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A non-local rare mutations model for quasispecies and prisoner's dilemma: Numerical assessment of qualitative behaviour

Published online by Cambridge University Press:  20 July 2015

ANNA LISA AMADORI ,
MAYA BRIANI  and
ROBERTO NATALINI
ANNA LISA AMADORI
Affiliation:
Dipartimento di Scienze Applicate, Università di Napoli “Parthenope”, Naples, Italy email: annalisa.amadori@uniparthenope.it
MAYA BRIANI
Affiliation:
Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle Ricerche, Rome, Italy email: m.briani@iac.cnr.it, roberto.natalini@cnr.it
ROBERTO NATALINI
Affiliation:
Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle Ricerche, Rome, Italy email: m.briani@iac.cnr.it, roberto.natalini@cnr.it
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Abstract

An integro-differential model for evolutionary dynamics with mutations is investigated by improving the understanding of its behaviour using numerical simulations. The proposed numerical approach can handle also density dependent fitness, and gives new insights about the role of mutation in the preservation of cooperation.

Keywords

Coevolutionary dynamicsmutationsnumerical approximation of partial integro-differential eqxsuationsquasispeciesprisoner's dilemma
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 1 , February 2016 , pp. 87 - 110
Copyright
Copyright © Cambridge University Press 2015 

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References

[1] Amadori, A. L., Calzolari, A., Natalini, R. & Torti, B. (2012) Rare mutations in evolutionary dynamics. preprint arXiv:1211.4170.Google Scholar
[2] Champagnat, N., Ferrière, R. & Méléard, S. (2008) From individual stochastic processes to macroscopic models in adaptive evolution. Stoch. Models 24 (sup. 1), 2–44.Google Scholar
[3] Dieckmann, U. & Law, R. (2000) Relaxation projections and the method of moments. In: Dieckmann, U., Law, R. and Metz, J. A. J. (editors), The Geometry of Ecological Interactions: Simplifying Spatial Complexity, Cambridge University Press, Cambridge, pp. 412–455.CrossRefGoogle Scholar
[4] Diekmann, O., Jabin, P. E., Mischler, S. & Perthame, B. (2005) The dynamics of adaptation: An illuminating example and a Hamilton–Jacobi approach. Theor. Population Biol. 67 (4), 257–271.Google Scholar
[5] Eigen, M. & Schuster, P. (1979) The Hypercycle: A Principle of Natural Self-Organization, Springer-Verlag, Berlin (west).Google Scholar
[6] Hofbauer, J. & Sigmund, K. (1998) Evolutionary Games and Population Dynamics, Cambridge University Press, Cambridge.Google Scholar
[7] Maynard Smith, J. & Price, G. R. (1973) The logic of animal conflict. Nature 246, 15–18.CrossRefGoogle Scholar
[8] Metz, J. A., Geritz, S. A., Meszéna, G., Jacobs, F. J. & Van Heerwaarden, J. (1996) Adaptive dynamics, a geometrical study of the consequences of nearly faithful reproduction. Stoch. Spatial Struct. Dyn. Syst. 45, 183–231.Google Scholar
[9] Morton, K. W. & Mayers, D. F. (1998) Numerical Solution of Partial Differential Equations, Cambridge University Press, Cambridge UK.Google Scholar
[10] Nowak, M. A. (2006) Evolutionary Dynamics. Exploring the Equations of Life, The Belknap Press of Harvard University Press, Cambridge, MA.Google Scholar
[11] Nowak, M. A. (2012) Evolving cooperation. J. Theor. Biol. 299, 1–8.Google Scholar
[12] Stadler, P. & Schuster, P. (1992) Mutation in autocatalytic reaction networks. J. Math. Biol. 30 (6), 597–632.Google Scholar