A coalescent dual process in a Moran model with genic selection, and the lambda coalescent limit

Area of Science:

• Population Genetics
• Mathematical Biology
• Evolutionary Dynamics

Background:

• Studies neutral populations with skewed reproductive success.
• Existing models often simplify selection mechanisms.

Purpose of the Study:

• Derive a coalescent dual process for continuous-time Moran models incorporating viability selection.
• Extend dual process construction for multi-type Moran models with genic selection.

Main Methods:

• Derivation of a coalescent dual process for Moran models with viability selection.
• Analysis of convergence to a Markov jump process (lamda-Fleming-Viot process) in infinite population limits.
• Development of a branching-coalescing dual process tracking gene ancestry.

Main Results:

• Established a coalescent dual for Moran models with viability selection.
• Demonstrated convergence of non-neutral Moran models to the lamda-Fleming-Viot process.
• Characterized the dual as a branching-coalescing process similar to the Ancestral Selection Graph.

Conclusions:

• The derived coalescent dual provides a powerful tool for analyzing non-neutral population genetics.
• The lamda-Fleming-Viot process and its dual offer new insights into gene ancestry under viability selection.
• Applications include expressing transition functions of Moran and lamda-coalescent models.