Regular Article - Statistical and Nonlinear Physics
Path to fixation of evolutionary processes in graph-structured populations
Department of Physics, Isfahan University of Technology, 84156-83111, Isfahan, Iran
Accepted: 3 February 2021
Published online: 9 February 2021
We study the spreading of a single mutant in graph-structured populations with a birth-death update rule. We use a mean-field approach and a Markov chain dynamics to investigate the effect of network topology on the path to fixation. We obtain approximate analytical formulas for average time versus the number of mutants in the fixation process starting with a single mutant for several network structures, namely, cycle, complete graph, two- and three-dimensional lattices, random graph, regular graph, Watts–Strogatz network, and Barabási–Albert network. In the case of the cycle and complete graph, the results are accurate and in line with the results obtained by other methods. In the case of two- and three-dimensional lattice structures, some efforts are made in other studies to provide an analytical justification for simulation results of the evolutionary process, but they can explain just the onset of the fixation process, not the whole process. The results of the analytical approach of the present paper are well fitted to the simulation results throughout the whole fixation process. Moreover, we analyze the dynamics of evolution for a number of complex structures, and in all cases, we obtain analytical results which are in good agreement with simulations. Our results may shed some light on the process of fixation during the whole path to fixation.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2021