Fixation probabilities on superstars, revisited and revised

Area of Science:

• Evolutionary biology
• Mathematical modeling
• Graph theory

Background:

• Population structures significantly influence evolutionary dynamics.
• Evolutionary amplifiers, such as superstars, enhance natural selection by suppressing random drift.
• Previous results on superstar amplifiers were recently challenged.

Purpose of the Study:

• To correct invalidated proofs concerning the superstar evolutionary amplifier.
• To derive improved bounds for fixation probability in the Moran process on superstars.
• To investigate the robustness of amplification in superstar structures.

Main Methods:

• Correcting mathematical proofs for the Moran process on graphs.
• Deriving new upper and lower bounds for fixation probability.
• Analyzing the impact of population size (N) and structural parameter (H) on evolutionary amplification.
• Investigating the sensitivity of amplification to selection and mutation processes.

Main Results:

• The fixation probability for superstars approaches 1-1/(r(4)H) as population size (N) and structural parameter (H) approach infinity.
• Superstars effectively eliminate random drift, offering substantial selective advantages for beneficial mutations.
• Amplification in superstars is sensitive to variations in selection and mutation rates.

Conclusions:

• The corrected analysis reaffirms the power of superstars as evolutionary amplifiers.
• Superstars maintain their ability to provide strong selective advantages in large populations and complex structures.
• The phenomenon of evolutionary amplification in superstars is not robust to changes in underlying evolutionary processes.