A coalescent dual process in a Moran model with genic selection

Area of Science:

• Population Genetics
• Mathematical Biology
• Stochastic Processes

Background:

• The Moran model and Wright-Fisher diffusion are fundamental in population genetics.
• Understanding allele dynamics under selection is crucial for evolutionary studies.
• Existing models often simplify or omit the complexities of genic selection.

Purpose of the Study:

• To derive a coalescent dual process for a multi-type Moran model incorporating genic selection.
• To expand transition functions for Moran models and Wright-Fisher diffusion limits.
• To apply the coalescent dual to the harmonic measure problem for allele loss and survival.

Main Methods:

• Utilized a generator approach to derive the coalescent dual process.
• Employed a graphical representation of the Moran model to identify the dual process.
• Extended existing dual process constructions for diffusion models with selection.

Main Results:

• Successfully derived a coalescent dual process for multi-type Moran models with genic selection.
• Established connections between the coalescent dual and existing models like the Ancestral Selection Graph.
• Provided a novel solution to the harmonic measure problem concerning allele loss and surviving alleles.

Conclusions:

• The derived coalescent dual process offers a powerful new tool for analyzing population genetic models with selection.
• This framework enhances the reconstruction of genealogical histories in the presence of selection.
• The application to the harmonic measure problem demonstrates the practical utility of the new dual process.