Frequency-dependent fitness induces multistability in coevolutionary dynamics

Journal of the Royal Society Interface

Volumn 9, Issue 77, 2012, Pages 3387-3396

  Arnoldt, Hinrich ^a,b   Timme, Marc ^a   Grosskinsky, Stefan ^c  

^a MAX PLANCK INSTITUTE FOR DYNAMICS AND SELF ORGANIZATION   (Germany)

^b UNIVERSITY OF GÖTTINGEN   (Germany)

^c UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

Dynamic fitness; Multistability; Population dynamics; Stochastic switching

Indexed keywords

HEALTH; POPULATION DYNAMICS; STOCHASTIC SYSTEMS;

COEVOLUTIONARY DYNAMICS; DIFFERENT MECHANISMS; EVOLUTIONARY DYNAMICS; FREQUENCY-DEPENDENT; GAME-THEORETIC; GENERIC FEATURES; GENETIC DRIFTS; LINEAR FREQUENCY DEPENDENCE; META-STABLE STATE; MULTISTABILITY; MUTATION RATES; NON-TRIVIAL; NONLINEAR FREQUENCY; RANDOM SAMPLING; STOCHASTIC SWITCHING; SYSTEM PROPERTY; THEORETICAL RESEARCH;

DYNAMICS;

ARTICLE; COEVOLUTION; COEVOLUTIONARY DYNAMICS; DYNAMICS; FITNESS; FREQUENCY DEPENDENT SELECTION; GENE FREQUENCY; GENE MUTATION; GENE SWITCHING; GENETIC DRIFT; GENOTYPE; MATHEMATICAL MODEL; MOLECULAR DYNAMICS;

EID: 84868535032     PISSN: 17425689     EISSN: 17425662     Source Type: Journal    
DOI: 10.1098/rsif.2012.0464     Document Type: Article

References (26)

1. Drossel, B. 2001 Biological evolution and statistical physics. Adv. Phys. 50, 209-295. (doi:10.1080/00018730 110041365)
2. Blythe, R. A. & McKane, A. J. 2007 Stochastic models of evolution in genetics, ecology and linguistics. J. Stat. Mech. 2007, P07018. (doi:10.1088/1742-5468/2007/07/P07018)
3. Crow, J. F. & Kimura, M. 1970 An introduction to population genetics theory. New York, NY: Harper & Row Publishers.
4. Turner, P. E. & Chao, L. 1999 Stochastic models of evolution in genetics, ecology and linguistics. Nature 398, 441-443. (doi:10.1038/18913)
5. Gore, J., Youk, H. & van Oudenaarden, A. 2009 Snowdrift game dynamics and facultative cheating in yeast. Nature 459, 253-256. (doi:10.1038/ nature07921)
6. McCauley, D. E. & Brock, M. T. 1998 Frequencydependent fitness in silene vulgaris, a gynodioecious plant. Evolution 52, 30-36. (doi:10.2307/2410917)
7. Antal, T., Nowak, M. A. & Traulsen, A. 2009 Strategy abundance in games for arbitrary mutation rates. J. Theor. Biol. 257, 340-344. (doi:10.1016/j.jtbi.2008. 11.023)
8. Antal, T. & Scheuring, I. 2006 Fixation of strategies for an evolutionary game in finite populations. Bull. Math. Biol. 68, 1923-1944. (doi:10.1007/s11538-006-9061-4)
9. Antal, T., Traulsen, A., Ohtsuki, H., Tarnita, C. E. & Nowak, M. A. 2009 Mutation-selection equilibrium in games with multiple strategies. J. Theor. Biol. 258, 614-622. (doi:10.1016/j.jtbi.2009.02.010)
10. Assaf, M. & Mobilia, M. 2010 Large fluctuations and fixation in evolutionary games. J. Stat. Mech. 2010, P09009. (doi:10.1088/1742-5468/2010/09/ p09009)
11. Taylor, C., Fudenberg, D., Sasaki, A. & Nowak, M. A. 2004 Evolutionary game dynamics in finite populations. Bull. Math. Biol. 66, 1621-1644. (doi:10.1016/j.bulm. 2004.03.004)
12. Traulsen, A., Claussen, J. C. & Hauert, C. 2005 Coevolutionary dynamics: from finite to infinite populations. Phys. Rev. Lett. 95, 238701. (doi:10.1103/PhysRevLett.95. 238701)
13. Traulsen, A., Claussen, J. C. & Hauert, C. 2006 Coevolutionary dynamics in large, but finite populations. Phys. Rev. E 74, 011901. (doi:10.1103/PhysRevE.74.011901)
14. Wu, B., Gokhale, C. S., Wang, L. & Traulsen, A. 2012 How small are mutation rates? J. Math. Biol. 64, 803-827. (doi:10.1007/s00285-011-0430-8)
15. Pohley, H.-J. & Thomas, B. 1983 Non-linear ESS-models and frequency dependent selection. Biosystems 16, 87-100. (doi:10.1016/0303-2647(83)90030-8)
16. Durett, R. & Schmidt, D. 2008Waiting for two mutations: with applications to regulatory sequence evolution and the limits of Darwinian evolution. Genetics 180, 1501-1509. (doi:10.1534/genetics.107.082610)
17. Sasaki, A. & Nowak, M. A. 2003 Mutation landscapes. J. Theor. Biol. 224, 241-247. (doi:10.1016/S0022- 5193(03)00161-9)
18. Nee, S. 2006 Birth-death models in macroevolution. Annu. Rev. Ecol. Evol. Syst. 37, 1-17. (doi:10.1146/annurev.ecolsys.37.091305.110035)
19. Moran, P. A. P. 1962 The statistical processes of evolutionary theory. Oxford, UK: Clarendon Press.
20. Risken, H. 1989 The Fokker-Planck equation. Berlin, Germany: Springer.
21. Imhof, L. A., Fudenberg, D. & Nowak, M. A. 2005 Evolutionary cycles of cooperation and defection. Proc. Natl Acad. Sci. USA 102, 10 797-10 800. (doi:10.1073/pnas. 0502589102)
22. Bladon, A. J., Galla, T. & McKane, A. J. 2010 Evolutionary dynamics, intrinsic noise, and cycles of cooperation. Phys. Rev. E 81, 066122. (doi:10.1103/PhysRevE.81. 066122)
23. Claussen, J. C. & Traulsen, A. 2005 Non-Gaussian fluctuations arising from finite populations: exact results for the evolutionary Moran process. Phys. Rev. E 71, 025101(R). (doi:10.1103/PhysRevE.71.025101)
24. Ohta, T. 2002 Inaugural article: near-neutrality in evolution of genes and gene regulation. Proc. Natl Acad. Sci. USA 99, 16 134-16 137.(doi:10.1073/pnas.252626899)
25. Jain, K. & Krug, J. 2007 Deterministic and stochastic regimes of asexual evolution on rugged fitness landscapes. Genetics 175, 1275-1288. (doi:10.1534/genetics.106. 067165)
26. Gross, T. & Blasius, B. 2008 Adaptive coevolutionary networks: a review. J. R. Soc. Interface 5, 259-271. (doi:10.1098/rsif.2007.1229)