Abstract:

Evolutionary dynamics, Moran process, and fixation probability are important concepts in the field of complex systems, particularly in the context of genetic evolution. Understanding each of these concepts plays a crucial role in comprehending the evolutionary process, and they can be effectively studied through modeling and the use of evolutionary graph theory.

Evolutionary dynamics examines population changes over time, and the Moran process is one of the models within evolutionary dynamics. The Moran process illustrates how population changes occur through differences in the fitness of species over time, under the influence of evolutionary mechanisms such as natural selection and genetic drift. This process is particularly useful for studying the evolution of small populations over discrete time steps. Fixation probability refers to the probability of a genetic trait becoming established and spreading throughout a population.

Evolutionary dynamics investigates how this fixation probability is influenced by evolutionary processes such as natural selection and genetic drift. Through the application of evolutionary dynamics methods, one can predict the fixation probability and the time required for the fixation of genetic traits. Therefore, evolutionary dynamics is a broad concept that explores population changes and evolution over discrete time steps. The Moran process, time, and fixation probability examine the transfer and establishment of genetic traits within populations.

Keywords: Evolutionary dynamics, Evolutionary graph theory, Moran process, Fixation time, Fixation probability, Complex systems