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A new modelling approach to insect reproduction with same-shape reproduction distribution and rate summation: with particular reference to Russian wheat aphid

Published online by Cambridge University Press:  21 January 2009

Z.S. Ma  and
E.J. Bechinski
Z.S. Ma*
Affiliation:
Division of Entomology, University of Idaho, Moscow, ID 83844, USA
E.J. Bechinski
Affiliation:
Division of Entomology, University of Idaho, Moscow, ID 83844, USA
*
*Author for correspondence Fax: (208) 885-9052 E-mail: [email protected]
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Abstract

Same-shape distribution model and rate summation approach are widely used to describe the insect developmental process. In this approach, by integrating a nonlinear deterministic developmental rate model and a probabilistic same-shape distribution model, the proportion of the cohort completing development is quantified as a function of accumulating developmental rates, which themselves are temperature dependent. This method is considered to be more accurate in modelling insect phenology because it can address a well-known biological fact, individual variability, that insect individual developmental rates respond to temperature differently, and because rate-summation essentially simulates developmental rates under variable temperatures instead of constant temperatures. By comparing insect development and reproduction with respect to their responses to temperatures, we argue for the extension of the same-shape and rate-summation approaches to modelling insect reproduction process under variable temperatures. We justify our arguments by the fact that individual variation universally exists in almost all biological characteristics, and the phenomenon that insect development and reproduction respond to temperature very similarly, which is supported by some endocrinological evidences reported in literature. In addition, the approach for testing the applicability of the original same-shape developmental modelling, experimentally verifying the sameness of the same-shape curves or that the shape of the curves is invariant with respect to the temperature regimes, equally applies to our extended version for reproduction modelling. We successfully tested the extension and its applicability with our experimental data of 1800 Russian wheat aphids' (RWA) (Diuraphis noxia (Mordvilko)) reproduction under various temperature and plant growth stage regimes. We also extended Taylor's (1981) nonlinear model for insect development to describe RWA mean (median) nymphal production under different temperatures and barley plant growth stages. Three same-shape distribution models, Weibull distribution, Stinner's model and logistic model, are used to construct the same-shape reproduction distribution models for RWA. The extensions performed in this paper contribute a new modelling approach for predicting insect reproduction under field variable temperatures and plant growth stages. The prediction model can be parameterized with data from typical laboratory demography experiments and further integrated into simulation models for insect population dynamics. Finally, we discussed why the sameness test of the same-shape distribution curves is sufficient in validating the approach and proposed a strategy for dealing with exceptional cases where the sameness test fails.

Keywords

same-shape reproduction distributiondistribution modelrate summationreproduction modelRussian wheat aphid
Type
Research Paper
Information
Bulletin of Entomological Research , Volume 99 , Issue 5 , October 2009 , pp. 445 - 455
Copyright
Copyright © 2009 Cambridge University Press

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References

BMDP (1993) BMDP Statistical Software Manuals. Release 7, vol. 1 & 2. BMDP Inc.Google Scholar
Curry, G.L. & Feldman, R.M. (1978) Foundations of Stochastic Development. Journal of Theoretical Biology 74, 397–410.CrossRefGoogle ScholarPubMed
Curry, G.L., Feldman, R.M. & Smith, K.C. (1978) A stochastic model of a temperature-dependent population. Theoretical Population Biology 13, 197–213.CrossRefGoogle ScholarPubMed
Deng, J.L. (1982) Control problems of Grey System. System and Control Letters 5, 288–294.Google Scholar
Deng, J.L. (1989) Introduction to Grey System theory. Journal of Grey System 1, 1–24.Google Scholar
Kramer, D.A., Stinner, R.E. & Hain, F.P. (1991) Time versus rate in parameter estimation of nonlinear temperature-dependent development models. Environmental Entomology 20(2), 484–488.CrossRefGoogle Scholar
Logan, J.A. (1988) Toward an expert system for development of pest simulation models. Environmental Entomology 17(2), 359–376.CrossRefGoogle Scholar
Logan, J.A. & Weber, L.A. (1989) Population model design system (PMDS), User Guide. Blacksburg, VA, USA, Department of Entomology, Virginia Polytechnic Institute and State University.Google Scholar
Ma, Z.S. (1991) Studies on the population aggregation dynamics of Dendrolimus tabulaeformis. Journal of Biomathematics 6(1), 78–86 (in Chinese with English abstract).Google Scholar
Ma, Z.S. (1997) Demography and survival analysis of Russian wheat aphid populations. PhD thesis, University of Idaho, Moscow, ID, USA.Google Scholar
Ma, Z.S. & Bechinski, E.J. (2008a) Developmental and Phenological Modeling of Russian Wheat Aphid. Annals of Entomological Society of America 101(2), 351–361.CrossRefGoogle Scholar
Ma, Z.S. & Bechinski, E.J. (2008b) A Survival analysis-based simulation model for Russian wheat aphid population dynamics. Ecological Modeling 216, 323–332.CrossRefGoogle Scholar
Ma, Z.S. & Zhang, Z.Z. (1990) Application of Grey Clustering analysis to natural habitat unit of insect populations. Journal of Grey Systems 2(2), 179–187.Google Scholar
Ratte, H.T. (1984) Temperature and insect development. pp. 33–66in Hoffman, K.H. (Ed.) Environmental Physiology and Biochemistry. Berlin, Germany, Springer-Verlag.Google Scholar
Regniere, J. (1983) An oviposition model for the spruce budworm, Choristoneura fumiferana (Lepidoptera: Tortricidae). Canadian Entomologists 115, 1371–1382.CrossRefGoogle Scholar
Regniere, J. (1984) A method of describing and using variability in development rates for the simulation of insect phenology. Canadian Entomologists 116, 1367–1376.CrossRefGoogle Scholar
Sharpe, P.J.H., Curry, G.L., DeMichele, D.W. & Cole, C.L. (1977) Distribution model of organism development times. Journal of Theoretical Biology 66, 21–38.CrossRefGoogle ScholarPubMed
Stinner, R.E., Butler, G.D., Bachelor, J.S. & Tuttle, C. (1975) Simulation of temperature dependent development in population dynamics models. Canadian Entomologists 107, 1167–1174.CrossRefGoogle Scholar
Taylor, F. (1981) Ecology and evolution of physiological time in insects. The American Naturalist 117(1), 1–23.CrossRefGoogle Scholar
Wagner, T.L., Wu, H., Sharpe, P.J. & Coulson, R.N. (1984) Modeling distribution of insect development time: a literature review and application of the Weibull function. Annals of the Entomological Society of America 77, 475–487.CrossRefGoogle Scholar
Wagner, T.L., Wu, H., Feldman, R.M., Sharpe, P.J.H. & Coulson, R.N. (1985) Multiple-cohort approach for simulating development of insect population under variable temperatures. Annals of the Entomological Society of America 78, 691–704.CrossRefGoogle Scholar
Zadoks, J.C., Chang, T.T. & Konzak, C.F. (1974) A decimal code for the growth stages of cereal. Weed Research 14, 415–421.CrossRefGoogle Scholar