Most undirected random graphs are amplifiers of selection for Birth-death dynamics, but suppressors of selection for death-Birth dynamics

TL;DR

This study reveals that most undirected random graphs tend to amplify selection under Birth-death dynamics but suppress it under death-Birth dynamics, highlighting the nuanced influence of population structure on evolution.

Contribution

It demonstrates that almost any undirected random graph acts as an amplifier for Birth-death updating but as a suppressor for death-Birth updating, showing the importance of process details.

Findings

Almost all undirected random graphs are amplifiers for Birth-death dynamics.

The same graphs are mostly suppressors for death-Birth dynamics.

Population structure effects depend on the specific evolutionary process.

Abstract

We analyze evolutionary dynamics on graphs, where the nodes represent individuals of a population. The links of a node describe which other individuals can be displaced by the offspring of the individual on that node. Amplifiers of selection are graphs for which the fixation probability is increased for advantageous mutants and decreased for disadvantageous mutants. A few examples of such amplifiers have been developed, but so far it is unclear how many such structures exist and how to construct them. Here, we show that almost any undirected random graph is an amplifier of selection for Birth-death updating, where an individual is selected to reproduce with probability proportional to its fitness and one of its neighbors is replaced by that offspring at random. If we instead focus on death-Birth updating, in which a random individual is removed and its neighbors compete for the empty spot, then the same ensemble of graphs consists of almost only suppressors of selection for which the fixation probability is decreased for advantageous mutants and increased for disadvantageous mutants. Thus, the impact of population structure on evolutionary dynamics is a subtle issue that will depend on seemingly minor details of the underlying evolutionary process.