Fixation of the Moran process on trees

Abstract

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.