Establishment of Locally Adapted Mutations Under Divergent Selection

Area of Science:

• Evolutionary Biology
• Population Genetics
• Mathematical Biology

Background:

• Understanding how new mutations establish and spread within populations is crucial for explaining local adaptation.
• Branching processes offer a powerful mathematical framework for modeling population dynamics and evolutionary processes.

Purpose of the Study:

• To derive an analytical approximation for the establishment probability of locally adapted mutations.
• To investigate the impact of gene flow, deme asymmetry, and density regulation on adaptation.
• To explore how gene flow influences the rate of local adaptation.

Main Methods:

• Utilized a multi-type branching process framework to model establishment probabilities.
• Derived a closed-form analytical approximation for a symmetric two-deme model.
• Extended the model to include multiple demes, asymmetric gene flow, and asymmetric carrying capacities.

Main Results:

• Developed the first analytical closed-form approximation for establishment probability with arbitrary migration rates.
• Found that establishment probability is influenced by the deme of origin and selection advantage.
• Demonstrated that intermediate gene flow can maximize establishment probability and facilitate local adaptation.

Conclusions:

• The study provides a novel analytical tool for understanding the evolution of local adaptation.
• Gene flow plays a complex role, with intermediate levels potentially accelerating adaptation.
• Density regulation can significantly impact the establishment of beneficial mutations.