Dynamics of fixation probability in a population with fluctuating size

Area of Science:

• Evolutionary Biology
• Population Genetics
• Mathematical Biology

Background:

• Stochastic population size changes are common in biological processes like cancer and bacterial growth.
• Existing models often focus on exponentially growing populations.
• This study considers linear mean population growth, relevant to genetic hitchhiking in neutral populations.

Purpose of the Study:

• To investigate the impact of population size fluctuations on first passage statistics.
• To analyze fixation probability of mutants in a population with linearly growing mean size.
• To understand the role of temporal correlations in these dynamics.

Main Methods:

• Utilized a conditional Wright-Fisher process model.
• Employed analytical and numerical methods to study correlation functions.
• Examined fixation probability and the distribution of fixation population size.

Main Results:

• Fixation probability is approximated by uncorrelated models at short/long times but is lower at intermediate times.
• The distribution of fixation population size differs qualitatively between correlated and uncorrelated models.
• The conditional Wright-Fisher process is neither stationary nor Gaussian; inverse population size variance shows complex temporal behavior.

Conclusions:

• Temporal correlations are crucial for accurate modeling of mutant fixation in fluctuating populations.
• Ignoring correlations leads to significant deviations, particularly at intermediate timescales.
• This highlights the need to incorporate temporal dynamics in population genetics research.