Stochastic fluctuations in frequency-dependent selection: a one-locus, two-allele and two-phenotype model

Area of Science:

• Evolutionary biology
• Population genetics
• Mathematical modeling

Background:

• Frequency-dependent selection is a key evolutionary mechanism.
• Stochastic fluctuations influence evolutionary dynamics.
• Understanding these dynamics is crucial for predicting allele and phenotype frequencies.

Purpose of the Study:

• Investigate stochastic fluctuations in a one-locus, two-allele, two-phenotype model.
• Compare steady-state statistics with existing evolutionary game dynamics.
• Analyze the predictability of phenotypic frequencies and the sensitivity of variance to population size.

Main Methods:

• Mathematical modeling of frequency-dependent selection.
• Analysis of steady-state statistics of allele and phenotypic frequencies.
• Comparison with established evolutionary game dynamics models.

Main Results:

• Steady-state allele frequency fluctuations resemble those in standard evolutionary game dynamics for phenotypic equilibria.
• Deterministic models are inadequate for predicting the expectation of phenotypic frequency for interior stable equilibria.
• Phenotypic frequency variance is more sensitive to population size for genotypic equilibria than phenotypic equilibria.
• Allele and phenotypic frequencies are approximately independent for genotypic equilibria, but not for phenotypic equilibria.

Conclusions:

• Stochastic effects significantly alter evolutionary predictions compared to deterministic models.
• The interplay between allele and phenotypic frequencies is complex and depends on equilibrium type.
• Population size plays a critical role in shaping phenotypic variance under stochasticity.