probit and logistic models fit the data sets well but the former is much better in terms of small least squares (numerical) errors. Meanwhile, the generalized inverse matrix technique achieved similar accuracy results to those from the maximum likelihood estimation, but is less time consuming and computationally demanding.

Keywords: mortality estimation, probit models, logistic model, generalized inverse matrix approach, pest control simulation

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1079090

References:

[1] Ben-Israel A, Greville TNE (2003) Generalized Inverses: Theory and Applications, 2nd ed. New York, NY: Springer
[2] Bliss CI (1940) The relation between exposure time, concentration and toxicity in experiments on insecticides. Annals of the Entomological Society of America 33(4): pp. 721-766
[3] Collins PJ (1998) Resistance to grain protectants and fumigants in insect pests of stored products in Australia. In: Proc First Australian Postharvest Technical Conference (ed by Banks HJ, et al) Canberra, Australia, pp 55-57
[4] Collins PJ, Daglish GJ, Bengston M, Lambkin TM, Pavic H (2002) Genetics of resistance to phosphine in Rhyzopertha dominica (Coleoptera: Bostrichidae). Journal of Economic Entomology 95(4): 862-869
[5] Collins PJ, Daglish, GJ, Pavic, H, Kopittke, RA (2005) Response of mixed-age cultures of phosphine resistant and susceptible strains of lesser grain borer, Rhyzopertha dominica, to phosphine at a range of concentrations and exposure periods. Journal of Stored Products Research 41: 373-385
[6] Dobson AJ, Barnett AG (2008) Introduction to Generalized Linear Models (3rd ed.), Boca Raton, FL: Chapman and Hall/CRC
[7] Finney DJ (1971) Probit Analysis (3rd ed.) Cambridge University Press
[8] Hagstrum, D.W., Flinn, P.W. (1990) Simulations comparing insect species differences in response to wheat storage conditions and management practices. Journal of Economic Entomology 83 (6) 2469- 2475.
[9] Pimentel MAG, Faroni LA, Totola MR, Guedes RNC (2007). Phosphine resistance, respiration rate and fitness consequences in stored-product insects. Pest Manag Sci 63: 876-881
[10] Schlipalius DI, Collins PJ, Mau Y, Ebert PR (2006) New tools for management of phosphine resistance. Outlooks on Pest Management 17: 52-56
[11] Schlipalius DI, Chen W, Collins PJ, Nguyen T, Reilly PEB, Ebert PR (2008) Gene interactions constrain the course of evolution of phosphine resistance in the lesser grain borer, Rhyzopertha dominica. Heredity 100: 506-516
[12] Shi M, Renton M (2011) Numerical algorithms for estimation and calculation of parameters in modelling pest population dynamics and evolution of resistance in modelling pest population dynamics and evolution of resistance. Mathematical Biosciences, 233(2): 77-89
[13] Shi M, Renton M, Ridsdill-Smith J, Collins PJ (2002) Constructing a new individual-based model of phosphine resistance in lesser grain borer (Rhyzopertha dominica): do we need to include two loci rather than one? Pest Science, in press, DOI 10.1007/s10340-012-0421-6
[14] Wolberg JR (2005) Data analysis using the method of least squares: extracting the most information from experiments. Springer.