Continuous approximations for the fixation probability of the Moran processes on star graphs

Area of Science:

• Evolutionary dynamics
• Mathematical biology
• Population genetics

Background:

• Introduces generalized birth-death (BD) and death-birth (DB) processes with constant fitness.
• Highlights limitations of constant fitness models in capturing complex population dynamics.

Purpose of the Study:

• To analyze generalized BD and DB processes with frequency-dependent fitness functions under weak selection.
• To investigate population dynamics on large star graphs, focusing on fixation probabilities.
• To explore the role of star graph structure in modulating evolutionary outcomes.

Main Methods:

• Developed approximations for fixation probabilities using ordinary differential equations (ODEs).
• Analyzed frequency-dependent fitness functions, including linear cases from evolutionary games.
• Provided error bounds for the death-birth (DB) process approximation (order 1/N).

Main Results:

• Derived ODE approximations for fixation probabilities in large populations on star graphs.
• Demonstrated that star graphs can act as amplifiers, suppressors, or remain isothermal based on initial mutant placement.
• Identified an analytical threshold for these structural effects.

Conclusions:

• The star graph structure significantly influences evolutionary outcomes by modulating selection.
• Approximations are accurate for moderate population sizes and diverse frequency-dependent fitness functions.
• Extends previous models by incorporating more general fitness landscapes and graph structures.