A logistic branching process for population genetics.

Area of Science:

• Population Genetics
• Mathematical Biology
• Evolutionary Dynamics

Background:

• Existing models like Wright-Fisher and unconstrained branching processes have limitations in representing natural population dynamics.
• Population size fluctuations are crucial in evolutionary processes but often imposed externally in models.
• Understanding the impact of regulated population size on genetic drift and selection is essential.

Purpose of the Study:

• To present a novel logistic branching process model for population genetics.
• To investigate how intrinsic population size regulation and fluctuation affect evolutionary outcomes.
• To compare the new model's predictions with established models like Wright-Fisher.

Main Methods:

• Developed a logistic branching process model incorporating regulated population size.
• Analyzed coalescent properties (time, shape, structure) and compared them to existing models.
• Examined the fixation probability of beneficial mutations under fluctuating population sizes.

Main Results:

• The model shares key coalescent properties with Wright-Fisher and branching process models.
• Intrinsic population size fluctuation enhances fixation prospects for beneficial mutations with constant relative viability.
• This finding contrasts with results from the Wright-Fisher model under fluctuating population sizes.

Conclusions:

• The developed logistic branching process model offers a more realistic representation of population dynamics.
• Population size fluctuation, when intrinsic, can promote the fixation of advantageous genetic variants.
• Distinguishing between expected/realized and absolute/relative viabilities is key to understanding these dynamics.