Fixation of the Moran process on trees

Abstract

Fixation time of evolutionary processes on graph-structured populations is highly affected by the underlying graph structure. In this article, we study the spreading of a single mutant on trees. We show that the number of leaves (terminal nodes) plays a crucial role in the fixation process. Our results show that the fastest fixation process occurs when approximately $\frac{1}{4}$ of nodes are leaves. Estimated fixation time based on the number of leaves in tree graphs is valid even when the tree is generated by specific mechanisms and has specific topologies and degree distributions.

Predicting Fixation Paths in the Moran Process:A Machine Learning Approach

“…The second outcome occurs when residents reproduce and suppress the single mutant, leading to residents fixing the population. This update rule introduces two important concepts in the Moran process [32][33][34][35][36][37]. The first concept is the fixation probability, which refers to the probability that a single mutant will fix in the population.…”