Exact results for fixation probability of bithermal evolutionary graphs

Area of Science:

• Evolutionary dynamics
• Mathematical biology
• Population genetics

Background:

• The fixation probability is crucial for understanding evolutionary dynamics.
• Evolutionary graphs (EGs) model structured populations, but exact analytical results are scarce.
• EG topology can influence the spread of beneficial mutations.

Purpose of the Study:

• To develop a new technique for computing exact fixation probabilities in evolutionary graphs.
• To analyze the impact of different evolutionary processes on mutation dynamics.
• To provide analytical insights into the role of population structure.

Main Methods:

• Utilizing the fixed point of probability generating functions for exact calculations.
• Applying the method to a subset of bithermal graphs.
• Validating results with numerical simulations across all bithermal graphs.

Main Results:

• An exact analytical solution for fixation probability was derived for a large subset of bithermal graphs.
• Numerical simulations confirmed the solution's validity for all bithermal graphs.
• The study elucidates how birth-death and death-birth processes differentially amplify or suppress beneficial mutations.

Conclusions:

• The fixed point of probability generating functions is a powerful tool for analyzing evolutionary dynamics on graphs.
• Population structure and demographic processes interact to shape evolutionary outcomes.
• This work advances our understanding of evolutionary processes in spatially structured populations.