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Interacting Age Structured Populations

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Book cover Mathematical Ecology

Part of the book series: Biomathematics ((BIOMATHEMATICS,volume 17))

Abstract

Both the study of interacting species without age structure and single species with age structure have had a long history in theoretical ecology, beginning with studies in the “golden age” of ecology (Scudo and Ziegler, 1978) by Lotka and Volterra. Only much more recently have there been studies on the dynamics of interacting, age structured models. Such models can quickly get extraordinarily complex, so in this review I will concentrate on the simplest models.

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References

  • Auslander, D.M., Oster, G.F., Huffaker, C.B. (1974). Dynamics of interacting populations. J. Franklin Institute 297: 345–376

    Article  Google Scholar 

  • Beddington, J.R., Free, C.A. (1976). Age structure effects in predator-prey interactions. Theo. Pop. Biol. 9: 15–24

    Google Scholar 

  • Cushing, J. (1977). Integrodifferential Equations and Delay Models in Population Dynamics. Lecture Notes in Biomathematics 20, Springer-Verlag

    MATH  Google Scholar 

  • Cushing, J., Saleem, M. (1982). A predator-prey model with age structure. J. Math. Biol 14: 231–250

    Google Scholar 

  • Gazis, D.C., Montroll, E.W., Ryniker, J.E. (1973). Age-specific, deterministic model of predator prey populations: application to Isle Royale. IBM J. Res. Devel. 17: 47–53

    Article  Google Scholar 

  • Gilpin, M., Ayala, F. (1973). Global models of growth and competition. Proc. Nat. Acad. Sci. 70: 3590–3593

    Article  MATH  Google Scholar 

  • Gurtin, M.E., Levine, D.S. (1979). On predator-prey interactions with predation dependent on age of prey. Math. Biosci. 47: 207–219

    Google Scholar 

  • Hassell, M.P., Comins, H.N. (1976). Discrete time models for two species competition. Theo. Pop. Biol. 9: 202–221

    Article  MathSciNet  Google Scholar 

  • Hastings, A. (1983). Age dependent predation is not a simple process. I. Continuous time models. Theo. Pop. Biol. 25: 347–362

    Google Scholar 

  • Hastings, A., Wollkind, D. (1982). Age structure in predator-prey systems. I. A general model and a specific example. Theo. Pop. Biol. 21: 44–56

    Article  MathSciNet  MATH  Google Scholar 

  • McDonald, N. (1976). Time delay in predator-prey models. Math. Biosci. 28: 321–330

    Google Scholar 

  • McDonald, N. (1977). Time delay in predator-prey models. II. Bifurcation theory. Math. Biosci. 33: 227–234

    Article  Google Scholar 

  • McDonald, N. (1978). Time Lags in Biological Models. Springer-Verlag, New York

    Google Scholar 

  • Mech, D. ( 1966 ). The wolves of Isle Royale. U.S. Govt. Printing Office, Washington

    Google Scholar 

  • Pennycuick, C J., Compton, R.M., Beckingham, L. (1968). A computer model for simulating the growth of a population or of two interacting populations. J. theor. Biol. 18: 316–329

    Article  Google Scholar 

  • Prub, J. (1981). Equilibrium solutions of age-specific population dynamics of several species. J. Math. Biol. 11: 65–84

    Google Scholar 

  • Scudo, F., Ziegler, J. (1978). The golden age of theoretical ecology: 1923–1940, Springer-Verlag, New York

    MATH  Google Scholar 

  • Smith, R.H., Mead, R. (1974). Age structure and stability in models of predator-prey systems. Theor. Pop. Biol. 6: 308–322

    Google Scholar 

  • Travis, C., Post, W., De Angelis, D., Perkowski, J. (1980). Analysis of compensatory Leslie matrix models for competing

    Google Scholar 

  • Werner, E. (1977). Species packing and niche complementarity in three sunfishes. Amer. Nat. 11: 553–578

    Article  Google Scholar 

  • Wilbur, H. (1980). Complex life cycles. Annu. Rev. Ecol. Syst. 11: 67–93

    Google Scholar 

  • Wollkind, D., Hastings, A., Logan, J. (1982). Age structure in predator-prey systems. II. Functional response and stability and the paradox of enrichment. Theo. Pop. Biol. 21: 57–68

    Article  MathSciNet  MATH  Google Scholar 

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© 1986 Springer-Verlag Berlin Heidelberg

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Hastings, A. (1986). Interacting Age Structured Populations. In: Hallam, T.G., Levin, S.A. (eds) Mathematical Ecology. Biomathematics, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69888-0_11

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  • DOI: https://doi.org/10.1007/978-3-642-69888-0_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-69890-3

  • Online ISBN: 978-3-642-69888-0

  • eBook Packages: Springer Book Archive

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