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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Auslander, D.M., Oster, G.F., Huffaker, C.B. (1974). Dynamics of interacting populations. J. Franklin Institute 297: 345–376
Beddington, J.R., Free, C.A. (1976). Age structure effects in predator-prey interactions. Theo. Pop. Biol. 9: 15–24
Cushing, J. (1977). Integrodifferential Equations and Delay Models in Population Dynamics. Lecture Notes in Biomathematics 20, Springer-Verlag
Cushing, J., Saleem, M. (1982). A predator-prey model with age structure. J. Math. Biol 14: 231–250
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
Gilpin, M., Ayala, F. (1973). Global models of growth and competition. Proc. Nat. Acad. Sci. 70: 3590–3593
Gurtin, M.E., Levine, D.S. (1979). On predator-prey interactions with predation dependent on age of prey. Math. Biosci. 47: 207–219
Hassell, M.P., Comins, H.N. (1976). Discrete time models for two species competition. Theo. Pop. Biol. 9: 202–221
Hastings, A. (1983). Age dependent predation is not a simple process. I. Continuous time models. Theo. Pop. Biol. 25: 347–362
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
McDonald, N. (1976). Time delay in predator-prey models. Math. Biosci. 28: 321–330
McDonald, N. (1977). Time delay in predator-prey models. II. Bifurcation theory. Math. Biosci. 33: 227–234
McDonald, N. (1978). Time Lags in Biological Models. Springer-Verlag, New York
Mech, D. ( 1966 ). The wolves of Isle Royale. U.S. Govt. Printing Office, Washington
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
Prub, J. (1981). Equilibrium solutions of age-specific population dynamics of several species. J. Math. Biol. 11: 65–84
Scudo, F., Ziegler, J. (1978). The golden age of theoretical ecology: 1923–1940, Springer-Verlag, New York
Smith, R.H., Mead, R. (1974). Age structure and stability in models of predator-prey systems. Theor. Pop. Biol. 6: 308–322
Travis, C., Post, W., De Angelis, D., Perkowski, J. (1980). Analysis of compensatory Leslie matrix models for competing
Werner, E. (1977). Species packing and niche complementarity in three sunfishes. Amer. Nat. 11: 553–578
Wilbur, H. (1980). Complex life cycles. Annu. Rev. Ecol. Syst. 11: 67–93
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
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
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