On inferring evolutionary stability in finite populations using infinite population models

Area of Science:

• Evolutionary biology
• Population genetics

Background:

• Models of natural selection often assume infinite populations, where rare, selected-against mutations are assumed to go extinct.
• In finite populations, rare mutations can persist and even fixate, a phenomenon not captured by infinite population models.

Purpose of the Study:

• To determine when infinite-population models accurately predict evolutionary outcomes in large, finite populations.
• To identify conditions where selection opposing mutation invasion also opposes fixation.

Main Methods:

• Analysis of evolutionary models with varying population sizes.
• Investigation of mutation dynamics under different selection pressures.

Main Results:

• Infinite-population models do not universally predict evolutionary outcomes in large populations; selection can oppose invasion but favor fixation for rare mutations of small effect.
• This phenomenon occurs even with smooth fitness functions and biologically sensible selection processes.
• Sufficient conditions were identified in the snowdrift game where selection against rare mutants precludes their fixation in large populations.

Conclusions:

• The assumption of infinite populations can be misleading for predicting evolutionary trajectories.
• Understanding the nuances of selection in finite populations is crucial for accurate evolutionary modeling.
• The specific selection process significantly influences which trait ultimately fixes, regardless of population size.