Stationary solutions for metapopulation Moran models with mutation and selection.

Area of Science:

• Population Genetics
• Mathematical Biology
• Ecology

Background:

• Metapopulation models are crucial for understanding population dynamics across fragmented habitats.
• Genetic drift, mutation, and selection are key evolutionary forces shaping metapopulation genetics.
• Analyzing complex metapopulation models often requires significant computational resources.

Purpose of the Study:

• To develop a simplified, effective model for metapopulation genetics.
• To analyze the impact of network structure and island size on genetic diversity.
• To provide a computationally tractable framework for studying evolutionary dynamics in metapopulations.

Main Methods:

• Construction of an individual-based metapopulation model incorporating migration, mutation, selection, and genetic drift.
• Application of diffusion approximation and time-scale separation for model reduction.
• Validation of the reduced model against stochastic simulations.

Main Results:

• An effective one-variable description of the metapopulation model was derived.
• The effective model parameters depend on network structure and island sizes.
• Predictions from the reduced theory closely matched simulation results across various parameters.

Conclusions:

• The developed effective model offers a powerful analytical tool for metapopulation genetics.
• Fast-variable elimination provides accurate insights into slow population dynamics.
• This approach simplifies the study of evolution in complex, structured populations.