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Models of Development in Insect Populations

  • Conference paper
Estimation and Analysis of Insect Populations

Part of the book series: Lecture Notes in Statistics ((LNS,volume 55))

Abstract

The features of development essential to analyses of insect population dynamics, development time and mortality, are discussed in the context of convolution and network models. Whether representing one or several successive stages of a life cycle, a model in either class is designed from relevant statistics of development time and mortality. Network models are emphasized, and Erlang and Bessel networks are discussed in particular. Use of networks in models of population systems is discussed briefly with examples.

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References

  • Athans, M., M. L. Dertouzos, R. N. Spann & S. J. Mason. 1974. Systems, Networks, and Computation. McGraw—Hill, New York.

    Google Scholar 

  • Balabanian, N. 1958. Network Synthesis. Prentice Hall, Englewood Cliffs, N.J.

    Google Scholar 

  • Caswell, H. 1972. A simulation study of a time lag population model. J. Theor. Biol 34: 419 – 439.

    Article  Google Scholar 

  • Cooper, G. R. & C. D. McGillem. 1967. Methods of Signal and System Analysis. Holt, Rinehart, and Winston, New York.

    Google Scholar 

  • Cooper, R. B. 1972. Introduction to Queueing Theory. MacMillan, New York.

    MATH  Google Scholar 

  • Curry, G. L. & R. M. Feldman. 1987. Mathematical Foundations of Population Dynamics. Texas A&M University Press, College Station.

    MATH  Google Scholar 

  • Curry, G. L., R. M. Feldman & P. J. H. Sharpe. 1978. Foundations of stochastic development. J. Theor. Biol 74: 397 – 410.

    Article  Google Scholar 

  • Director, S. W. & R. A. Rohrer. 1972. Introduction to Systems Theory. McGraw—Hill, New York.

    MATH  Google Scholar 

  • Gross, D. & C. M. Harris. 1974. Fundamentals of Queueing Theory. J. Wiley & Sons, New York.

    MATH  Google Scholar 

  • Gutierrez, A. P., D. W. DeMichele, Y. Wang, G. L. Curry, R. Skeith & L. G. Brown. 1980. The systems approach to research and decision making for cotton pest control. In C. B. Huffaker [ed.] New Technology of Pest Control. J. Wiley & Sons, New York.

    Google Scholar 

  • Johnson, D. W., C. S. Barfield & G. E. Allen. 1983. Temperature—dependent development model for the velvetbean caterpillar (Lepidoptera: Noctuidae). Environ. Ent. 12 (6): 1657 – 1663.

    Google Scholar 

  • Koenig, H. E., Y. Tokad & H. K. Kesavan. 1967. Analysis of Discrete Physical Systems. McGraw—Hill, New York.

    Google Scholar 

  • Lathi, B. P. 1965. Signals, Systems, and Communication. J. Wiley & Sons, New York.

    MATH  Google Scholar 

  • Leslie, P. H. 1945. On the use of matrices in certain population mathematics. Biometrika 33: 183 – 212.

    Article  MathSciNet  MATH  Google Scholar 

  • Leslie, P H. 1948. Some further notes on the use of matrices in population mathematics. Biometrika 35: 213 – 245.

    MathSciNet  MATH  Google Scholar 

  • Lotka, A. J. 1925. Elements of Physical Biology. Williams and Wilkins, Baltimore.

    MATH  Google Scholar 

  • Manetsch, T.J. 1976. Time—varying distributed delays and their use in aggregative models of large systems. IEEE Trans. Sys. Man. Cybern. 6: 547 – 553.

    Article  Google Scholar 

  • Martens, H. R. & D. R. Allen. 1969. Introduction to System Theory. C. E. Merrill, Columbus, OH.

    Google Scholar 

  • McGillem, C. D. & G. R. Cooper. 1974. Continuous and Discrete Signal and System Analysis. Holt, Rinehart and Winston, New York.

