The effective size of fluctuating populations

Area of Science:

• Population genetics
• Mathematical biology
• Stochastic processes

Background:

• The Wright-Fisher model is a cornerstone of population genetics.
• Effective population size (Ne) is crucial for understanding genetic drift and diversity.
• Previous studies often assumed uncorrelated population size fluctuations.

Purpose of the Study:

• To investigate the impact of autocorrelated population size fluctuations on effective population size.
• To compare inbreeding and variance effective sizes in this context.
• To challenge the assumption that Ne equals the harmonic mean of population size under fluctuating conditions.

Main Methods:

• Utilized a Wright-Fisher model with an autocorrelated stochastic process for population size.
• Defined and analyzed both inbreeding effective size and variance effective size.
• Derived asymptotic expressions for effective size under specific conditions (large population, strong autocorrelation).

Main Results:

• Demonstrated that inbreeding and variance effective sizes are equivalent for this model.
• Showed that effective size deviates from the harmonic mean when population size fluctuations are autocorrelated.
• Found that positive autocorrelation increases effective size, while negative autocorrelation decreases it.

Conclusions:

• Autocorrelation in population size is a critical factor influencing effective population size.
• The harmonic mean is an inadequate approximation for effective size with autocorrelated fluctuations.
• The direction and strength of autocorrelation significantly alter effective population size dynamics.