Epstein Secrets

1992, 2002, Hofbauer 1999). Evolutionary graph theory is an extension of spatial games to more general popu- lation structures and social networks (Lieberman et al 2005, Ohtsuki et al 2006a,b, Pacheco et al 2006, Szabo & Fath 2007, Taylor et al 2007a, Santos at al 2008, RI et al 2008). The members of the

ho-interacts-with-whom changes during the evolutionary process (Fig 2.2). For mathematical convenience we con- sider evolutionary game dynamics in a Wright-Fisher process with constant population size [63]. A frequency dependent Moran process [110] or a pairwise comparison process [156], which is more realist

t in common, they interact several times. An interaction is given by the usual payoff matrix. The system evolves according to synchronous updating (Wright-Fisher process). There are discrete, non-overlapping generations. All individuals update at the same time. The population size is constant. Individuals re

Science, 303, 793-799. 0.14] Nowak, M.A., Sigmund, K., 2005. Evolution of indirect reciprocity. Nature 427, 1291- 1298. (115] Ohtsuki H, Hauert C, Lieberman E, Nowak MA, 2006a. A simple nile for the evolution of cooperation on graphs and social networks. Nature, 441, 502-505. [116] Ohtsuki, H., Iwasa, Y

Evolutionary updating occurs according to the frequency dependent Moran process (Nowak et al, 2004; Taylor et al, 2004) or the frequency dependent Wright-Fisher process (Imhof & Nowak, 2006). Reproduction is proportional to fitness and subject to a mutation rate u. With probability 1 — u the offspring inheri

A., 2005. Evolutionary cycles of coop- eration and defection. PNAS, 102, 1079710800. [63] Imhof LA, Nowak MA, 2006. Evolutionary game dynamics in a Wright-Fisher process. J. Math. Biol 52, 667-681. [64] Jansen VA, van Baalen M, 2006. Altruism through beard chromodynkunics. Nature, 440, 663-666. [65] Kandor

r, C Taylor (2005). Grammar structure and the dynamics of language evolution. In Proceedings of the 8th European Conference on Artificial Lifc. 80. Lieberman E, C Hauert, MA Nowak (2005). Evolutionary dynamics on graphs. Nature 433: 312-316. 81. Lieberman E, C Hauert, MA Nowak (2005). Evolutionary dynami

nergy and discounting of cooperation in social dilemmas. I theor Biol 239: 195-202. 125. Imhof LA, MA Nowak (2006). Evolutionary game dynamics in a Wright-Fisher process. Math Biol 52: 667-681. 126. Iwasa Y, MA Nowak, F Michor (2006). Evolution of resistance during clonal expansion. Genetics 172: 2557-2566.