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Related Experiment Videos

Wright-Fisher diffusion bridges.

Robert C Griffiths1, Paul A Jenkins2, Dario Spanò3

  • 1Department of Statistics, University of Oxford, United Kingdom.

Theoretical Population Biology
|October 11, 2017
PubMed
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The Wright-Fisher diffusion bridge models allele frequency trajectories. This study reveals a new interpretation of coalescent genealogy in bridges, showing bidirectional coalescence and providing a novel simulation algorithm and urn model representation.

Area of Science:

  • Population genetics
  • Mathematical biology
  • Evolutionary dynamics

Background:

  • The Wright-Fisher diffusion model is fundamental for understanding allele frequency changes in populations.
  • Coalescent theory describes the ancestral relationships of genes in a population.
  • Wright-Fisher diffusion bridges, particularly with zero initial and final frequencies, model transient allele dynamics.

Purpose of the Study:

  • To provide a new interpretation of coalescent genealogy in Wright-Fisher diffusion bridges.
  • To analyze the genealogy structure under both neutral and selective conditions.
  • To develop a new algorithm for simulating neutral Wright-Fisher bridges and explore alternative modeling approaches.

Main Methods:

  • Mathematical modeling using Wright-Fisher diffusion bridge processes.
Keywords:
Coalescent processes in Wright–Fisher diffusion bridgesWright–Fisher diffusion bridges

Related Experiment Videos

  • Analysis of coalescent genealogy from a time t within the bridge.
  • Derivation of allele frequency density and development of an exact simulation algorithm.
  • Modeling genealogy using branching Pólya urns.

    • Main Results:

    • A novel interpretation of coalescent genealogy in Wright-Fisher bridges, characterized by bidirectional coalescence from time t to 0 and T.
    • Demonstration that both neutral and selected Wright-Fisher bridges exhibit bidirectional branching and coalescing properties.
    • Development of an exact simulation algorithm for neutral Wright-Fisher bridges.
    • Establishment of a connection between Wright-Fisher bridges and classical urn models via branching Pólya urns.

    Conclusions:

    • Wright-Fisher diffusion bridges offer a unique framework for studying allele frequency dynamics and genealogy.
    • The bidirectional coalescence structure is a key feature of these bridges, even under selection.
    • The new simulation algorithm and urn model representation provide valuable tools for theoretical and empirical research in population genetics.