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Related Experiment Video

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Following the Dynamics of Structural Variants in Experimentally Evolved Populations

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Published on: February 3, 2023

Coalescent approximation for structured populations in a stationary random environment.

S Sagitov¹, P Jagers, V Vatutin

¹Mathematical Statistics, Chalmers University of Technology and University of Gothenburg, SE-412 96 Gothenburg, Sweden. serik@chalmers.se

Theoretical Population Biology

|July 13, 2010

Summary

This study introduces a new model for population genetics, showing how random migration affects genetic diversity. It develops a novel "quenched" effective population size (EPS) for populations with changing environments.

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Area of Science:

Population Genetics
Mathematical Biology
Stochastic Processes

Background:

The Wright-Fisher model is a fundamental tool in population genetics for understanding genetic drift.
Previous models often assumed constant migration probabilities between subpopulations.
Understanding the impact of environmental variability on population structure is crucial.

Purpose of the Study:

To establish convergence to the Kingman coalescent for a structured Wright-Fisher model with random migration.
To introduce and define a novel 'quenched' effective population size (EPS) accounting for random environments.
To compare the quenched EPS with the traditional 'annealed' EPS derived from averaged migration rates.

Main Methods:

Developed a mathematically rigorous framework for analyzing population genealogies.
Introduced a stochastic model where migration probabilities vary randomly over time.
Derived a new formula for effective population size in a random environment.

Main Results:

Demonstrated convergence to the Kingman coalescent for the genealogy under fast, random migration.
Defined the quenched EPS, capturing the dynamics of populations in fluctuating environments.
Showed that the quenched EPS differs from the annealed EPS, highlighting the importance of environmental randomness.

Conclusions:

The study provides a new theoretical framework for population genetics in random environments.
The quenched EPS offers a more accurate measure of population size for populations experiencing environmental variability.
Findings have implications for understanding biodiversity and evolutionary dynamics in changing ecological conditions.