Epstein Secrets

rsity Cambridge, Massachusetts June 2009 EFTA00748858 @2009 - Corina Elena Tarnita All rights reserved. EFTA00748859 Thesis advisor Author Martin A. Nowak Corina Elena Tarnita Evolutionary Dynamics in Structured Populations Abstract Life is that which evolves. Evolutionary dynamics shape the living

apter 5 is published as: "Mutation-selection equilibrium in games with multiple strategies", T. Antal, A. Traulsen, H. Ohtsuki, C.E. Tarnita, M.A., Nowak. J. Theor. Biol., doi:10.1016/j.jtbi.2009.02.010, 2009. Chapter 6 is submitted as: "Mutation-selection equilibrium in games with mixed strategies"

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

eractions (Anderson & May 1991, Nowak & May 1994), the evolution of metabolic pathways (Pfeiffer et al 2001), theoretical approaches to immunology (Nowak et al 1991, 1995), and the study of animal and human behavior (Parker 1974, Enquist & Leimar 1983, McNamara & Houston 1986, Milinski 1987, Fudenber

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

s: Cooperation and bifurcation. Theor Popul Biol 73: 257-263. 208. Jones S, W Chen, G Parmigiani, F Diehl, N Beerenwinkel, T Antal, A Traulsen, MA Nowak, C Siegel, VE Velculescu, KW Kinzler, B Vogelstein, J Willis, SD Markowitz (2008). Comparative lesion sequencing provides insights into tumor evolut

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.