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2015, 12(4): 687-697. doi: 10.3934/mbe.2015.12.687

Mathematical probit and logistic mortality models of the Khapra beetle fumigated with plant essential oils

1. 

Department of Mathematics, Najran University, Najran,1988, Saudi Arabia

2. 

Zoology Department, Faculty of Science, Kafrelsheikh University, Kafr El sheikh3516, Egypt, Egypt

Received  May 2014 Revised  November 2014 Published  April 2015

In the current study, probit and logistic models were employed to fit experimental mortality data of the Khapra beetle, Trogoderma granarium (Everts) (Coleoptera: Dermestidae), when fumigated with three plant oils of the gens Achillea. A generalized inverse matrix technique was used to estimate the mortality model parameters instead of the usual statistical iterative maximum likelihood estimation. As this technique needs to perturb the observed mortality proportions if the proportions include 0 or 1, the optimal perturbation in terms of minimum least squares ($L_2$) error was also determined. According to our results, it was better to log-transform concentration and time as explanatory variables in modeling mortality of the test insect. Estimated data using the probit model were more accurate in terms of $L_2$ errors, than the logistic one. Results of the predicted mortality revealed also that extending the fumigation period could be an effective control strategy, even, at lower concentrations. Results could help in using a relatively safe and effective strategy for the control of this serious pest using alternative control strategy to reduce the health and environmental drawbacks resulted from the excessive reliance on the broadly toxic chemical pesticides and in order to contribute safeguard world-wide grain supplies.
Citation: Alhadi E. Alamir, Gomah E. Nenaah, Mohamed A. Hafiz. Mathematical probit and logistic mortality models of the Khapra beetle fumigated with plant essential oils. Mathematical Biosciences & Engineering, 2015, 12 (4) : 687-697. doi: 10.3934/mbe.2015.12.687
References:
[1]

A. Agresti, An Introduction to Categorical Data Analysis,, $2^{nd}$ edition, (2007). doi: 10.1002/0470114754.

[2]

C. H. Bell and S. M. Wilson, Phosphine tolerance and resistance in Trogoderma granarium Everts (Coleoptera: Dermestidae),, J. Stored Prod. Res., 31 (1995), 199. doi: 10.1016/0022-474X(95)00012-V.

[3]

A. Ben and T. Greville, Generalized Inverses: Theory and Applications,, Springer press, (2003).

[4]

C. I. Bliss, The relation between exposure time, concentration and toxicity in experiments on insecticides,, Ann. Entomol. Soc. Am., 33 (1940), 721. doi: 10.1093/aesa/33.4.721.

[5]

E. J. Bond, Manual of Fumigation for Insect Control,, in: FAO Plant Production and Protection Paper, (1984).

[6]

S. Boyer, H. Zhang and G. Lempérière, A review of control methods and resistance mechanisms in stored-product insects,, B. Entomol. Res., 102 (2012), 213. doi: 10.1017/S0007485311000654.

[7]

M. Q. Chaudhry, A review of the mechanisms involved in the action of phosphine as an insecticide and phosphine resistance in stored-product insects,, Pestic Sci., 49 (1997), 213. doi: 10.1002/(SICI)1096-9063(199703)49:3<213::AID-PS516>3.3.CO;2-R.

[8]

P. J. Collins, G. Daglish, H. Pavic and R. Kopittke, 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,, J. Stored Prod. Res., 41 (2005), 373. doi: 10.1016/j.jspr.2004.05.002.

[9]

P. Eliopoulos, New approaches for tackling Khapra beetle,, CAB Rev., 8 (2013), 1.

[10]

D. J. Finny, Probit Analysis,, $3^{nd}$ edition, (1971).

[11]

W. Hermawan, S. Nakajima, R. Tsukuda, K. Fujisaki and F. Nakasuji, Isolation of an antifeedant compound from Andrographis paniculata (Acanthaceae) against the diamond back, Plutella xylostella (Lepidoptera: Yponomeutidae),, Appl. Entomol. Zool, 32 (1997), 551.

[12]

M. B. Isman, Botanical insecticides, deterrents, and repellents in modern agriculture and an increasingly regulated world,, Annu. Rev. Entomol., 51 (2006), 45. doi: 10.1146/annurev.ento.51.110104.151146.

[13]

M. B. Isman, C. Machial, S. Miresmailli and L. Bainard, Essential oil-based pesticides: New insights from old chemistry,, in Pesticide Chemistry (Wiley-VCH, (2007), 201. doi: 10.1002/9783527611249.ch21.

[14]

K. Lilford, G. Fulford, D. Schlipalius and A. Ridley, Fumigation of stored-grain insects-a two locus model of phosphine resistance,, in The 18th World IMACS Congress and MODSIM09, (2009).

