Stochastic selection in both haplophase and diplophase

Area of Science:

• Population Genetics
• Evolutionary Biology
• Mathematical Biology

Background:

• Understanding allele frequency dynamics is crucial in evolutionary biology.
• Previous models often assume constant selection coefficients and segregation parameters.
• Incorporating stochasticity in these parameters provides a more realistic evolutionary framework.

Purpose of the Study:

• To analyze a population genetic model with random zygotic selection, gametic selection, and non-Mendelian segregation.
• To investigate the long-term evolutionary outcomes under these stochastic conditions.
• To compare the stochastic model's predictions with those of deterministic models.

Main Methods:

• Developed a diffusion approximation for the population genetic model.
• Analyzed the stochastic process to identify limiting outcomes.
• Assumed selection coefficients and segregation parameter are uncorrelated random variables.

Main Results:

• Identified four possible limiting outcomes for allele frequencies.
• These include almost sure fixation or loss, convergence to a stationary distribution, or frequency-dependent fixation/loss.
• The stochastic model's outcomes closely resemble those of deterministic models.

Conclusions:

• Stochasticity in evolutionary forces can lead to diverse allele frequency trajectories.
• The model provides a framework for understanding the interplay of selection, segregation, and random fluctuations.
• Findings enhance our understanding of evolutionary dynamics beyond deterministic predictions.