Acta mathematica scientia, Series B >
EVOLUTIONARY DYNAMICS ON ONE-DIMENSIONAL CYCLE WITH SHIFTING MECHANISM AND TINY MUTATION RATE
Received date: 2014-01-26
Revised date: 2014-03-18
Online published: 2015-01-20
Supported by
Supported by National Natural Science Foundation of China (71231007, 50909073).
In this paper we study the impact of tiny mutation on the evolutionary dynamics on one-dimensional cycle with shifting mechanism. The evolutionary success is evaluated by investigating the stationary distribution of the ergodic process with the idea of viscosity solutions. The cooperative behaviors in ecosystem and social system are briefly discussed by applying the results to the prisoner’s dilemma game.
Key words： evolutionary games; Moran process; Markov chain; prisoner’s dilemma game
WANG XianJia,LAN Jun,DONG QianJin, LEI GuoLiang . EVOLUTIONARY DYNAMICS ON ONE-DIMENSIONAL CYCLE WITH SHIFTING MECHANISM AND TINY MUTATION RATE[J]. Acta mathematica scientia, Series B, 2015 , 35(1) : 95 -104 . DOI: 10.1016/S0252-9602(14)60142-9
[1] Antal T, Scheuring I. Fixation of strategies for an evolutionary game in finite populations. Bull Math Biol,
2006, 68(8): 1923–1944
[2] Allen B, Nowak M A. Evolutionary shift dynamics on a cycle. J Theor Biol, 2012, 311: 28–39
[3] Bo X Y, Yang J M. Evolutionary ultimatum game on complex networks under incomplete information.
Physica A, 2010, 389(5): 1115–1123
[4] Goodnight C J. Multilevel selection: the evolution of cooperation in non-kin groups. Population Ecology,
2005, 47(1): 3–12
[5] Hofbauer J, Sigmund K. The Theory of Evolution and Dynamical Systems. Cambridge, UK: Cambridge
University Press, 1988
[6] Jackson M O. Networks and economic behavior. Annu Rev Econ, 2009, 1(1): 489–513
[7] Maynard S J, Price G R. The logic of animal conflict. Nature, 1973, 246: 15–18
[8] Maynard S J. Evolution and the Theory of Games. Cambridge, UK: Cambridge University Press, 1982
[9] Ohtsuki H, Iwasa Y, Nowak M A. Indirect reciprocity provides only a narrow margin of efficiency for costly
punishment. Nature, 2009, 457(7225): 79–82
[10] Pacheco J M, Traulsen A, Nowak M A. Active linking in evolutionary games. J Theor Biol, 2006, 243(3):
437–443
[11] Qin S M, Zhang G Y, Chen Y. Coevolution of game and network structure with adjustable linking. Physica
A, 2009, 388(23): 4893–4900
[12] Smith J, Van Dyken J D, Zee P C. A generalization of Hamilton’s rule for the evolution of microbial
cooperation. Science, 2010, 328(5986): 1700–1703
[13] Taylor P D, Wild G, Gardner A. Direct fitness or inclusive fitness: How shall we model kin selection. J
Evol Biol, 2007, 20(1): 301–309
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