[15]

S. Lowe, M. Browne, S. Boudjelas and M. de Poorter, 100 of the world's worst invasive alien species, The global invasive species database,, in: World Conservation Union, (2000).

[16]

G. Nenaah, Toxic and antifeedant activities of potato glycoalkaloids against Trogoderma granarium (Coleoptera: Dermestidae),, J. Stored Prod. Res., 47 (2011), 185. doi: 10.1016/j.jspr.2010.11.003.

[17]

G. Nenaah, Chemical composition, insecticidal and repellence activities of essential oils of three Achillea species against the Khapra beetle (Coleoptera: Dermestidae),, J. Pest Sci., 87 (2014), 273. doi: 10.1007/s10340-013-0547-1.

[18]

G. Nenaah, Chemical composition, toxicity and growth inhibitory activities of essential oils of three Achillea species and their nanoemulsions against Tribolium castaneum (Herbst),, Ind. Crop Prod., 53 (2014), 252.

[19]

G. Nenaah and S. Ibrahim, Chemical composition and the insecticidal activity of certain plants applied as powders and essential oils against two stored-products coleopteran beetles,, J. Pest Sci., 84 (2011), 393. doi: 10.1007/s10340-011-0354-5.

[20]

P. Pretheep-Kumar, S. Mohan and P. Balasubramanian, Insecticide Resistance-stored-product,, mechanism and management strategies, (2010).

[21]

S. Rajendran, Postharvest pest losses. New York in: Pimentel,, in D. (Ed), (2002).

[22]

S. Rajendran and V. Sriranjini, Plant products as fumigants for stored-product insect control,, J. Stored Prod. Res., 44 (2008), 126. doi: 10.1016/j.jspr.2007.08.003.

[23]

C. Regnault-Roger, C. Vincent and J. T. Arnason, Essential oils in insect control: Low-risk products in a high-stakes world,, Annu. Rev. Entomol., 57 (2012), 405. doi: 10.1146/annurev-ento-120710-100554.

[24]

M. Shi, P. Collins, J. Smith and M. Renton, Individual-based modelling of the efficacy of fumigation tactics to control lesser grain borer (Rhyzopertha dominica) in stored grain,, J. Stored Prod. Res., 51 (2012), 23. doi: 10.1016/j.jspr.2012.06.003.

[25]

M. Shi and M. Renton, Modelling mortality of a stored grain insect pest with fumigation: Probit, logistic or Cauchy model?,, Math. Biosci., 243 (2013), 137. doi: 10.1016/j.mbs.2013.02.005.

[26]

M. Shi and M. Renton, 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,, Math. Biosci., 233 (2011), 77. doi: 10.1016/j.mbs.2011.06.005.

[27]

M. Shi, M. Renton, J. Ridsdill-Smith and P. J. Collins, 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?,, J. Pest Sci., 85 (2012), 451. doi: 10.1007/s10340-012-0421-6.

[28]

R. G. Winks, The toxicity of phosphine to adults of Tribolium castaneum (Herbst): phosphine-induced narcosis,, J. Stored Prod. Res., 21 (1985), 25. doi: 10.1016/0022-474X(85)90056-6.

[29]

J. R. Wolberg, Data analysis using the method of least squares,, Extracting the Most Information From Experiments, (2005).

show all references

References:
[1]

A. Agresti, An Introduction to Categorical Data Analysis,, $2^{nd}$ edition, (2007). doi: 10.1002/0470114754.

[2]

C. H. Bell and S. M. Wilson, Phosphine tolerance and resistance in Trogoderma granarium Everts (Coleoptera: Dermestidae),, J. Stored Prod. Res., 31 (1995), 199. doi: 10.1016/0022-474X(95)00012-V.

[3]

A. Ben and T. Greville, Generalized Inverses: Theory and Applications,, Springer press, (2003).

[4]

C. I. Bliss, The relation between exposure time, concentration and toxicity in experiments on insecticides,, Ann. Entomol. Soc. Am., 33 (1940), 721. doi: 10.1093/aesa/33.4.721.

[5]

E. J. Bond, Manual of Fumigation for Insect Control,, in: FAO Plant Production and Protection Paper, (1984).

[6]

S. Boyer, H. Zhang and G. Lempérière, A review of control methods and resistance mechanisms in stored-product insects,, B. Entomol. Res., 102 (2012), 213. doi: 10.1017/S0007485311000654.

[7]

M. Q. Chaudhry, A review of the mechanisms involved in the action of phosphine as an insecticide and phosphine resistance in stored-product insects,, Pestic Sci., 49 (1997), 213. doi: 10.1002/(SICI)1096-9063(199703)49:3<213::AID-PS516>3.3.CO;2-R.

