Abstract
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.
Highlights
Evolutionary dynamics is the study of the mathematical principles governing the evolution of biological organisms
The most significant contribution of the current work was the coupling between dynamics and structure, resulting in a violation in the isothermal theorem
We examined the model numerically for the star graph and used the simulation for the two main categories of complex networks, i.e. small-world and scale-free networks
Summary
Data Availability Statement: The results of simulations and the used codes are available at: 1https://mail.znu.ac.ir/webmail-prof/?/Min/Share/ JypFMmAd8F 2-https://mail.znu.ac.ir/webmailprof/?/Min/Share/qTtZbAF6ta. We examine an evolutionary model that considers the effect of competition between the mutated individuals for acquiring more resources. This competition has an effect on the death rate of mutants. There is a competition between cells for consuming oxygen, and cancer cells are far more sensitive to the amount of oxygen in the environment than normal cells. This means the death rate of a cancer cell grows by increasing the number of its neighbors.
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