Approximating fixation probabilities in the generalized Moran process.

Abstract

Problem Definition Population and evolutionary dynamics have been extensively studied, usually with the assumption that the evolving population has no spatial structure. One of the main models in this area is the Moran process [17]. The initial population contains a single “mutant” with fitness r > 0, with all other individuals having fitness 1. At each step of the process, an individual is chosen at random, with probability proportional to its fitness. This individual reproduces, replacing a second individual, chosen uniformly at random, with a copy of itself. Lieberman, Hauert, and Nowak introduced a generalization of the Moran process, where the members of the population are placed on the vertices of a connected graph which is, in general, directed [13, 19]. In this model, the initial population again consists of a single mutant of fitness r > 0 placed on a vertex chosen uniformly at ...