[8]

P. J. Collins, G. Daglish, H. Pavic and R. Kopittke, 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,, J. Stored Prod. Res., 41 (2005), 373. doi: 10.1016/j.jspr.2004.05.002.

[9]

P. Eliopoulos, New approaches for tackling Khapra beetle,, CAB Rev., 8 (2013), 1.

[10]

D. J. Finny, Probit Analysis,, $3^{nd}$ edition, (1971).

[11]

W. Hermawan, S. Nakajima, R. Tsukuda, K. Fujisaki and F. Nakasuji, Isolation of an antifeedant compound from Andrographis paniculata (Acanthaceae) against the diamond back, Plutella xylostella (Lepidoptera: Yponomeutidae),, Appl. Entomol. Zool, 32 (1997), 551.

[12]

M. B. Isman, Botanical insecticides, deterrents, and repellents in modern agriculture and an increasingly regulated world,, Annu. Rev. Entomol., 51 (2006), 45. doi: 10.1146/annurev.ento.51.110104.151146.

[13]

M. B. Isman, C. Machial, S. Miresmailli and L. Bainard, Essential oil-based pesticides: New insights from old chemistry,, in Pesticide Chemistry (Wiley-VCH, (2007), 201. doi: 10.1002/9783527611249.ch21.

[14]

K. Lilford, G. Fulford, D. Schlipalius and A. Ridley, Fumigation of stored-grain insects-a two locus model of phosphine resistance,, in The 18th World IMACS Congress and MODSIM09, (2009).

[15]

S. Lowe, M. Browne, S. Boudjelas and M. de Poorter, 100 of the world's worst invasive alien species, The global invasive species database,, in: World Conservation Union, (2000).

[16]

G. Nenaah, Toxic and antifeedant activities of potato glycoalkaloids against Trogoderma granarium (Coleoptera: Dermestidae),, J. Stored Prod. Res., 47 (2011), 185. doi: 10.1016/j.jspr.2010.11.003.

[17]

G. Nenaah, Chemical composition, insecticidal and repellence activities of essential oils of three Achillea species against the Khapra beetle (Coleoptera: Dermestidae),, J. Pest Sci., 87 (2014), 273. doi: 10.1007/s10340-013-0547-1.

[18]

G. Nenaah, Chemical composition, toxicity and growth inhibitory activities of essential oils of three Achillea species and their nanoemulsions against Tribolium castaneum (Herbst),, Ind. Crop Prod., 53 (2014), 252.

[19]

G. Nenaah and S. Ibrahim, Chemical composition and the insecticidal activity of certain plants applied as powders and essential oils against two stored-products coleopteran beetles,, J. Pest Sci., 84 (2011), 393. doi: 10.1007/s10340-011-0354-5.

[20]

P. Pretheep-Kumar, S. Mohan and P. Balasubramanian, Insecticide Resistance-stored-product,, mechanism and management strategies, (2010).

[21]

S. Rajendran, Postharvest pest losses. New York in: Pimentel,, in D. (Ed), (2002).

[22]

S. Rajendran and V. Sriranjini, Plant products as fumigants for stored-product insect control,, J. Stored Prod. Res., 44 (2008), 126. doi: 10.1016/j.jspr.2007.08.003.

[23]

C. Regnault-Roger, C. Vincent and J. T. Arnason, Essential oils in insect control: Low-risk products in a high-stakes world,, Annu. Rev. Entomol., 57 (2012), 405. doi: 10.1146/annurev-ento-120710-100554.

[24]

M. Shi, P. Collins, J. Smith and M. Renton, Individual-based modelling of the efficacy of fumigation tactics to control lesser grain borer (Rhyzopertha dominica) in stored grain,, J. Stored Prod. Res., 51 (2012), 23. doi: 10.1016/j.jspr.2012.06.003.

[25]

M. Shi and M. Renton, Modelling mortality of a stored grain insect pest with fumigation: Probit, logistic or Cauchy model?,, Math. Biosci., 243 (2013), 137. doi: 10.1016/j.mbs.2013.02.005.

[26]

M. Shi and M. Renton, 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,, Math. Biosci., 233 (2011), 77. doi: 10.1016/j.mbs.2011.06.005.

[27]

M. Shi, M. Renton, J. Ridsdill-Smith and P. J. Collins, 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?,, J. Pest Sci., 85 (2012), 451. doi: 10.1007/s10340-012-0421-6.

[28]

R. G. Winks, The toxicity of phosphine to adults of Tribolium castaneum (Herbst): phosphine-induced narcosis,, J. Stored Prod. Res., 21 (1985), 25. doi: 10.1016/0022-474X(85)90056-6.

[29]

J. R. Wolberg, Data analysis using the method of least squares,, Extracting the Most Information From Experiments, (2005).

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