Quasi-neutral evolution in populations under small demographic fluctuations

Area of Science:

• Evolutionary dynamics
• Population genetics
• Mathematical biology

Background:

• Eco-evolutionary dynamics in finite populations are crucial for understanding species adaptation.
• Quasi-neutrality, where types have similar reproductive output but different birth/death rates, simplifies evolutionary models.
• Stochastic fluctuations in population size add complexity to theoretical models.

Purpose of the Study:

• To analytically investigate eco-evolutionary dynamics in finite populations with fluctuating sizes.
• To determine how population turnover rates affect fixation probabilities and selection.
• To extend previous findings on the contact and Moran processes to a broader analytical framework.

Main Methods:

• Solving the Kolmogorov forward equation for minimally fluctuating populations.
• Analytical derivation of fixation probabilities under varying turnover rates.
• Numerical simulations to validate results for general fluctuating populations and non-quasi-neutral cases.

Main Results:

• Fixation probability decreases as population turnover rate increases.
• Selection favors mutants when their turnover rate is sufficiently low.
• Selection opposes mutants when their turnover rate is sufficiently high, extending prior numerical and analytical work.

Conclusions:

• Population turnover is a critical factor modulating selection in finite populations.
• The study provides an analytical proof for the contact process, unifying findings across different population models.
• Results highlight the importance of considering demographic stochasticity and turnover in evolutionary studies.