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

003). II. /butte C. & Doeba. M. Spatial structure often inhibits the evolution of cooperation In the snowdrift game. Nature 428,643-646 (2000. 12. Komarova, N. L Spatial stochastic models for cancer initiation and progression. Bull. Math. Biol. 68. 1573-1599 (2006). 13. Pere. M. & SzolnokL A. Social di

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

t phylogenctic networks: A new methodology for reconstructing the evolutionary history of natural languages. Language 81: 382-420. 90. Nowak MA, NL Komarova (2005). The evolution of altruism: From game theory to human language. In Spiritual Information, ed. CL Harper. Templeton Foundation Press, 308-314.

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.

C.R.M., McMichael, A.J., 1995. Antigenic oscillations and shifting inununodominance in HIV-1 infections. Na- ture 375, 606-611. [108] Nowak, M.A., Komarova, N.L., Niyogi, P., 2002. Computational and evolutionary aspects of language. Nature 417, 611-617. [109] Nowak, M.A., Krakauer, D.C., (1999). The ev