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Science 303 (5659): 793-799

Copyright © 2004 by the American Association for the Advancement of Science

Evolutionary Dynamics of Biological Games

Martin A. Nowak1*, and Karl Sigmund2,3

Abstract: Darwinian dynamics based on mutation and selection form the core of mathematical models for adaptation and coevolution of biological populations. The evolutionary outcome is often not a fitness-maximizing equilibrium but can include oscillations and chaos. For studying frequency-dependent selection, game-theoretic arguments are more appropriate than optimization algorithms. Replicator and adaptive dynamics describe short- and long-term evolution in phenotype space and have found applications ranging from animal behavior and ecology to speciation, macroevolution, and human language. Evolutionary game theory is an essential component of a mathematical and computational approach to biology.

1 Program for Evolutionary Dynamics, Department of Mathematics, Department of Organismic and Evolutionary Biology, Harvard University, 1 Brattle Square, Cambridge, MA 02138, USA.
2 Faculty for Mathematics, University of Vienna, Nordberggasse 15, A-1090 Vienna, Austria.
3 International Institute for Applied Systems Analysis (IIASA), A-2361 Laxenburg, Austria.

* To whom correspondence should be addressed. E-mail: martin_nowak{at}

Aspiration dynamics of multi-player games in finite populations.
J. Du, B. Wu, P. M. Altrock, and L. Wang (2014)
J R Soc Interface 11, 20140077
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Frequency-dependent assistance as a way out of competitive exclusion between two strains of an emerging virus.
F. Perefarres, G. Thebaud, P. Lefeuvre, F. Chiroleu, L. Rimbaud, M. Hoareau, B. Reynaud, and J.-M. Lett (2014)
Proc R Soc B 281, 20133374
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Strategies for cellular decision-making.
T. J. Perkins and P. S. Swain (2014)
Mol Syst Biol 5, 326
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A synthetic Escherichia coli predator-prey ecosystem.
F. K. Balagadde, H. Song, J. Ozaki, C. H. Collins, M. Barnet, F. H. Arnold, S. R. Quake, and L. You (2014)
Mol Syst Biol 4, 187
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Forecasting craniofacial growth in individuals with class III malocclusion by computational modelling.
P. Auconi, M. Scazzocchio, E. Defraia, J. A. McNamara, and L. Franchi (2014)
Eur J Orthod 36, 207-216
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Bacterial cheating drives the population dynamics of cooperative antibiotic resistance plasmids.
E. A. Yurtsev, H. X. Chao, M. S. Datta, T. Artemova, and J. Gore (2014)
Mol Syst Biol 9, 683
   Abstract »    Full Text »    PDF »
From Matter to Self-Organizing Life.
A. Traulsen (2013)
Science 342, 39-40
   Abstract »    Full Text »    PDF »
Adaptation of the Osmotolerant Yeast Zygosaccharomyces rouxii to an Osmotic Environment Through Copy Number Amplification of FLO11D.
J. Watanabe, K. Uehara, and Y. Mogi (2013)
Genetics 195, 393-405
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O Brave New World with Such Games.
B. Allen and M. A. Nowak (2013)
Science 341, 844
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Exploiting ecological principles to better understand cancer progression and treatment.
D. Basanta and A. R. A. Anderson (2013)
Interface Focus 3, 20130020
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Manipulated into giving: when parasitism drives apparent or incidental altruism.
C. P. Doncaster, A. Jackson, and R. A. Watson (2013)
Proc R Soc B 280, 20130108
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Evolution of fairness in the one-shot anonymous Ultimatum Game.
D. G. Rand, C. E. Tarnita, H. Ohtsuki, and M. A. Nowak (2013)
PNAS 110, 2581-2586
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Eco-evolutionary feedbacks, adaptive dynamics and evolutionary rescue theory.
R. Ferriere and S. Legendre (2012)
Phil Trans R Soc B 368, 20120081
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The dynamics of adapting, unregulated populations and a modified fundamental theorem.
J. P. O'Dwyer (2012)
J R Soc Interface 10, 20120538
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Multiple strategies in structured populations.
C. E. Tarnita, N. Wage, and M. A. Nowak (2011)
PNAS 108, 2334-2337
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Imitation dynamics of vaccination behaviour on social networks.
F. Fu, D. I. Rosenbloom, L. Wang, and M. A. Nowak (2011)
Proc R Soc B 278, 42-49
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Evolutionary games in the multiverse.
C. S. Gokhale and A. Traulsen (2010)
PNAS 107, 5500-5504
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Stochastic evolutionary dynamics of direct reciprocity.
L. A. Imhof and M. A. Nowak (2010)
Proc R Soc B 277, 463-468
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Evolutionary dynamics in structured populations.
M. A. Nowak, C. E. Tarnita, and T. Antal (2010)
Phil Trans R Soc B 365, 19-30
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Application of game theory to the interaction between plant viruses during mixed infections.
S. Martin and S. F. Elena (2009)
J. Gen. Virol. 90, 2815-2820
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Evolution of cooperation by phenotypic similarity.
T. Antal, H. Ohtsuki, J. Wakeley, P. D. Taylor, and M. A. Nowak (2009)
PNAS 106, 8597-8600
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Evolutionary dynamics in set structured populations.
C. E. Tarnita, T. Antal, H. Ohtsuki, and M. A. Nowak (2009)
PNAS 106, 8601-8604
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Evolutionary dynamics of collective action in N-person stag hunt dilemmas.
J. M Pacheco, F. C Santos, M. O Souza, and B. Skyrms (2009)
Proc R Soc B 276, 315-321
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A Path Toward Fairness: Preferential Association and the Evolution of Strategies in the Ultimatum Game.
Y.-S. Chiang (2008)
Rationality and Society 20, 173-201
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The Evolution of Trust in Non-Simultaneous Exchange Situations.
G. Bravo and L. Tamburino (2008)
Rationality and Society 20, 85-113
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Probabilistic participation in public goods games.
T. Sasaki, I. Okada, and T. Unemi (2007)
Proc R Soc B 274, 2639-2642
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Evolution of DNA Double-Strand Break Repair by Gene Conversion: Coevolution Between a Phage and a Restriction-Modification System.
K. Yahara, R. Horie, I. Kobayashi, and A. Sasaki (2007)
Genetics 176, 513-526
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Upstream reciprocity and the evolution of gratitude.
M. A Nowak and S. Roch (2007)
Proc R Soc B 274, 605-610
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Improved evolutionary optimization from genetically adaptive multimethod search.
J. A. Vrugt and B. A. Robinson (2007)
PNAS 104, 708-711
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Five Rules for the Evolution of Cooperation.
M. A. Nowak (2006)
Science 314, 1560-1563
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The Origin of Life and the Left-Handed Amino-Acid Excess: The Furthest Heavens and the Deepest Seas?.
G. Goodman and M. E. Gershwin (2006)
Experimental Biology and Medicine 231, 1587-1592
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Evolutionary games on cycles.
H. Ohtsuki and M. A Nowak (2006)
Proc R Soc B 273, 2249-2256
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The evolution of hyperactivity, impulsivity and cognitive diversity.
J. Williams and E. Taylor (2006)
J R Soc Interface 3, 399-413
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Destructive cycles: the role of genomic instability and adaptation in carcinogenesis.
B. L. Schneider and M. Kulesz-Martin (2004)
Carcinogenesis 25, 2033-2044
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The Evolutionary Origin of Cooperators and Defectors.
M. Doebeli, C. Hauert, and T. Killingback (2004)
Science 306, 859-862
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