Epstein Secrets

allowing self-loops and assigning weights to edges. Self-loops are natural. They indicate that the offspring can replace the parent °. The standard Moran process is given by a complete graph with self-loops. In the proof1°. we start by defining a subset of vertices called a hub and partitioning the r

ri, L. & Wodarz, D. Complex role of space in the crossing of fitness valleys by asexual populations. I. R. Soc. Interface 11. 20140014 (2014). 17. Lieberman, E. Hawn. C & Nowak. M. A. Evolutionary dynamics on graphs. Nature 433,312-316 (2005). 18. Broom. M. & Rychtlt.1. An analysis of the fixation proba

ure 438: T148-T150. 64. Claussen J, Traulsen A (2005). Nongaussian fluctuations arising from finite populations: Exact results for the evolutionary Moran process. Phys Rev E 71: 025101. 65. Docbeli M, C Hauert (2005). Models of cooperation based on the Prisoner's Dilemma and the Snowdrift game. Ecol

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

t much larger than the degree, as well as the phenotype space. 2.5.1 The well-mixed population As first example we consider the frequency dependent Moran process in a well mixed population of size N (Nowak et al 2004, Taylor et al 2004, Nowak 2006a) (Fig.la). In the language of evolutionary graph the

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

weak selection (as opposed to 6 cc 1) shall become clear at the end of this section. The dynamics of the system is given by the frequency dependent Moran process. In each time step a randomly chosen individual is replaced by a copy of an individual chosen with probability proportional to its payoff.

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