    MATH  Google Scholar 

  • Nicholson, A. J. & V. A. Bailey. 1935. The balance of animal populations. Proc. Zool. Soc. Lond. 1: 551 – 598.

    Google Scholar 

  • Papoulis, A. 1980. Circuits and Systems. Holt, Rinehart and Winston, New York.

    Google Scholar 

  • Pearl, R. & L. J. Reed. 1920. On the rate of growth of the population of the United States since 1790 and its mathematical representation. Proc. Natl. Acad. Sci. U.S.A. 6: 275 – 288.

    Article  Google Scholar 

  • Ruesink, W. G. 1976. Status of the Systems Approach to Pest Management. Ann. Rev. Entomol. 21: 27 – 44.

    Article  Google Scholar 

  • Sharpe, P. J. H., G. L. Curry, D. W. DeMichele & C. L. Cole. 1977. Distribution model of organism development times. J. Theor. Biol. 66: 21 – 38.

    Article  Google Scholar 

  • Shearer, J. L., A. T. Murphy & H. H Richardson. 1967. Introduction to System Dynamics. Addison—Wesley, Reading, MA.

    Google Scholar 

  • Shoemaker, C. A. 1980. The role of systems analysis in integrated pest management. In C. B. Huffaker [ed.], New Technology of Pest CJontrol. J. Wiley & Sons, New York.

    Google Scholar 

  • Smerage, G. H. 1985. Bessel Delay Networks for Population Models. Trans. ASAE 28: 1269 – 1278.

    Google Scholar 

  • Storch, L. 1954. Synthesis of constant-time-delay ladder networks using Bessel polynomials. Proc. IRE 42: 1666 – 1675.

    Article  MathSciNet  Google Scholar 

  • Tummala, R. L., W. G. Ruesink k D. L. Haynes. 1975. A discrete component approach to the management of the cereal leaf beetle ecosystem. Environ. Entomol. 4: 175 – 86.

    Google Scholar 

  • Van Valkenburg, M. E. 1960. Introduction to Modern Network Synthesis. J. Wiley & Sons, New York.

    Google Scholar 

  • Verhuist, P. F. 1838. Notice sur la loi que la population suits dons son accroissement. Corresp. Math. Phys. 10: 113 – 121.

    Google Scholar 

  • Volterra, V. 1926. Variazione e fluttuazioni de numero d’individui in specie animali conviventi. Mem. Accad. Lincei 2: 31 – 113.

    Google Scholar 

  • Wagner, T. L., H. Wu, R. M. Feldman, P. J. H. Sharpe & R. N. Coulson. 1985. Multiple—Cohort Approach for Simulating Development of Insect Populations Under Variable Temperatures. Forum: Ann. Ent. Soc. Am. 78: 691 – 704.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Agricultural Engineering, University of Florida, Gainesville, FL, 32611, USA

    Glen H. Smerage

Authors
  1. Glen H. Smerage
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Editor information

Editors and Affiliations

  1. Departments of Statistics and Zoology, University of Wyoming, Laramie, WY, 82071, USA

    Lyman L. McDonald

  2. Department of Mathematics and Statistics, University of Otago, Dunedin, New Zealand

    Bryan F. J. Manly

  3. Department of Plant, Soil and Insect Sciences, University of Wyoming, Laramie, WY, 82071, USA

    Jeffrey A. Lockwood

  4. Departments of Entomology and Forestry, Virginia Polytechnic Institute, Blacksburg, VA, 24061, USA

    Jesse A. Logan

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© 1989 Springer-Verlag Berlin Heidelberg

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Smerage, G.H. (1989). Models of Development in Insect Populations. In: McDonald, L.L., Manly, B.F.J., Lockwood, J.A., Logan, J.A. (eds) Estimation and Analysis of Insect Populations. Lecture Notes in Statistics, vol 55. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3664-1_22

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  • DOI: https://doi.org/10.1007/978-1-4612-3664-1_22

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96998-5

  • Online ISBN: 978-1-4612-3664-1

  • eBook Packages: Springer Book Archive

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