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Temperature-dependent predator-prey mite ecosystem on apple tree foliage

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Summary

The biological control of the McDaniel spider mite, which is a pest on apple tree foliage, by a predacious mite species, which feeds upon it, is represented by a continuous-discrete time hybrid model incorporating temperature effects explicityland mite metamorphosis implicitly. The results of this model can be shown to provide good agreement when compared with relevant field data.

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References

  • Forrester, J. W.: Industrial Dynamics. Cabridge, Mass: M.I.T. Press, 1961.

    Google Scholar 

  • Holling, C. S.: The functional response of predator to prey density and its role in micicry and population regulation. Mem. Ent. Soc. Can.45, 1–60 (1965)

    Google Scholar 

  • Hoyt, S. C.: Integrated chemical control of insects and biological control of mites on apples in Washington. M. Econ. Entomol.62, 74–86 (1969)

    Google Scholar 

  • Leslie, P. H.: On the use of matrices in certain population mathematics. Biometrika33, 185–212 (1945)

    MathSciNet  Google Scholar 

  • Lin, C. C., Segel, L. A.: Mathematics Applied to Deterministic Problems in the Natural Sciences, New York: Macmillan, 1974

    MATH  Google Scholar 

  • Logan, J. A.: SIMBUG: a pest management simulation language. I. Maintenance and reference manual. Melanderia (in press) (1978)

  • Logan, J. A., Wollkind, D. J., Hoyt, S. C., Tanigoshi, L. K.: An analytical model for description of temperature dependent rate phenomena in arthropods. Environ. Entomol.5, 1130–1140 (1976)

    Google Scholar 

  • Oaten, A., Murdoch, W. M.: Functional response and stability in predator-prey systems. Amer. Natur.109, 289–298 (1975)

    Article  Google Scholar 

  • Powell, M. J. D.: A FORTRAN Subroutine for Solving Systems of Nonlinear Algebraic Equations (Rep. R. 5947) Herwell: U.N. Atomic Energy Establish., 1968.

    Google Scholar 

  • Royama, T.: A comparative study of models for predation and parasitism. Researches in Population Ecology, Supplement No. 1. Kyoto, Japan: The Society of Population Ecology, pp. 1–90, 1971.

    Google Scholar 

  • Selby, S. M., editor: CRC Standard Mathematical Tables. Cleveland: Chemical Rubber Company, 1974.

    Google Scholar 

  • Smith, J. M.: Models in Ecology. Cambrige, England: Cambridge University Press, 1974.

    MATH  Google Scholar 

  • Tanigoshi, L. K., Hoyt, S. C., Browne, R. W., Logan, J. A.: Influence of temperature on population increase ofTetranychus mcdanieli (Acarina: Tetranychidae). Ann. Entomol. Soc. Am.68, 972–978 (1975a).

    Google Scholar 

  • Tanigoshi, L. K., Hoyt, S. C., Browne, R. W., Logan, J. A.: Influence of temperature on population increase ofMetaseiulus occidentalis (Acarina: Phytoseidae). Ann. Entomol. Soc. Am.68, 979–986 (1975b).

    Google Scholar 

  • Tanigoshi, L. K., Hoyt, S. C., Browne, R. W., Lagier, R. F.: Empirical analysis of variable temperature regions on life stage and development ofTetranychus mcdanieli (Acarina: Tetranychidae). Ann. Entomol. Soc. Am.69, 712–716 (1976).

    Google Scholar 

  • Webster, R. L.: Mites of economic importance in the Pacific Northwest. J. Econ. Entomol.41, 677–687 (1948).

    Google Scholar 

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Wollkind, D.J., Logan, J.A. Temperature-dependent predator-prey mite ecosystem on apple tree foliage. J. Math. Biology 6, 265–283 (1978). https://doi.org/10.1007/BF02547801

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  • DOI: https://doi.org/10.1007/BF02547801

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