Self-loops in Evolutionary Graph Theory: Friends or Foes?

Abstract

Evolutionary dynamics in spatially structured populations has been studied for a long time. More recently, the focus has been to construct structures that speeds up evolution -- so called amplifiers of selection. It has been shown that for a structure to amplify selection, self-loops are necessary when mutants appear predominately in nodes that change often. As a result, for low mutation rates, self-looped amplifiers attain higher steady-state average fitness in the mutation-selection than well-mixed populations. But, what happens when the mutation rate increases such that fixation probabilities alone no longer describe the dynamics? We show that self-loops effects are detrimental outside the low mutation rate regime. In the intermediate and high mutation rate regime, amplifiers of selection attain lower steady-state average fitness than the complete graph and the suppressor of selection. We also provide an estimate of mutation rate beyond which the mutation-selection dynamics on a graph deviates from the weak mutation rate approximation. This involves computing how the average fixation time scales with the population size for several graphs.

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

“…In EGT, individuals within populations are represented as nodes, while the relationships between them are depicted through edges. Therefore, the structure of populations is summarized by the topology of graphs [20][21][22][23][24][25][26][27][28][29][30][31].…”