![]() ![]() ![]() The games with self-dependent (cross-dependent) payoffs are characterized by matrices consisting of uniform rows (columns). Among these basis games four classes can be distinguished as it is already found for the three-strategy games. ![]() The symmetric four-strategy games are decomposed into a linear combination of 16 basis games represented by orthogonal matrices. We show that for a range of fitness values of the mutants, the Comet and Comet-swarm graphs have fixation probability strictly larger than the fixation probability of the Star graph, for fixed population size and at the limit of large populations, respectively. In this work we present the Comet and Comet-swarm families of undirected graphs. In the regime of undirected graphs, the strongest amplifier known has been the Star graph, and the existence of undirected graphs with stronger amplification properties has remained open for over a decade. In this work we focus on symmetric population structures represented as undirected graphs. Amplifiers of natural selection are population structures which increase the fixation probability of advantageous mutants, as compared to the baseline case of well-mixed populations. The fixation probability is a fundamental quantity of natural selection, and known to depend on the population structure. The fixation probability is the probability that a new mutant introduced in a homogeneous population eventually takes over the entire population. ![]()
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