Population genetics on islands connected by an arbitrary network: an analytic approach

Area of Science:

• Population Genetics
• Mathematical Biology
• Evolutionary Dynamics

Background:

• Understanding how population structure influences genetic diversity is crucial for evolutionary studies.
• Previous models often simplify migration patterns or selection pressures.
• Subdivided populations present unique challenges for genetic analysis.

Purpose of the Study:

• To develop a systematic analytical framework for population genetics in structured populations.
• To investigate the interplay of migration and selection across different deme networks.
• To model allele frequency dynamics in haploid populations with frequency-independent selection.

Main Methods:

• Formulation as an individual-based model.
• Application of diffusion approximation to derive nonlinear coupled stochastic differential equations.
• Elimination of fast-time variables for model reduction and analysis.

Main Results:

• Analysis of migration-selection balance leading to polymorphic equilibria.
• Demonstration of non-trivial population dynamics in a simple hub migration network.
• Validation of the model against simulation results across diverse parameters.

Conclusions:

• The developed method provides a systematic approach applicable to arbitrary migration networks.
• Population subdivision can lead to complex and non-intuitive genetic behaviors.
• The model accurately captures allele frequency dynamics in structured populations.