Abstract
We investigate the population dynamics of a semivoltine species whose juvenile development takes two years to complete, and is followed by a very short reproductive adult stage. Reproduction is synchronized so at any given time the juvenile population consists of two cohorts. Coexistence of the two cohorts requires that the strength of intea-cohort competition exceeds that of inter-cohort competition, an extension of the competitive exclusion principle. The population may exhibit population cycles with low integer period. We identify two mechanisms for two-year cycles, and note that four-year cycles are a natural consequence of overcompensation. Three year cycles can occur and we discuss the mechanisms involved.
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Bellows, T. S., Jr.: The descriptive properties of some models for density dependence. J. Anim. Ecol. 50, 139–156 (1981)
Bellows, T. S., Jr.: Analytical model for laboratory populations of Callosobruchus Chinensis and C. Maculatus (Coleoptera:Bruchidae). J. Anim. Ecol. 51, 263–287 (1982)
Blythe, S. P., Nisbet, R. M., Gurney, W. S. C.: The dynamics of population models with distributed maturation periods. Theor. Popul. Biol. 25, 289–311 (1984)
Briggs, C. J.: Competition among parasitoid species on a stage-structured host, and its effect on host suppression. Am. Nat. 141, 372–397
Briggs, C. J., Nisbet, R. M., Murdoch, W. W.: Coexistence of competing parasitoid species on a host with a variable life cycle. Theor. Popul. Biol. (in press, 1993)
Crowley, P. H., Nisbet, R. M., Gurney, W. S. C., Lawton, J. H.: Population regulation in animals with complex life-histories: Formulation and analysis of a damselfly model. Adv. Ecol. Res. 17, 1–58 (1987)
Cushing, J. M.: A simple model of cannibalism. Math. Biosci. 53, 47–71 (1991)
Cushing, J. M., Li, J.: On Ebenman's model for the dynamics of a population with competing juveniles and adults. Bull. Math. Biol. 51, 687–713 (1989)
Cushing J. M., Li, J.: Intra-specific competition and density-dependent juvenile growth. Bull. Math. Biol. 54, 503–519 (1992)
Ebenman, B.: Niche differences between age and classes and intraspecific competition in age-structured populations J. Theor. Biol. 124, 25 (1987)
Ebenman, B.: Competition between age-classes and population dynamics. J. Theor. Biol. 131, 389–400 (1988)
Guckenheimer, J., Oster, G., Ipaktchi, A.: The dynamics of density-dependent population models. J. Math Biol. 4, 101–147 (1977)
Gurney, W. S. C., Nisbet, R. M.: Fluctuation periodicity, generation separation, and expression of larval competition. Theor. Popul. Biol. 28, 150–180 (1985)
Hamrin, S. F., Persson, L.: Asymmetrical competition between age classes as a factor causing population oscillations in an obligate planktivorous fish species. Oikos 47, 223 (1986)
Hassell, M. P.: Density dependence in simple species populations. J. Anim. Ecol. 44, 263–295 (1975)
Hassell, M. P., Lawton, J. H., May, R M.: Patterns of behaviour in single species populations. J. Anim. Ecol. 45, 471–486 (1976)
Kot, M., Schaffer, W. M.: The effects of seasonality on discrete models of population growth. Theor. Popul. Biol. 26, 340–360 (1984)
Iooss, G.: Bifurcations of Maps and Applications. Amsterdam: North Holland 1979
Lauwerier, H. A., Metz, J. A. J.: Hopf Bifurcation in Host-Parasitoid Models. IMAJ. Math Appl. Med. Biol. 3, 191–210 (1986)
Liu, W.: Acta. Math. Appl. Sin. (in review, 1992)
Loreau, M.: Competition between age-classes and stability of stage structured populations: a re-examination of Ebenman's model. J. Theor. Biol. 144, 567–571 (1990)
Marsden, J. E., McCracken, M.: The Hopf Bifurcation and Its Applications. Berlin Heidelberg New York: Springer 1976
May, R. M.: Stability and Complexity in Model Ecosystems, 2nd. ed. Princeton: Princeton University Press 1974a
May, R. M.: Biological populations with non-overlapping generations: Stable points, stable cycles, and chaos. Science 186, 645–647 (1974b)
May, R. M.: Biological populations obeying difference equations: Stable points, stable cycles, and chaos. J. Theor. Biol. 49, 511–524 (1975)
May, R. M.: Simple mathematical models with very complex dynamics. Nature (London) 261 459–467 (1976)
May, R M., Conway, G. R., Hassell, M. P., Southwood T. R. E.: Time delays, density-dependence and single species oscillations. J. Anim. Ecol. 47, 249–267 (1974)
May, R M., Oster, G. F.: Bifurcations and dynamic complexity in simple ecological model. Am. Nat. 110, 573–599 (1976)
Metropolis, N., Stein, M. L., Stein, P. R.: Stable states of a non-linear transformation. Num. Math. 10, 1–19 (1967)
Mira, C.: Chaotic Dynamics. Singapore: World Scientific 1987
Mittlebach, G. G., Chesson, P. L.: Predarion risk: indirect effects on fish populations In: Kerfoot, W. C., Sih, A. (eds.) Predarion: direct and indirect effects on aquatic communities, pp. 315–332. Hannover, NH, USA: New England University Press 1987
Nisbet, R. M., Gurney, W. S. C.: Models of uniform larval competition. In: Levin, S. A., Hallam, T., (eds.) Biomathematics: Mathematical Ecology. Berlin Heidelberg New York: Springer 1984
Nisbet, R. M., Murdoch, W. W., Stewart-Oaten, A.: Consequences for adult fish stocks of human-induced mortality on immatures. In: Schnmitt, R. J., Osenberg, C. (eds.) Environmental Impact Assessment: Conceptual issues and Application in Coastal Marine Environments. University of California Press (in press, 1993)
Onyiah, L. C.: Simple nonlinear models for semivoltine populations. PhD thesis, University of Strathclyde, Glasgow, UK 1989
Press, W. H., Flannery, B. P., Teukolsky, S. A., Vettering, W. T.: Numerical Recipes (The Art of Scientific Computing). Cambridge: Cambridge University Press 1986
Rodriguez, D. J.: Models of growth with density dependence in more than one stage. Theor. Popul. Biol. 34, 93–119 (1988)
Ruelle, D.: Elements of Differentiable Dynamics and Bifurcation Theory. Boston: Academic Press 1989
Tschumy, W. O.: Competition between juveniles and adults in age-structured populations. Theor. Popul. Biol. 21, 255–268 (1981)
van der Bosch, F., de Roos, A. M., Gabriael, W.: Cannibalism as a life-boat mechanism. J. Math. Biol. 26, 619–633 (1988)
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Nisbet, R.M., Onyiah, L.C. Population dynamic consequences of competition within and between age classes. J. Math. Biol. 32, 329–344 (1994). https://doi.org/10.1007/BF00160164
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DOI: https://doi.org/10.1007/BF00160164