Work

The Moran Process on a Random Graph

Year: 2025

Type: article

Abstract: ABSTRACT We study the fixation probability for two versions of the Moran process on the random graph at the threshold for connectivity. The Moran process models the spread of a mutant population in a network. Throughout the process, there are vertices of two types, mutants, and non‐mutants. Mutants have fitness and non‐mutants have fitness 1. The process starts with a unique individual mutant located at the vertex . In the Birth‐Death version of the process a random vertex is chosen proportionally to its fitness and then changes the type of a random neighbor to its own. The process continues until the set of mutants is empty or . In the Death‐Birth version, a uniform random vertex is chosen and then takes the type of a random neighbor, chosen according to fitness. The process again continues until the set of mutants is empty or . The fixation probability is the probability that the process ends with . We show that asymptotically correct estimates of the fixation probability depend only on the degree of and its neighbors. In some cases we can provide values for these estimates and in other places we can only provide non‐linear recurrences that could be used to compute values.

Source: Random Structures and Algorithms

DOI: 10.1002/rsa.70003

Authors: Alan Frieze, Wesley Pegden

Institution: Carnegie Mellon University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,550

Funders: National Science Foundation, National Science Foundation of Sri Lanka