Stage Structure Models Applied in Evolutionary Ecology

  • R. M. Nisbet
  • W. S. C. Gurney
  • J. A. J. Metz
Part of the Biomathematics book series (BIOMATHEMATICS, volume 18)


Mathematical models of physiologically structured populations are now well established within the mainstream of theoretical ecology (Metz and Diekmann, 1986, and references therein), but to date their utilisation in many areas of ecology has been restricted by two types of difficulty. First, the numerical solution of the partial differential equations that arise naturally in the description of many structured populations is far from straightforward, and although promising methods are currently being developed (e.g. de Roos, 1988), the numerically unsophisticated worker does not have ready access to well-tested “off-the-shelf” computer packages such as are available for models posed in terms of ordinary differential equations, difference equations, or Leslie matrices. Second, practical applications of structured models demand large quantities of biological information, and it is seldom easy to formulate models that only require parameters which can be calculated from existing data.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Blythe, S.P., Nisbet, R.M., Gurney, W.S.C. (1982) Instability and complex dynamic behaviour in population models with long time delays. Theor. Pop. Biol. 22, 147–176.CrossRefMATHMathSciNetGoogle Scholar
  2. Blythe, S.P., Nisbet, R.M., Gurney, W.S.C. (1984) Population models with distributed maturation periods. Theor. Pop. Biol. 25, 289–311CrossRefMATHMathSciNetGoogle Scholar
  3. Brillinger, D.R., Guckenheimer, J., Guttorp, P., Oster, G. (1980) Empirical modelling of population time series data: The case of age and density dependent vital rates. Lectures on Mathematics in the Life Sciences 13, 65–90. American Mathematical SocietyGoogle Scholar
  4. Charlesworth, B. (1980) Evolution in Age-Structured Populations. Cambridge University PressMATHGoogle Scholar
  5. Crow, J.F. (1986) Basic Concepts in Population, Quantitative, and Evolutionary Genetics. Freeman, New YorkGoogle Scholar
  6. Crowley, P.H., Nisbet, R.M., Gurney, W.S.C., Lawton, J.W. (1987) Population regulation in animals with complex life histories: Formulation and analysis of a damselfly model. Adv. Ecol. Res. 17,1–59CrossRefGoogle Scholar
  7. Gurney, W.S.C, Blythe, S.P. Nisbet, R.M. (1980) Nicholson’s blowflies revisited. Nature 187, 17–21CrossRefGoogle Scholar
  8. Gurney, W.S.C, Nisbet, R.M, Blythe, S.P. (1986) The systematic formulation of stage structure models. In: Metz. J.A.J, Diekmann, O. (eds.) The Dynamics of Physiologically Structured Populations, Springer, Berlin Heidelberg New York London Paris TokyoGoogle Scholar
  9. Gurney, W.S.C, Nisbet, R.M. (1985) Generation separation, fluctuation periodicity and the expression of larval competition. Theor. Pop. Biol. 28, 150–180CrossRefMATHMathSciNetGoogle Scholar
  10. Gurney, W.S.C, Nisbet, R.M, Lawton, J.H. (1983) The systematic formulation of tractable single species population models including age-structure. J. Anim. Ecol. 52, 479–495.CrossRefGoogle Scholar
  11. Hale, J. (1977) Theory of Functional Differential Equations. Springer, Berlin Heidelberg New York TokyoCrossRefMATHGoogle Scholar
  12. Hastings, A. (1984) Evolution in a seasonal environment: simplicity lost? Evolution 38, 350–358Google Scholar
  13. Hedrick, P.W. (1983) Genetics of Populations. Science Books International, BostonGoogle Scholar
  14. May, R.M. (1974) Stability and Complexity in Model Ecosystems. Princeton University Press, Princeton, N.JGoogle Scholar
  15. Maynard Smith, J. (1974) Models in Ecology. Cambridge University Press, Cambridge, EnglandGoogle Scholar
  16. Metz, J.A.J, Diekmann, O. (eds.) (1986) The Dynamics of Physiologically Structured Populations.Springer, Berlin Heidelberg New York London Paris TokyoMATHGoogle Scholar
  17. Murdoch, W.W, Nisbet, R.M, Blythe, S.P, Gurney, W.S.C, Reeve, J.D. (1987) An invulnerable age class and stability in delay-differential parasitoid-host models. Am. Nat. 129, 263–282.CrossRefGoogle Scholar
  18. Nicholson, A.J. (1954) An outline of the dynamics of animal populations. Aust. J. Zool. 2, 9–65CrossRefGoogle Scholar
  19. Nicholson, A.J. (1957) The self adjustment of populations to change. Cold Spring Harbour Symposium on Quantitative Biology 22, 153–173Google Scholar
  20. Nisbet, R.M., Blythe, S.P., Gurney, W.S.C., Metz, J.A.J. (1986) Stage structure models with distinct growth and development processes. IMA J. Math. Appl. Med. and Biol. 2, 57–68CrossRefMathSciNetGoogle Scholar
  21. Nisbet, R.M., Gurney, W.S.C. (1982) Modelling Fluctuating Populations. Wiley and Sons, London New York ChichesterMATHGoogle Scholar
  22. Nisbet, R.M., Gurney, W.S.C. (1983) The systematic formulation of population models for insects withdynamically varying instar duration. Theor. Pop. Biol. 23, 114–135CrossRefMATHMathSciNetGoogle Scholar
  23. Nisbet, R.M., Gurney, W.S.C. (1986) Age structure models. In: Hallam, T.G., Levin, S.A. (eds.) Mathematical ecology. Springer, Berlin Heidelberg New York London Paris TokyoGoogle Scholar
  24. Oster, G. (1976) Internal variables in population dynamics. In: Lectures in Mathematics in the Life Sciences 8, 37–68MathSciNetGoogle Scholar
  25. Readshaw, J.L., Cuff, W.R. (1980) A model of Nicholson’s blowfly cycles and its relevance to predation theory. J. Anim. Ecol. 49, 1005–1010CrossRefMathSciNetGoogle Scholar
  26. Readshaw, J.L., van Gerwen, A.C.M. (1983) Age specific survival, fecundity, and fertility of the adult blowfly Lucilia cuprina in relation to crowding, protein food and population cycles. J. Anim. Ecol. 52, 879–888CrossRefGoogle Scholar
  27. de Roos, A. (1988) Numerical methods for structured population models: The escalator boxcar train.Numerical Methods for Partial Differential Equations 4, 173–195CrossRefMATHMathSciNetGoogle Scholar
  28. Roughgarden, J. (1979) Theory of population genetics and evolutionary Ecology: an Introduction. Macmillan, New YorkGoogle Scholar
  29. Stokes, T.K. (1985) PhD thesis University of Strathclyde, Glasgow UKGoogle Scholar
  30. Stokes, T.K., Gurney, W.S.C., Nisbet, R.M., Blythe, S.P. (1988) Parameter evolution in a laboratory insect population. Theor. Pop. Biol. 34, 248–265CrossRefMATHGoogle Scholar
  31. Varley, G.C., Gradwell, G.R., Hassell, M.P. (1973) Insect Population Ecology. Blackwell Scientific Publications, LondonGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • R. M. Nisbet
  • W. S. C. Gurney
  • J. A. J. Metz

There are no affiliations available

Personalised recommendations