Evolutionary dynamics on degree-heterogeneous graphs.

The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model dynamics) or by an individual giving birth to an offspring that takes over a random neighbor node (invasion process dynamics). The fixation probability for one species to take over a population of N individuals depends crucially on the dynamics and on the local environment. Starting with a single fitter mutant at a node of degree k, the fixation probability is proportional to k for voter model dynamics and to 1/k for invasion process dynamics.

[1]  V. Eguíluz,et al.  Conservation laws for the voter model in complex networks , 2004, cond-mat/0408101.

[2]  M. Kimura.  The Neutral Theory of Molecular Evolution: Introduction , 1983 .

[3]  S. Redner.  A guide to first-passage processes , 2001 .

[4]  P. A. P. Moran,et al.  Random processes in genetics , 1958, Mathematical Proceedings of the Cambridge Philosophical Society.

[5]  T. Liggett.  Interacting Particle Systems , 1985 .

[6]  D. Sherrington.  Stochastic Processes in Physics and Chemistry , 1983 .

[7]  W. Ewens.  Mathematical Population Genetics , 1980 .

[8]  M. Whitlock,et al.  The effective size of a subdivided population. , 1997, Genetics.

[9]  C. Hauert,et al.  Coevolutionary dynamics: from finite to infinite populations. , 2004, Physical review letters.

[10]  Duncan J Watts,et al.  A simple model of global cascades on random networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Krapivsky.  Kinetics of monomer-monomer surface catalytic reactions. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[12]  Alessandro Vespignani,et al.  Velocity and hierarchical spread of epidemic outbreaks in scale-free networks. , 2003, Physical review letters.

[13]  S. Redner,et al.  Voter model on heterogeneous graphs. , 2004, Physical review letters.

[14]  Drew Fudenberg,et al.  Evolutionary game dynamics in finite populations , 2004, Bulletin of mathematical biology.

[15]  K. Holsinger.  The neutral theory of molecular evolution , 2004 .

[16]  B. Bainbridge,et al.  Genetics , 1981, Experientia.

[17]  W. Ebeling.  Stochastic Processes in Physics and Chemistry , 1995 .

[18]  Krapivsky,et al.  Exact results for kinetics of catalytic reactions. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[20]  Martin A. Nowak,et al.  Evolutionary dynamics on graphs , 2005, Nature.

[21]  Sidney Redner,et al.  A guide to first-passage processes , 2001 .

[22]  M. A. Muñoz,et al.  Modeling Cooperative Behavior in the Social Sciences , 2005 .

[23]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[24]  Petter Holme,et al.  A Network-Based Threshold Model for the Spreading of fads in Society and Markets , 2005, Adv. Complex Syst..

[25]  F. C. Santos,et al.  Scale-free networks provide a unifying framework for the emergence of cooperation. , 2005, Physical review letters.