Local stability of evolutionary attractors for continuous structured populations

Monatshefte fur Mathematik

Volumn 165, Issue 1, 2012, Pages 117-144

  Raoul, Gaël ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

ESS; Evolutionary attractor; Long time asymptotics; Population dynamics; Selection competition

Indexed keywords

EID: 84855664002     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00605-011-0354-9     Document Type: Article

References (14)

1. Calcina A., Cuadrado S.: Small mutation rate and evolutionarily stable strategies in infinite dimensional adaptive dynamics. J. Math. Biol. 48, 135-159 (2004).
2. Champagnat N., Ferrière R., Ben Arous G.: The canonical equation of adaptive dynamics: a mathematical view. Selection 2, 71-81 (2001).
3. Champagnat N., Ferrière R., Méléard S.: Unifying evolutionary dynamics: from individual stochastic processes to macroscopic models. Theor. Popul. Biol. 69, 297-321 (2006).
4. Desvillettes L., Jabin P.E., Mischler S., Raoul G.: On selection dynamics for continuous populations. Commun. Math. Sci. 6(3), 729-747 (2008).
5. Diekmann, O.: Beginner's guide to adaptive dynamics. Banach Center Publ., vol. 63, pp. 47-86. Polish Acad. Sci., Warsaw (2004).
6. Diekmann O., Jabin P.E., Mischler S., Perthame B.: The dynamics of adaptation: an illuminating example and a Hamilton-Jacobi approach. Theor. Popul. Biol. 67, 257-271 (2005).
7. Dieckmann U., Doebeli M.: On the origin of species by sympatric speciation. Nature 400, 354-357 (1999).
8. Dieckmann U., Law R.: The dynamical theory of coevolution: a derivation from stochastic ecological processes. J. Math. Biol. 34, 579-612 (1996).
9. Geritz S., 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).
10. Hofbauer J., Sigmund K.: Evolutionary games and population dynamics. Cambridge University Press, Cambridge (1998).
11. Jabin, P. E., Raoul, G.: On selection dynamics for competitive interactions. preprint, CMLA-ENS Cachan 17 (2009) (submitted).
12. Metz J.A. J., Geritz S.A. H., Meszéna G., Jacobs F.J. A., van Heerwaareden J.S.: Adaptive dynamics: a geometrical study of the consequences of nearly faithful reproduction. In Stochastic and spatial structures of dynamical systems. In: van Strien, S. J., Lunel, S. M. V. (eds.) Stochastic and spatial structures of dynamical systems, pp. 183-231. Elsevier, North Holland (1996).
13. Rudin, W.: Real and complex analysis, 3rd edn. Mc Graw-Hill series in higher mathematics, Chapt 7. Mc Graw-Hill, London.
14. Waxman D., Gavrilets S.: 20 questions on adaptive dynamics. J. Evol. Biol. 18, 1139-1154 (2005).