Abstract.
We study the resident-invader dynamics for a given class of models of unstructured populations of finite-dimensional strategies. We prove various results on the existence and uniqueness of ω-limit sets in the interior of the resident-invader population state space, and we classify the generically possible types of dynamics in terms of the invasion conditions when the resident and invader strategies are similar to one another.
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Dercole, F.: Evolutionary dynamics through bifurcation analysis: methods and applications. Ph.D. Thesis. Department of Electronics and Information. Politecnico di Milano, 2002
Dercole, F., Ferriere, R., Rinaldi, S.: Ecological bistability and evolutionary reversals under asymmetric competition. Evolution 56, 1081–1090 (2002)
Dieckmann, U., Law, R.: The dynamical theory of coevolution: a derivation from stochastic ecological processes. J. Math. Biol. 34, 579–612 (1996)
Diekmann, O., Mylius, S.D., ten Donkelaar, J.R.: Saumon a la Kaitala et Getz, sauce hollandaise. Evol. Ecol. Res. 1, 261–275 (1999)
Geritz, S.A.H., Gyllenberg, M., Jacobs, F.J.A., Parvinen, K.: Invasion dynamics and attractor inheritance. J. Math. Biol. 44, 548–560 (2002)
Geritz, S.A.H., Kisdi, E., Meszena, G., Metz, J.A.J.: Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol. Ecol. 12, 35–57 (1998)
Geritz, S.A.H., Metz, J.A.J., Kisdi, E., Meszena, G.: Dynamics of adaptation and evolutionary branching. Phys. Rev. Letters. 78, 2024–2027 (1997)
Gyllenberg, M., Metz, J.A.J.: On fitness in structured metapopulations. J. Math. Biol. 43, 545–560 (2001)
Gyllenberg, M., Parvinen, K.: Necessary and sufficient conditions for evolutionary suicide. Bul. Math. Biol. 63, 981–993 (2001)
Hofbauer, J., Sigmund, K.: Evolutionary games and population dynamics. Cambridge University Press, Cambridge, UK, 1998
Meszena, G., Kisdi, E., Dieckmann, U., Geritz, S.A.H., Metz, J.A.J.: Evolutionary optimization models and matrix games in the unified perspective of adaptive dynamics. Selection 2, 193–210 (2001)
Metz, J.A.J., Gyllenberg, M.: How should we define fitness in structured metapopulation models? Including an application to the calculation of evolutionarily stable dispersal strategies. Proc. R. Soc. Lond. B. 268, 499–508 (2001)
Metz, J.A.J., Geritz, S.A.H., Meszena, G., Jacobs, F.J.A., Van Heerwaarden, J.S.: Adaptive dynamics, a geometrical study of the consequences of nearly faithful reproduction. In: Van Strien, S.J., Verduyn-Lunel, S.M. (eds.), Stochastic and spatial structures of dynamical systems. North Holland, Amsterdam, 1996, pp. 183–231
Metz, J.A.J., Nisbet, R.M., Geritz, S.A.H.: How should we define ‘fitness’ for general ecological scenarios. Trends Ecol. Evol. 7, 198–202 (1992)
Mylius, S.D., Diekmann, O.: On evolutionarily stable life-histories, optimization and the need to be specific about density dependence. OIKOS 74, 218–224 (1995)
Mylius, S.D., Diekmann, O.: The resident strikes back: Invader induced switching of resident attractor. J. Theor. Biol. 211, 297–311 (2001)
Nemytskii, V.V., Stepanov, V.V.: Qualitative theory of differential equations. Dover Publications, New York, 1989
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This work was supported by the Academy of Finland
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Geritz, S. Resident-invader dynamics and the coexistence of similar strategies. J. Math. Biol. 50, 67–82 (2005). https://doi.org/10.1007/s00285-004-0280-8
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DOI: https://doi.org/10.1007/s00285-004-0280-8