Abstract
In this paper we present, in terms of invasion fitness functions, a sufficient condition for a coexistence of two strategies which are not protected from extinction when rare. In addition, we connect the result to the local characterization of singular strategies in the theory of adaptive dynamics. We conclude with some illustrative examples.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Boldin B, Geritz SAS, Kisdi E (2009) Superinfections and adaptive dynamics of pathogen virulence revisited: a critical function analysis. Evol Ecol Res 11: 153–175
Christiansen FB, Loeschke V (1980) Evolution and intraspecific exploitation competition I. One-locus theory for small additve gene effects. Theor Popul Biol 18: 297–313
Claessen D, Dieckmann U (2002) Ontogenetic niche shift and evolutionary branching in structured populations. Evol Ecol Res 4: 189–217
Dieckmann U (1997) Can adaptive dynamics invade. Trends Ecol Evol 12: 128–131
Doebeli M, Block HJ, Leimar O, Dieckmann U (2007) Multimodal pattern formation in phenotype distributions of sexual populations. Proc R Soc 274: 347–357
Ferriere R, Gatto M (1993) Chaotic population dynamics can result from natural selection. Proc Biol Sci 251: 33–38
Gavrilets S (2004) Fitness landscapes and the origin of species. Princeton University Press, Princeton
Geritz SAH (2005) Resident-invader dynamics and the coexistence of similar strategies. J Math Biol 50: 67–82
Geritz SAH, Kisdi É, Meszéna G, Metz JAJ (1998) Evolutionarily singular strategies and the adaptive growth and branching of the evolutioary tree. Evol Ecol 12: 35–57
Geritz SAH, Gyllenberg M, Jacobs FJA, Parvinen K (2002) Invasion dynamics and attractor inheritance. J Math Biol 44: 548–560
Gyllenberg M, Metz JAJ (2001) On fitness in structured metapopulations. J Math Biol 43: 545–560
Hoekstra RF, Bijlsma R, Dolman AJ (1985) Polymorphism from environmental heterogeneity: models are only robust if the heterozygote is close in fitness to the favoured homozygote in each environment. Genet Res Camb 45: 299–314
Kisdi É, Meszéna G (1993) Density dependent life history evolution in fluctuating environments. In: Clark CW, Yoshimura J (eds) Adaptation in a Stochastic Environment. Lecture Notes in Biomathematics 98:26–62
Kisdi É, Meszéna G (1995) Life history with lottery competition in a stochastic environment: ESSs which do not prevail. Theor Pop Biol 47: 191–211
Kisdi É, Jacobs FJA, Geritz SAH (2001) Red queen evolution by cycles of evolutionary branching and extinction. Selection 1–2: 161–176
Kisdi É, Priklopil T (2010) Evolutionary branching of a magic trait. J Math Biol. doi:10.1007/s00285-010-0377-1
Kuznetsov YA (1998) Elements of applied bifurcation theory. Springer, New York
Levene H (1953) Genetic equilibrium when more than one ecological niche is available. Am Nat 87: 331–333
Matsuda H (1985) Evolutionarily stable strategies for predator switching. J Theor Biol 115: 351–366
Metz JAJ, Nisbet RM, Geritz SAH (1992) How should we define “fitness” for general ecological scenarios?. Trends Ecol Evol 7: 198–202
Metz JAJ, Geritz SAH, Meszéna G, Jacobs FJA, Van Heerwaarden JS (1996) Adaptive dynamics: a geometrical study of the consequences of nearly faithful reproduction. In: van Strien SJ, Verduyn Lunel SM (eds) Stochastic and spatial structures of dynamical systems. Elsevier, North-Holland, pp 183–231
Motro U (1982) Optimal rates of dispersal I. Haploid populations. Theor Popul Biol 21: 394–411
Novak S (2011) The number of equilibria in the diallelic Levene model with multiple demes. Theor Popul Biol 79: 97–101
Poulsen ET (1979) A model for population regulation with density- and frequency-dependent selection. J Math Biol 8: 325–343
Prout T (1968) Sufficient conditions for multiple niche polymorphism. Am Nat 102: 493–496
Rueffler C, Van Dooren TJM, Metz JAJ (2004) Adaptive walks on changing landscapes: Levins? approach extended. Theor Popul Biol 65: 165–178
van Tienderen PH, de Jong G (1986) Sex ration under the haystack model: polymorphism may occur. J Theor Biol 122: 69–81
Wiggins S (1990) Introduction to applied nonlinear dynamical systems and Chaos. Springer, New York
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Priklopil, T. On invasion boundaries and the unprotected coexistence of two strategies. J. Math. Biol. 64, 1137–1156 (2012). https://doi.org/10.1007/s00285-011-0448-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00285-011-0448-y