Year class coexistence or competitive exclusion for strict biennials?

Journal of Mathematical Biology

Volumn 46, Issue 2, 2003, Pages 95-131

  Davydova, N V ^a   Diekmann, O ^a   Van Gils, S A ^b  

^a UTRECHT UNIVERSITY   (Netherlands)

^b UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

Competitive exclusion; Periodical insects; Semelparous species

Indexed keywords

HEXAPODA; INSECTA;

AGING; ANIMAL; ARTICLE; BIOLOGICAL MODEL; COMPETITIVE BEHAVIOR; COMPUTER SIMULATION; COOPERATION; ECOSYSTEM; EVOLUTION; PERIODICITY; PHYSIOLOGY; PLANT PHYSIOLOGY; POPULATION DYNAMICS; REPRODUCTION; SENSITIVITY AND SPECIFICITY;

AGING; ANIMALS; COMPETITIVE BEHAVIOR; COMPUTER SIMULATION; COOPERATIVE BEHAVIOR; ECOSYSTEM; EVOLUTION; MODELS, BIOLOGICAL; PERIODICITY; PLANT PHYSIOLOGY; POPULATION DYNAMICS; REPRODUCTION; SENSITIVITY AND SPECIFICITY;

EID: 0141723485     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00285-002-0167-5     Document Type: Article

References (31)

1. Baker, J.: Unpublished manuscript
2. Behncke, H.: Periodical cicadas. J. Math. Biol. 40, 413-431 (2000)
3. Bergh, M.O., Getz, W.M.: Stability of discrete age-structured and aggregated delay-difference population models.: J. Math. Biol. 26, 551-581 (1988)
4. Bulmer, M.G.: Periodical Insects. The American Naturalist 111, 1099-1117 (1977)
5. Chossat, P., Golubitsky, M.: Symmetry-increasing bifurcation of chaotic attractors. Phys. D 32(3), 423-436 (1988)
6. Cushing, J.M., Li, J.: Intra-specific competition and density dependent juvenile growth. Bull. Math. Biol. 54, 503-519 (1992)
7. Davydova N.V.: Dynamics and bifurcations in families of single year class maps. In preparation
8. Devaney, R.L.: An Introduction to Chaotic Dynamical Systems. Second Edition. Addison-Wesley Publishing Company, 1989
9. Diekmann, O., Gils, S.A. van: Difference Equations with Delay. Japan J. Indust. Appl. Math. 17, 73-84 (2000)
10. Diekmann, O., Gyllenberg, M., Huang, H., Kirkilionis, M., Metz, J.A.J., Thieme, H.R.: On the Formulation and Analysis of General Deterministic Structured Population Models. II. Nonlinear Theory. J. Math. Biol. 43, 157-189 (2001)
11. Diekmann, O., Gyllenberg, M., Metz, J.A.J.: Steady state analysis of structured population models. Preprint
12. Diekmann, O., Mylius, S.D., Donkelaar, J.R. ten: Saumon à la Kaitala et Getz, sauce hollandaise. Evol. Ecol. Res. 1, 261-275 (1999)
13. Ebenman, B.: Niche Differences Between Age Classes and Intraspecific Competition in Age-structured Population. J. Theor. Biol. 124, 25-33 (1987)
14. Ebenman, B.: Competition Between Age Classes and Population Dynamics. J. Theor. Biol. 131, 389-400 (1988)
15. Heliövaara, K., Väisänen, R., Simon, C.: Evolutionary ecology of periodical insects. Tree 9, 475-480 (1994)
16. Hofbauer, J., Sigmund, K.: Evolutionary Games and Population Dynamics. Cambridge University Press, 1998
17. Hoppensteadt, F.C., Keller, J.B.: Synchronization of periodical cicada emergences. Science 194, 335-337 (1976)
18. Kuznetsov, Yu.A.: Elements of Applied Bifurcation Theory. Second Edition. New York: Springer-Verlag, 1998
19. Kuznetsov, Yu.A., Levitin V.V.: CONTENT: A multiplatform environment for analyzing dynamical systems. Dynamical Systems Laboratory, CWI, Amsterdam (1997) [ftp://ftp.cwi.nl/pub/CONTENT]
20. May, R.M., Oster, G.F.: Bifurcations and dynamical complexity in simple ecological models. Am. Nat. 110, 573-599 (1976)
21. Melo, W. de, Strien, S. van.: One-Dimensional Dynamics. Springer-Verlag, 1993
22. Murray, J.D.: Mathematical Biology. Springer-Verlag, 1989
23. Mylius, S.D., Diekmann, O.: The resident strikes back: invader-induced switching of resident attractor. To appear in J. Theor. Biol.
24. Nisbet, R.M., Onyiah, L.C.: Population dynamics consequences of competition within and between age classes. J. Math. Biol. 32, 329-344 (1994)
25. Roos, A.M. de, Metz, J.A.J., Evers, E., Leipoldt, A.: A size dependent predator-prey interaction: who pursues whom? J. Math. Biol. 28, 609-643 (1990)
26. Silva, J.A.L., Hallam, T.G.: Effects of delay, truncations and density dependence in reproduction schedule on stability of nonlinear Leslie matrix models. J. Math. Biol. 31, 367-395 (1993)
27. Solberg, T.S.: Rare Phenomena in an Age-Structured Population Model. Master Thesis, University of Tromsø, 1998
28. Thunberg, H.: Periodicity versus Chaos in One-Dimensional Dynamics. SIAM Review 43, 3-30 (2001)
29. Wikan, A., Mjølhus, E.: Periodicity of 4 in Age-structured Population Models with Density Dependence. J. Theor. Biol. 173, 109-119 (1995)
30. Wikan, A., Mjølhus, E.: Overcompensatory recruitment and generation delay in discrete age-structured population models. J. Math. Biol. 35, 195-239 (1996)
31. Wikan, A.: Dynamic Consequences of Reproductive Delay in Leslie Matrix Models with Nonlinear Survival Probabilities. Math. Biosci. 146, 37-62 (1997)