The network structure affects the fixation probability when it couples to the birth-death dynamics in finite population

• Main Authors: Darooneh, A.H (Author), Dehghani, M.A (Author), Kohandel, M. (Author)
• Format: Article
• Language: English
• Published: Public Library of Science 2021
• Subjects: algorithm; Algorithms; article; Biological Evolution; biological model; biology; Computational Biology; evolution; Genetic Fitness; human; Models, Biological; Models, Statistical; mortality rate; mutation; Mutation; neoplasm; Neoplasms; population dynamics; Population Dynamics; probability; reproductive fitness; statistical model
• Online Access: View Fulltext in Publisher

 The study of evolutionary dynamics on graphs is an interesting topic for researchers in various fields of science and mathematics. In systems with finite population, different model dynamics are distinguished by their effects on two important quantities: fixation probability and fixation time. The isothermal theorem declares that the fixation probability is the same for a wide range of graphs and it only depends on the population size. This has also been proved for more complex graphs that are called complex networks. In this work, we propose a model that couples the population dynamics to the network structure and show that in this case, the isothermal theorem is being violated. In our model the death rate of a mutant depends on its number of neighbors, and neutral drift holds only in the average. We investigate the fixation probability behavior in terms of the complexity parameter, such as the scale-free exponent for the scale-free network and the rewiring probability for the small-world network. Copyright: © 2021 Dehghani et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.