Self-loops in evolutionary graph theory: Friends or foes?

Area of Science:

• Evolutionary biology
• Mathematical modeling
• Population genetics

Background:

• Spatially structured populations influence evolutionary dynamics.
• Structures can amplify selection, favoring beneficial mutations and hindering deleterious ones.
• Self-loops are crucial for selection amplification in dynamic, mutant-prone structures at low mutation rates.

Purpose of the Study:

• Investigate the impact of increasing mutation rates on selection amplification in structured populations.
• Determine the effects of self-loops on evolutionary dynamics beyond the low mutation rate regime.
• Identify the mutation rate threshold where weak mutation approximations fail.

Main Methods:

• Analysis of evolutionary dynamics on graphs with varying structures and mutation rates.
• Comparison of steady-state average fitness between different population structures (self-looped, complete graph, suppressors).
• Calculation of average fixation time scaling with population size to estimate mutation rate deviations.

Main Results:

• Self-loops enhance selection amplification at low mutation rates, leading to higher average fitness.
• At intermediate and high mutation rates, self-loops become detrimental, reducing average fitness compared to complete graphs.
• The study provides an estimate for the mutation rate beyond which weak mutation approximations become inaccurate.

Conclusions:

• The effectiveness of self-looped structures in amplifying selection is highly dependent on the mutation rate.
• Beyond a critical mutation rate, the benefits of self-loops diminish, and they can negatively impact evolutionary outcomes.
• Understanding these mutation rate dependencies is crucial for accurately modeling evolutionary dynamics in structured populations.