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

vided population. Evolution 35.477-488 (1981). 8. Nowak, M. A. & May. R. M. Evolutionary games and spatial chaos. Nature 359. 826429 (1992). 9. Durrett. It & Levi,.. S. A. Stochastic spatial models: a user's guide to ecological applications. Philos. Trans. R. Soc. Lond. Ser. B Blot Set 343.329-350 (

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

& Nowak 2008). Spatial models have also a long history of investigation in the study of ecosystems and ecological interactions (Levin & Paine 1974, Durrett 1988, Hassel et al 1991, Durrett & Levin 1994). There is also a literature on the dispersal behavior of animals (Hamilton & May 1977, Comins et al

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.

s, Cambridge, UK. [22] Doebeli, M., Knowlton, N., 1998. The evolution of interspecific mutualisms. P. Natl. Acad. Sci. U.S.A. 95, 8676-8680. [23] Durrett, R., 1988. Lecture Notes on Particle Systems and Percolation. Wadsworth & Brooks/Cole Advanced Books & Software, Stamford, CT. [24] Durrett It, Lev